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Couple this with M) 135.65 636.95 P 2 10 Q 3.09 (A) 412.78 636.95 P 3.09 (TLAB) 418.88 636.95 P 2 12 Q 3.7 (\325) 444.98 636.95 P 3.7 (s advanced data) 448.31 636.95 P 0.17 (analysis, visualisation tools and special purpose application domain toolboxes and) 135.65 622.95 P 2.91 (the user is presented with a uniform environment with which to explore the) 135.65 608.95 P (potential of genetic algorithms.) 135.65 594.95 T 1.02 (The Genetic Algorithm T) 135.65 568.95 P 1.02 (oolbox uses M) 260.1 568.95 P 2 10 Q 0.85 (A) 332.76 568.95 P 0.85 (TLAB) 338.87 568.95 P 2 12 Q 1.02 ( matrix functions to build a set of) 364.97 568.95 P 0.87 (versatile tools for implementing a wide range of genetic algorithm methods. The) 135.65 554.95 P 1.04 (Genetic Algorithm T) 135.65 540.95 P 1.04 (oolbox is a collection of routines, written mostly in m-\336les,) 237.48 540.95 P (which implement the most important functions in genetic algorithms.) 135.65 526.95 T FMENDPAGE %%EndPage: "1" 2 %%Page: "2" 2 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-2) 518.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Installation) 63.65 732.95 T 2 12 Q 2.37 (Instructions for installing the Genetic Algorithm T) 135.65 694.95 P 2.37 (oolbox can be found in the) 391.55 694.95 P 0.36 (M) 135.65 680.95 P 2 10 Q 0.3 (A) 146.31 680.95 P 0.3 (TLAB) 152.42 680.95 P 2 12 Q 0.36 ( installation instructions. It is recommended that the \336les for this toolbox) 178.51 680.95 P (are stored in a directory named genetic of) 135.65 666.95 T (f the main matlab/toolbox directory) 334.93 666.95 T (.) 504.71 666.95 T 3.33 (A number of demonstrations are available. A single-population binary-coded) 135.65 640.95 P -0.13 (genetic algorithm to solve a numerical optimization problem is implemented in the) 135.65 626.95 P -0.25 (m-\336le) 135.65 612.95 P 3 F -0.61 (sga.m) 167.04 612.95 P 2 F -0.25 (. The demonstration m-\336le) 203.02 612.95 P 3 F -0.61 (mpga.m) 332.93 612.95 P 2 F -0.25 ( implements a real-valued multi-) 376.1 612.95 P 1.29 (population genetic algorithm to solve a dynamic control problem. Both of these) 135.65 598.95 P (demonstration m-\336les are discussed in detail in the) 135.65 584.95 T 0 F (Examples) 382.16 584.95 T 2 F ( Section.) 428.79 584.95 T 1.06 (Additionally) 135.65 558.95 P 1.06 (, a set of test functions, drawn from the genetic algorithm literature,) 195.51 558.95 P 2.55 (are supplied in a separate directory) 135.65 544.95 P 2.55 (,) 315.12 544.95 P 3 F 6.11 (test_fns) 323.66 544.95 P 2 F 2.55 (, from the Genetic Algorithm) 381.23 544.95 P 0.05 (T) 135.65 530.95 P 0.05 (oolbox functions. A brief description of these test functions is given at the end of) 142.14 530.95 P 0.93 (the) 135.65 516.95 P 0 F 0.93 (Examples) 154.23 516.95 P 2 F 0.93 ( Section. A further document describes the implementation and use) 200.86 516.95 P (of these functions.) 135.65 502.95 T FMENDPAGE %%EndPage: "2" 3 %%Page: "3" 3 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-3) 518.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (An Overview of Genetic Algorithms) 63.65 732.95 T 2 12 Q -0.06 (In this Section we give a tutorial introduction to the basic Genetic Algorithm \050GA\051) 135.65 694.95 P (and outline the procedures for solving problems using the GA.) 135.65 680.95 T 1 16 Q (What ar) 135.65 652.29 T (e Genetic Algorithms?) 192.66 652.29 T 2 12 Q 0.56 (The GA is a stochastic global search method that mimics the metaphor of natural) 135.65 624.95 P 0.66 (biological evolution. GAs operate on a population of potential solutions applying) 135.65 610.95 P 2.41 (the principle of survival of the \336ttest to produce \050hopefully\051 better and better) 135.65 596.95 P 0.86 (approximations to a solution. At each generation, a new set of approximations is) 135.65 582.95 P 0.15 (created by the process of selecting individuals according to their level of \336tness in) 135.65 568.95 P 1.29 (the problem domain and breeding them together using operators borrowed from) 135.65 554.95 P 0.63 (natural genetics. This process leads to the evolution of populations of individuals) 135.65 540.95 P 2.41 (that are better suited to their environment than the individuals that they were) 135.65 526.95 P (created from, just as in natural adaptation.) 135.65 512.95 T 3.17 (Individuals, or current approximations, are encoded as strings,) 135.65 486.95 P 0 F 3.17 (chr) 463.14 486.95 P 3.17 (omosomes) 478.68 486.95 P 2 F 3.17 (,) 528.65 486.95 P 0.8 (composed over some alphabet\050s\051, so that the) 135.65 472.95 P 0 F 0.8 (genotypes) 357.07 472.95 P 2 F 0.8 ( \050chromosome values\051 are) 405.03 472.95 P 3.66 (uniquely mapped onto the decision variable \050) 135.65 458.95 P 0 F 3.66 (phenotypic) 374.11 458.95 P 2 F 3.66 (\051 domain. The most) 426.73 458.95 P 0.03 (commonly used representation in GAs is the binary alphabet {0, 1} although other) 135.65 444.95 P 1.05 (representations can be used, e.g. ternary) 135.65 430.95 P 1.05 (, integer) 331.97 430.95 P 1.05 (, real-valued etc. For example, a) 371.85 430.95 P 2.13 (problem with two variables,) 135.65 416.95 P 0 F 2.13 (x) 281.76 416.95 P 0 10 Q 1.78 (1) 287.08 413.95 P 2 12 Q 2.13 ( and) 292.08 416.95 P 0 F 2.13 (x) 319.66 416.95 P 0 10 Q 1.78 (2) 324.98 413.95 P 2 12 Q 2.13 (, may be mapped onto the chromosome) 329.98 416.95 P (structure in the following way:) 135.65 402.95 T -0.3 (where) 135.65 299.98 P 0 F -0.3 (x) 167.65 299.98 P 0 10 Q -0.25 (1) 172.98 296.98 P 2 12 Q -0.3 ( is encoded with 10 bits and) 177.97 299.98 P 0 F -0.3 (x) 312.82 299.98 P 0 10 Q -0.25 (2) 318.14 296.98 P 2 12 Q -0.3 ( with 15 bits, possibly re\337ecting the level of) 323.14 299.98 P -0.2 (accuracy or range of the individual decision variables. Examining the chromosome) 135.65 285.98 P 0.43 (string in isolation yields no information about the problem we are trying to solve.) 135.65 271.98 P 0.11 (It is only with the decoding of the chromosome into its phenotypic values that any) 135.65 257.98 P 1.35 (meaning can be applied to the representation. However) 135.65 243.98 P 1.35 (, as described below) 409.1 243.98 P 1.35 (, the) 509.64 243.98 P 0.55 (search process will operate on this encoding of the decision variables, rather than) 135.65 229.98 P 0.8 (the decision variables themselves, except, of course, where real-valued genes are) 135.65 215.98 P (used.) 135.65 201.98 T -0.19 (Having decoded the chromosome representation into the decision variable domain,) 135.65 175.98 P 1.94 (it is possible to assess the performance, or) 135.65 161.98 P 0 F 1.94 (\336tness) 356.04 161.98 P 2 F 1.94 (, of individual members of a) 386.03 161.98 P 3.53 (population. This is done through an objective function that characterises an) 135.65 147.98 P 0.6 (individual\325) 135.65 133.98 P 0.6 (s performance in the problem domain. In the natural world, this would) 187.63 133.98 P 0.08 (be an individual\325) 135.65 119.98 P 0.08 (s ability to survive in its present environment. Thus, the objective) 216.42 119.98 P 63.65 96.95 531.65 744.95 C 135.65 321.98 531.65 398.95 C 146.65 328.95 520.65 391.95 C 146.65 328.95 520.65 391.95 R 7 X 0 K V 3 12 Q 0 X (1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1) 157.35 369.97 T 170.49 343.64 158.95 346.95 170.49 350.26 170.49 346.95 4 Y V 282.42 350.26 293.95 346.95 282.42 343.64 282.42 346.95 4 Y V 170.49 346.95 282.42 346.95 2 L 0.5 H 0 Z N 297.08 382.95 297.08 337.95 2 L 2 Z 11 X N 311.49 343.64 299.95 346.95 311.49 350.26 311.49 346.95 4 Y 0 X V 495.42 350.26 506.95 346.95 495.42 343.64 495.42 346.95 4 Y V 311.49 346.95 495.42 346.95 2 L 0 Z N 0 F (x) 221.29 353.75 T 0 10 Q (1) 226.62 350.75 T 0 12 Q (x) 398.29 353.75 T 0 10 Q (2) 403.61 350.75 T 135.65 321.98 531.65 398.95 C 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "3" 4 %%Page: "4" 4 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-4) 518.33 61.29 T 2 12 Q 2.35 (function establishes the basis for selection of pairs of individuals that will be) 135.65 736.95 P (mated together during reproduction.) 135.65 722.95 T 0.45 (During the reproduction phase, each individual is assigned a \336tness value derived) 135.65 696.95 P 0.94 (from its raw performance measure given by the objective function. This value is) 135.65 682.95 P 1.18 (used in the selection to bias towards more \336t individuals. Highly \336t individuals,) 135.65 668.95 P 2.11 (relative to the whole population, have a high probability of being selected for) 135.65 654.95 P 2.56 (mating whereas less \336t individuals have a correspondingly low probability of) 135.65 640.95 P (being selected.) 135.65 626.95 T 0.54 (Once the individuals have been assigned a \336tness value, they can be chosen from) 135.65 600.95 P 5.22 (the population, with a probability according to their relative \336tness, and) 135.65 586.95 P 2.85 (recombined to produce the next generation. Genetic operators manipulate the) 135.65 572.95 P 0.61 (characters \050genes\051 of the chromosomes directly) 135.65 558.95 P 0.61 (, using the assumption that certain) 364.71 558.95 P 0.18 (individual\325) 135.65 544.95 P 0.18 (s gene codes, on average, produce \336tter individuals. The recombination) 187.63 544.95 P 0.68 (operator is used to exchange genetic information between pairs, or lar) 135.65 530.95 P 0.68 (ger groups,) 477.01 530.95 P 4.62 (of individuals. The simplest recombination operator is that of single-point) 135.65 516.95 P (crossover) 135.65 502.95 T (.) 180.95 502.95 T (Consider the two parent binary strings:) 135.65 476.95 T 3 F (P) 171.65 450.95 T 3 10 Q (1) 178.84 447.95 T 3 12 Q ( = 1 0 0 1 0 1 1 0) 184.84 450.95 T 2 F (, and) 314.37 450.95 T 3 F (P) 171.65 424.95 T 3 10 Q (2) 178.84 421.95 T 3 12 Q ( = 1 0 1 1 1 0 0 0) 184.84 424.95 T 2 F (.) 314.37 424.95 T 0.59 (If an integer position,) 135.65 398.95 P 0 F 0.59 (i) 244.27 398.95 P 2 F 0.59 (, is selected uniformly at random between 1 and the string) 247.6 398.95 P 0.97 (length,) 135.65 384.95 P 0 F 0.97 (l) 172.6 384.95 P 2 F 0.97 (, minus one [1,) 175.93 384.95 P 0 F 0.97 (l) 254.42 384.95 P 2 F 0.97 (-1], and the genetic information exchanged between the) 257.76 384.95 P 0.15 (individuals about this point, then two new of) 135.65 370.95 P 0.15 (fspring strings are produced. The two) 351.03 370.95 P (of) 135.65 356.95 T (fspring below are produced when the crossover point) 145.42 356.95 T 0 F (i = 5) 403.22 356.95 T 2 F ( is selected,) 426.64 356.95 T 3 F (O) 171.65 330.95 T 3 10 Q (1) 178.84 327.95 T 3 12 Q ( = 1 0 0 1 0 0 0 0) 184.84 330.95 T 2 F (, and) 314.37 330.95 T 3 F (O) 171.65 304.95 T 3 10 Q (2) 178.84 301.95 T 3 12 Q ( = 1 0 1 1 1 1 1 0) 184.84 304.95 T 2 F (.) 314.37 304.95 T 3.99 (This crossover operation is not necessarily performed on all strings in the) 135.65 278.95 P 0.87 (population. Instead, it is applied with a probability) 135.65 264.95 P 0 F 0.87 (Px) 387.77 264.95 P 2 F 0.87 ( when the pairs are chosen) 400.42 264.95 P -0.2 (for breeding. A further genetic operator) 135.65 250.95 P -0.2 (, called mutation, is then applied to the new) 324.02 250.95 P 1.8 (chromosomes, again with a set probability) 135.65 236.95 P 1.8 (,) 347.08 236.95 P 0 F 1.8 (Pm) 354.88 236.95 P 2 F 1.8 (. Mutation causes the individual) 370.87 236.95 P 1.06 (genetic representation to be changed according to some probabilistic rule. In the) 135.65 222.95 P 0.41 (binary) 135.65 208.95 P 0.41 (string) 172.7 208.95 P 0.41 ( representation,) 206.01 208.95 P 0.41 ( mutation will cause a single bit to change its state,) 283.36 208.95 P 0.74 (0) 135.65 194.95 P 4 F 0.74 (\336) 145.38 194.95 P 2 F 0.74 (1 or 1) 160.96 194.95 P 4 F 0.74 (\336) 194.15 194.95 P 2 F 0.74 ( 0. So, for example, mutating the fourth bit of) 205.99 194.95 P 3 F 1.77 (O) 434.89 194.95 P 3 10 Q 1.48 (1) 442.09 191.95 P 2 12 Q 0.74 ( leads to the new) 448.09 194.95 P (string,) 135.65 180.95 T 3 F (O) 171.65 154.95 T 3 10 Q (1m) 178.84 151.95 T 3 12 Q ( = 1 0 0 0 0 0 0 0) 190.84 154.95 T 2 F (.) 320.37 154.95 T 0.19 (Mutation is generally considered to be a background operator that ensures that the) 135.65 128.95 P 0.61 (probability of searching a particular subspace of the problem space is never zero.) 135.65 114.95 P FMENDPAGE %%EndPage: "4" 5 %%Page: "5" 5 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-5) 518.33 61.29 T 2 12 Q 1.57 (This has the ef) 135.65 736.95 P 1.57 (fect of tending to inhibit the possibility of conver) 210.43 736.95 P 1.57 (ging to a local) 458.64 736.95 P (optimum, rather than the global optimum.) 135.65 722.95 T 1.87 (After recombination and mutation, the individual strings are then, if necessary) 135.65 696.95 P 1.87 (,) 528.65 696.95 P 4.09 (decoded, the objective function evaluated, a \336tness value assigned to each) 135.65 682.95 P -0.01 (individual and individuals selected for mating according to their \336tness, and so the) 135.65 668.95 P 4.08 (process continues through subsequent generations. In this way) 135.65 654.95 P 4.08 (, the average) 462.55 654.95 P 3.36 (performance of individuals in a population is expected to increase, as good) 135.65 640.95 P 0.1 (individuals are preserved and bred with one another and the less \336t individuals die) 135.65 626.95 P -0.26 (out. The GA is terminated when some criteria are satis\336ed, e.g. a certain number of) 135.65 612.95 P 0.66 (generations, a mean deviation in the population, or when a particular point in the) 135.65 598.95 P (search space is encountered.) 135.65 584.95 T 1 16 Q (GAs versus T) 135.65 556.29 T (raditional Methods) 226.86 556.29 T 2 12 Q 1.06 (From the above discussion, it can be seen that the GA dif) 135.65 528.95 P 1.06 (fers substantially from) 421.6 528.95 P 3.43 (more traditional search and optimization methods. The four most signi\336cant) 135.65 514.95 P (dif) 135.65 500.95 T (ferences are:) 148.76 500.95 T (\245) 157.25 474.95 T (GAs search a population of points in parallel, not a single point.) 171.65 474.95 T (\245) 157.25 454.95 T 1.32 (GAs do not require derivative information or other auxiliary knowledge;) 171.65 454.95 P 1.1 (only the objective function and corresponding \336tness levels in\337uence the) 171.65 440.95 P (directions of search.) 171.65 426.95 T (\245) 157.25 406.95 T (GAs use probabilistic transition rules, not deterministic ones.) 171.65 406.95 T (\245) 157.25 386.95 T -0.26 (GAs work on an encoding of the parameter set rather than the parameter set) 171.65 386.95 P (itself \050except in where real-valued individuals are used\051.) 171.65 372.95 T 1.06 (It is important to note that the GA provides a number of potential solutions to a) 135.65 346.95 P 0.5 (given problem and the choice of \336nal solution is left to the user) 135.65 332.95 P 0.5 (. In cases where a) 444.75 332.95 P 0.44 (particular problem does not have one individual solution, for example a family of) 135.65 318.95 P 4.61 (Pareto-optimal solutions, as is the case in multiobjective optimization and) 135.65 304.95 P 3.39 (scheduling problems, then the GA is potentially useful for identifying these) 135.65 290.95 P (alternative solutions simultaneously) 135.65 276.95 T (.) 307.44 276.95 T FMENDPAGE %%EndPage: "5" 6 %%Page: "6" 6 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-6) 518.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Major Elements of the Genetic Algorithm) 63.65 732.95 T 2 12 Q 0.01 (The simple genetic algorithm \050SGA\051 is described by Goldber) 135.65 694.95 P 0.01 (g [1] and is used here) 428.67 694.95 P 0.09 (to illustrate the basic components of the GA. A pseudo-code outline of the SGA is) 135.65 680.95 P 1.58 (shown in Fig. 1. The population at time) 135.65 666.95 P 0 F 1.58 (t) 340.87 666.95 P 2 F 1.58 ( is represented by the time-dependent) 344.21 666.95 P 0.74 (variable) 135.65 652.95 P 0 F 0.74 (P) 178.02 652.95 P 2 F 0.74 (, with the initial population of random estimates being) 184.02 652.95 P 0 F 0.74 (P\0500\051) 453.87 652.95 P 2 F 0.74 (. Using this) 475.19 652.95 P 0.28 (outline of a GA, the remainder of this Section describes the major elements of the) 135.65 638.95 P (GA.) 135.65 624.95 T 1 16 Q (Population Repr) 135.65 336.01 T (esentation and Initialisation) 248.64 336.01 T 2 12 Q 0.3 (GAs operate on a number of potential solutions, called a population, consisting of) 135.65 308.67 P 2.4 (some encoding of the parameter set simultaneously) 135.65 294.67 P 2.4 (. T) 395.08 294.67 P 2.4 (ypically) 409.97 294.67 P 2.4 (, a population is) 447.83 294.67 P 0.25 (composed of between 30 and 100 individuals, although, a variant called the micro) 135.65 280.67 P 1.11 (GA uses very small populations, ~10 individuals, with a restrictive reproduction) 135.65 266.67 P (and replacement strategy in an attempt to reach real-time execution [2].) 135.65 252.67 T 0.4 (The most commonly used representation of chromosomes in the GA is that of the) 135.65 226.67 P 2.36 (single-level binary string. Here, each decision variable in the parameter set is) 135.65 212.67 P 0.23 (encoded as a binary string and these are concatenated to form a chromosome. The) 135.65 198.67 P 1.64 (use of Gray coding has been advocated as a method of overcoming the hidden) 135.65 184.67 P 4.2 (representational bias in conventional binary representation as the Hamming) 135.65 170.67 P 1.13 (distance between adjacent values is constant [3]. Empirical evidence of Caruana) 135.65 156.67 P 1.94 (and Schaf) 135.65 142.67 P 1.94 (fer [4] suggests that lar) 185 142.67 P 1.94 (ge Hamming distances in the representational) 303.11 142.67 P 5.36 (mapping between adjacent values, as is the case in the standard binary) 135.65 128.67 P 3.42 (representation, can result in the search process being deceived or unable to) 135.65 114.67 P 63.65 96.95 531.65 744.95 C 133.38 360.67 531.65 620.95 C 162.43 380.97 502.59 600.65 R 7 X 0 K V 2 12 Q 0 X (procedure GA) 198.43 592.65 T (begin) 198.43 577.65 T (t = 0;) 243.43 562.65 T (initialize P\050t\051;) 243.43 547.65 T (evaluate P\050t\051;) 243.43 532.65 T (while not finished do) 243.43 517.65 T (begin) 243.43 502.65 T (t = t + 1;) 315.43 487.65 T (select P\050t\051 from P\050t-1\051;) 315.43 472.65 T (reproduce pairs in P\050t\051;) 315.43 457.65 T (evaluate P\050t\051;) 315.43 442.65 T (end) 243.43 427.65 T (end.) 198.43 412.65 T 5 F (Figure 1: A Simple Genetic Algorithm) 234.43 386.65 T 146.89 370.34 518.14 611.28 R 0.5 H 2 Z N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "6" 7 %%Page: "7" 7 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-7) 518.33 61.29 T 2 12 Q 0.64 (ef) 135.65 736.95 P 0.64 (\336ciently locate the global minimum. A further approach of Schmitendor) 144.75 736.95 P 0.64 (gf) 496.04 736.95 P 0 F 0.64 (et-al) 509.66 736.95 P 2 F 5.3 ([5], is the use of logarithmic scaling in the conversion of binary-coded) 135.65 722.95 P 3.46 (chromosomes to their real phenotypic values. Although the precision of the) 135.65 708.95 P 1.48 (parameter values is possibly less consistent over the desired range, in problems) 135.65 694.95 P 0.3 (where the spread of feasible parameters is unknown, a lar) 135.65 680.95 P 0.3 (ger search space may be) 413.9 680.95 P 0.51 (covered with the same number of bits than a linear mapping scheme allowing the) 135.65 666.95 P -0.2 (computational burden of exploring unknown search spaces to be reduced to a more) 135.65 652.95 P (manageable level.) 135.65 638.95 T 0.33 (Whilst binary-coded GAs are most commonly used, there is an increasing interest) 135.65 612.95 P 0.52 (in alternative encoding strategies, such as integer and real-valued representations.) 135.65 598.95 P 1.37 (For some problem domains, it is ar) 135.65 584.95 P 1.37 (gued that the binary representation is in fact) 311.22 584.95 P 1.28 (deceptive in that it obscures the nature of the search [6]. In the subset selection) 135.65 570.95 P 0.8 (problem [7], for example, the use of an integer representation and look-up tables) 135.65 556.95 P 5.49 (provides a convenient and natural way of expressing the mapping from) 135.65 542.95 P (representation to problem domain.) 135.65 528.95 T 0.06 (The use of real-valued genes in GAs is claimed by W) 135.65 502.95 P 0.06 (right [8] to of) 392.27 502.95 P 0.06 (fer a number of) 457.2 502.95 P 1.02 (advantages in numerical function optimization over binary encodings. Ef) 135.65 488.95 P 1.02 (\336ciency) 493.68 488.95 P 0.45 (of the GA is increased as there is no need to convert chromosomes to phenotypes) 135.65 474.95 P -0.02 (before each function evaluation; less memory is required as ef) 135.65 460.95 P -0.02 (\336cient \337oating-point) 433.38 460.95 P -0.03 (internal computer representations can be used directly; there is no loss in precision) 135.65 446.95 P 1.89 (by discretisation to binary or other values; and there is greater freedom to use) 135.65 432.95 P 0.23 (dif) 135.65 418.95 P 0.23 (ferent genetic operators. The use of real-valued encodings is described in detail) 148.76 418.95 P 0.08 (by Michalewicz [9] and in the literature on Evolution Strategies \050see, for example,) 135.65 404.95 P ([10]\051.) 135.65 390.95 T 1.85 (Having decided on the representation, the \336rst step in the SGA is to create an) 135.65 364.95 P 0.93 (initial population. This is usually achieved by generating the required number of) 135.65 350.95 P 0.95 (individuals using a random number generator that uniformly distributes numbers) 135.65 336.95 P 1.57 (in the desired range. For example, with a binary population of) 135.65 322.95 P 0 F 1.57 (N) 453 322.95 P 0 10 Q 1.3 (ind) 461 319.95 P 2 12 Q 1.57 ( individuals) 473.77 322.95 P 1.57 (whose chromosomes are) 135.65 308.95 P 0 F 1.57 (L) 261.27 308.95 P 0 10 Q 1.31 (ind) 267.94 305.95 P 2 12 Q 1.57 ( bits long,) 280.71 308.95 P 0 F 1.57 (N) 336.08 308.95 P 0 10 Q 1.31 (ind) 344.08 305.95 P 4 12 Q 1.57 (\264) 361.42 308.95 P 0 F 1.57 (L) 372.58 308.95 P 0 10 Q 1.31 (ind) 379.24 305.95 P 2 12 Q 1.57 ( random numbers uniformly) 392.02 308.95 P (distributed from the set {0, 1} would be produced.) 135.65 294.95 T 3.16 (A variation is the) 135.65 268.95 P 0 F 3.16 (extended random initialisation) 234.23 268.95 P 2 F 3.16 ( procedure of Bramlette [6]) 387.8 268.95 P 1.02 (whereby a number of random initialisations are tried for each individual and the) 135.65 254.95 P 0.74 (one with the best performance is chosen for the initial population. Other users of) 135.65 240.95 P -0.01 (GAs have seeded the initial population with some individuals that are known to be) 135.65 226.95 P 2.31 (in the vicinity of the global minimum \050see, for example, [1) 135.65 212.95 P 2.31 (1] and [12]\051. This) 440.12 212.95 P 3.22 (approach is, of course, only applicable if the nature of the problem is well) 135.65 198.95 P -0.16 (understood beforehand or if the GA is used in conjunction with a knowledge based) 135.65 184.95 P (system.) 135.65 170.95 T 5.61 (The GA T) 135.65 144.95 P 5.61 (oolbox supports binary) 195.31 144.95 P 5.61 (, integer and \337oating-point chromosome) 316.35 144.95 P 3.8 (representations. Binary and integer populations may be initialised using the) 135.65 130.95 P 1.9 (T) 135.65 116.95 P 1.9 (oolbox function to create binary populations,) 142.14 116.95 P 3 F 4.55 (crtbp) 372.38 116.95 P 2 F 1.9 (. An additional function,) 408.36 116.95 P 3 F 3.25 (crtbase) 135.65 102.95 P 2 F 1.35 (, is provided that builds a vector describing the integer representation) 186.02 102.95 P FMENDPAGE %%EndPage: "7" 8 %%Page: "8" 8 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-8) 518.33 61.29 T 2 12 Q 3.99 (used. Real-valued populations may be initialised with the function) 135.65 736.95 P 3 F 9.57 (crtrp) 492.67 736.95 P 2 F 3.99 (.) 528.65 736.95 P 2.54 (Conversion between binary strings and real values is provided by the routine) 135.65 722.95 P 3 F (bs2rv) 135.65 708.95 T 2 F ( that supports the use of Gray codes and logarithmic scaling.) 171.63 708.95 T 1 16 Q (The Objective and Fitness Functions) 135.65 680.29 T 2 12 Q 2.47 (The objective function is used to provide a measure of how individuals have) 135.65 652.95 P -0.11 (performed in the problem domain. In the case of a minimization problem, the most) 135.65 638.95 P 1.87 (\336t individuals will have the lowest numerical value of the associated objective) 135.65 624.95 P 0.17 (function. This raw measure of \336tness is usually only used as an intermediate stage) 135.65 610.95 P 0.36 (in determining the relative performance of individuals in a GA. Another function,) 135.65 596.95 P 0.05 (the) 135.65 582.95 P 0 F 0.05 (\336tness function) 153.35 582.95 P 2 F 0.05 (, is normally used to transform the objective function value into) 225.7 582.95 P (a measure of relative \336tness [13], thus:) 135.65 568.95 T -0.29 (where) 135.65 514.76 P 0 F -0.29 (f) 167.66 514.76 P 2 F -0.29 ( is the objective function,) 170.99 514.76 P 0 F -0.29 (g) 294.13 514.76 P 2 F -0.29 ( transforms the value of the objective function to) 300.13 514.76 P 2.1 (a non-negative number and) 135.65 500.76 P 0 F 2.1 (F) 277.95 500.76 P 2 F 2.1 ( is the resulting relative \336tness. This mapping is) 285.28 500.76 P 1.97 (always necessary when the objective function is to be minimized as the lower) 135.65 486.76 P 3.03 (objective function values correspond to \336tter individuals. In many cases, the) 135.65 472.76 P -0.29 (\336tness function value corresponds to the number of of) 135.65 458.76 P -0.29 (fspring that an individual can) 392.24 458.76 P 0.33 (expect to produce in the next generation. A commonly used transformation is that) 135.65 444.76 P 1.03 (of proportional \336tness assignment \050see, for example, [1]\051. The individual \336tness,) 135.65 430.76 P 0 F 1.4 (F\050x) 135.65 416.76 P 0 10 Q 1.17 (i) 152.29 413.76 P 0 12 Q 1.4 (\051) 155.07 416.76 P 2 F 1.4 (, of each individual is computed as the individual\325) 159.07 416.76 P 1.4 (s raw performance,) 409.79 416.76 P 0 F 1.4 (f\050x) 509.22 416.76 P 0 10 Q 1.17 (i) 521.88 413.76 P 0 12 Q 1.4 (\051) 524.66 416.76 P 2 F 1.4 (,) 528.65 416.76 P (relative to the whole population, i.e.,) 135.65 402.76 T (,) 380.93 365.33 T 1.36 (where) 135.65 304.51 P 0 F 1.36 (N) 169.3 304.51 P 0 10 Q 1.13 (ind) 177.3 301.51 P 2 12 Q 1.36 ( is the population size and) 190.08 304.51 P 0 F 1.36 (x) 326.15 304.51 P 0 10 Q 1.13 (i) 331.47 301.51 P 2 12 Q 1.36 ( is the phenotypic value of individual) 334.25 304.51 P 0 F 1.36 (i) 525.32 304.51 P 2 F 1.36 (.) 528.65 304.51 P 1.87 (Whilst this \336tness assignment ensures that each individual has a probability of) 135.65 290.51 P 3.54 (reproducing according to its relative \336tness, it fails to account for negative) 135.65 276.51 P (objective function values.) 135.65 262.51 T 0.15 (A linear transformation which of) 135.65 236.51 P 0.15 (fsets the objective function [1] is often used prior) 293.92 236.51 P (to \336tness assignment, such that,) 135.65 222.51 T 0.2 (where) 135.65 168.32 P 0 F 0.2 (a) 168.15 168.32 P 2 F 0.2 ( is a positive scaling factor if the optimization is maximizing and negative) 174.14 168.32 P -0.1 (if we are minimizing. The of) 135.65 154.32 P -0.1 (fset) 272.83 154.32 P 0 F -0.1 (b) 293.04 154.32 P 2 F -0.1 ( is used to ensure that the resulting \336tness values) 299.04 154.32 P (are non-negative.) 135.65 140.32 T 288.09 536.76 379.21 550.95 C 0 12 Q 0 X 0 K (F) 289.09 541.75 T (x) 304.22 541.75 T 4 F (\050) 299.12 541.75 T (\051) 310.16 541.75 T 0 F (g) 334.73 541.75 T (f) 348.54 541.75 T (x) 359.68 541.75 T 4 F (\050) 354.58 541.75 T (\051) 365.61 541.75 T (\050) 343.44 541.75 T (\051) 372.21 541.75 T (=) 322.15 541.75 T -8.35 24.95 603.65 816.95 C 283.37 326.51 380.93 384.76 C 0 12 Q 0 X 0 K (F) 284.37 365.33 T (x) 299.5 365.33 T 0 9 Q (i) 305.29 361.55 T 4 12 Q (\050) 294.4 365.33 T (\051) 308.4 365.33 T 0 F (f) 343.44 375.55 T (x) 354.58 375.55 T 0 9 Q (i) 360.36 371.77 T 4 12 Q (\050) 349.48 375.55 T (\051) 363.47 375.55 T 0 F (f) 352.9 343.76 T (x) 364.04 343.76 T 0 9 Q (i) 369.83 339.98 T 4 12 Q (\050) 358.94 343.76 T (\051) 372.93 343.76 T 0 9 Q (i) 333.98 329.46 T 2 F (1) 347.41 329.46 T 4 F (=) 339.47 329.46 T 0 F (N) 335.47 360.27 T 0 6 Q (i) 341.82 357.82 T (n) 343.94 357.82 T (d) 347.4 357.82 T 4 18 Q (\345) 336.52 340.55 T 4 12 Q (=) 320.39 365.33 T 333.98 367.92 378.68 367.92 2 L 0.33 H 0 Z N -8.35 24.95 603.65 816.95 C 285.65 190.32 381.65 204.51 C 0 12 Q 0 X 0 K (F) 286.65 195.31 T (x) 301.79 195.31 T 4 F (\050) 296.68 195.31 T (\051) 307.72 195.31 T 0 F (a) 332.3 195.31 T (f) 339 195.31 T (x) 350.14 195.31 T 4 F (\050) 345.04 195.31 T (\051) 356.07 195.31 T 0 F (b) 374.65 195.31 T 4 F (+) 365.07 195.31 T (=) 319.71 195.31 T -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "8" 9 %%Page: "9" 9 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-9) 518.33 61.29 T 2 12 Q 0.91 (The linear scaling and of) 135.65 736.95 P 0.91 (fsetting outlined above is, however) 258.3 736.95 P 0.91 (, susceptible to rapid) 429.66 736.95 P 6.1 (conver) 135.65 722.95 P 6.1 (gence. The) 168.07 722.95 P 0 F 6.1 (selection) 235.88 722.95 P 2 F 6.1 ( algorithm \050see below\051 selects individuals for) 278.52 722.95 P 3.81 (reproduction on the basis of their relative \336tness. Using linear scaling, the) 135.65 708.95 P 2.09 (expected number of of) 135.65 694.95 P 2.09 (fspring is approximately proportional to that individuals) 249.94 694.95 P 0.83 (performance. As there is no constraint on an individual\325) 135.65 680.95 P 0.83 (s performance in a given) 409.76 680.95 P 6.32 (generation, highly \336t individuals in early generations can dominate the) 135.65 666.95 P 5.59 (reproduction causing rapid conver) 135.65 652.95 P 5.59 (gence to possibly sub-optimal solutions.) 316.4 652.95 P 0.26 (Similarly) 135.65 638.95 P 0.26 (, if there is little deviation in the population, then scaling provides only a) 179.52 638.95 P (small bias towards the most \336t individuals.) 135.65 624.95 T 0.33 (Baker [14] suggests that by limiting the reproductive range, so that no individuals) 135.65 598.95 P -0.13 (generate an excessive number of of) 135.65 584.95 P -0.13 (fspring, prevents premature conver) 304.27 584.95 P -0.13 (gence. Here,) 471.52 584.95 P 0.97 (individuals are assigned a \336tness according to their rank in the population rather) 135.65 570.95 P 0.72 (than their raw performance. One variable,) 135.65 556.95 P 0 F 0.72 (MAX) 343.76 556.95 P 2 F 0.72 (, is used to determine the bias, or) 368.41 556.95 P 0 F 0.65 (selective pr) 135.65 542.95 P 0.65 (essur) 190.81 542.95 P 0.65 (e) 215.68 542.95 P 2 F 0.65 (, towards the most \336t individuals and the \336tness of the others is) 221.01 542.95 P (determined by the following rules:) 135.65 528.95 T (\245) 157.25 502.95 T 0 F (MIN) 164.44 502.95 T 2 F ( = 2.0 -) 186.43 502.95 T 0 F (MAX) 224.17 502.95 T 2 F (\245) 157.25 482.95 T 0 F (INC) 164.44 482.95 T 2 F ( = 2.0) 184.44 482.95 T 4 F (\264) 215.19 482.95 T 2 F ( \050) 221.77 482.95 T 0 F (MAX) 228.76 482.95 T 2 F ( -1.0\051 /) 253.41 482.95 T 0 F (N) 288.72 482.95 T 0 10 Q (ind) 296.72 479.95 T 2 12 Q (\245) 157.25 462.95 T 0 F (LOW) 164.44 462.95 T 2 F ( =) 189.76 462.95 T 0 F (INC) 202.52 462.95 T 2 F ( / 2.0) 222.52 462.95 T 2.81 (where) 135.65 442.95 P 0 F 2.81 (MIN) 170.75 442.95 P 2 F 2.81 ( is the lower bound,) 192.74 442.95 P 0 F 2.81 (INC) 304.71 442.95 P 2 F 2.81 ( is the dif) 324.7 442.95 P 2.81 (ference between the \336tness of) 377.88 442.95 P 0.97 (adjacent individuals and) 135.65 428.95 P 0 F 0.97 (LOW) 258.13 428.95 P 2 F 0.97 ( is the expected number of trials \050number of times) 283.45 428.95 P 1.2 (selected\051 of the least \336t individual.) 135.65 414.95 P 0 F 1.2 (MAX) 311.73 414.95 P 2 F 1.2 ( is typically chosen in the interval [1.1,) 336.38 414.95 P 0.66 (2.0]. Hence, for a population size of) 135.65 400.95 P 0 F 0.66 (N) 316.12 400.95 P 0 10 Q 0.55 (ind) 324.11 397.95 P 2 12 Q 0.66 ( = 40 and) 336.89 400.95 P 0 F 0.66 (MAX) 387.59 400.95 P 2 F 0.66 ( = 1.1, we obtain) 412.24 400.95 P 0 F 0.66 (MIN) 499.24 400.95 P 2 F 0.66 ( =) 521.23 400.95 P -0.18 (0.9,) 135.65 386.95 P 0 F -0.18 (INC) 156.46 386.95 P 2 F -0.18 ( = 0.05 and) 176.45 386.95 P 0 F -0.18 (LOW) 232.81 386.95 P 2 F -0.18 ( = 0.025. The \336tness of individuals in the population may) 258.13 386.95 P (also be calculated directly as,) 135.65 372.95 T (,) 439.73 335.53 T (where) 135.65 299.28 T 0 F (x) 167.95 299.28 T 0 10 Q (i) 173.27 296.28 T 2 12 Q ( is the position in the ordered population of individual) 176.05 299.28 T 0 F (i) 437.9 299.28 T 2 F (.) 441.24 299.28 T -0.04 (Objective functions must be created by the user) 135.65 273.28 P -0.04 (, although a number of example m-) 363.03 273.28 P 0.7 (\336les are supplied with the T) 135.65 259.28 P 0.7 (oolbox that implement common test functions. These) 271.91 259.28 P 0.98 (objective functions all have the \336lename pre\336x) 135.65 245.28 P 3 F 2.36 (obj) 370.71 245.28 P 2 F 0.98 (. The T) 392.3 245.28 P 0.98 (oolbox supports both) 428.4 245.28 P 1.65 (linear and non-linear ranking methods,) 135.65 231.28 P 3 F 3.97 (ranking) 333.11 231.28 P 2 F 1.65 (, and includes a simple linear) 383.48 231.28 P 1.26 (scaling function,) 135.65 217.28 P 3 F 3.02 (scaling) 221.11 217.28 P 2 F 1.26 (, for completeness. It should be noted that the linear) 271.49 217.28 P -0.14 (scaling function is not suitable for use with objective functions that return negative) 135.65 203.28 P (\336tness values.) 135.65 189.28 T 1 16 Q (Selection) 135.65 160.61 T 2 12 Q 0.46 (Selection is the process of determining the number of times, or) 135.65 133.28 P 0 F 0.46 (trials) 445.13 133.28 P 2 F 0.46 (, a particular) 470.46 133.28 P 1.43 (individual is chosen for reproduction and, thus, the number of of) 135.65 119.28 P 1.43 (fspring that an) 459.51 119.28 P 224.57 321.28 439.73 354.95 C 0 12 Q 0 X 0 K (F) 225.57 335.53 T (x) 240.7 335.53 T 0 9 Q (i) 246.49 331.75 T 4 12 Q (\050) 235.6 335.53 T (\051) 249.59 335.53 T 2 F (2) 274.17 335.53 T 0 F (M) 292.75 335.53 T (A) 303.45 335.53 T (X) 311.48 335.53 T 4 F (-) 283.17 335.53 T 2 F (2) 331.39 335.53 T 0 F (M) 345.2 335.53 T (A) 355.89 335.53 T (X) 363.93 335.53 T 2 F (1) 383.84 335.53 T 4 F (-) 374.26 335.53 T (\050) 340.1 335.53 T (\051) 390.45 335.53 T 0 F (x) 404.51 345.75 T 0 9 Q (i) 410.29 341.97 T 2 12 Q (1) 425.37 345.75 T 4 F (-) 415.79 345.75 T 0 F (N) 398.14 327.91 T 0 9 Q (i) 406.61 324.13 T (n) 409.63 324.13 T (d) 414.66 324.13 T 2 12 Q (1) 431.73 327.91 T 4 F (-) 422.15 327.91 T (+) 321.81 335.53 T (=) 261.59 335.53 T 398.14 338.12 437.48 338.12 2 L 0.33 H 0 Z N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "9" 10 %%Page: "10" 10 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-10) 513.33 61.29 T 2 12 Q -0.28 (individual will produce. The selection of individuals can be viewed as two separate) 135.65 736.95 P (processes:) 135.65 722.95 T (1\051) 135.65 696.95 T 0.93 (determination of the number of trials an individual can expect to receive,) 171.65 696.95 P (and) 171.65 682.95 T (2\051) 135.65 662.95 T 2.6 (conversion of the expected number of trials into a discrete number of) 171.65 662.95 P (of) 171.65 648.95 T (fspring.) 181.42 648.95 T -0.07 (The \336rst part is concerned with the transformation of raw \336tness values into a real-) 135.65 628.95 P 0.47 (valued expectation of an individual\325) 135.65 614.95 P 0.47 (s probability to reproduce and is dealt with in) 310.06 614.95 P 0.51 (the previous subsection as \336tness assignment. The second part is the probabilistic) 135.65 600.95 P -0.19 (selection of individuals for reproduction based on the \336tness of individuals relative) 135.65 586.95 P 3.05 (to one another and is sometimes known as) 135.65 572.95 P 0 F 3.05 (sampling) 365.89 572.95 P 2 F 3.05 (. The remainder of this) 409.87 572.95 P 2.11 (subsection will review some of the more popular selection methods in current) 135.65 558.95 P (usage.) 135.65 544.95 T -0.17 (Baker [15] presented three measures of performance for selection algorithms,) 135.65 518.95 P 0 F -0.17 (bias) 508.66 518.95 P 2 F -0.17 (,) 528.65 518.95 P 0 F 3.37 (spr) 135.65 504.95 P 3.37 (ead) 150.53 504.95 P 2 F 3.37 ( and) 167.85 504.95 P 0 F 3.37 (ef\336ciency) 197.9 504.95 P 2 F 3.37 (. Bias is de\336ned as the absolute dif) 242.41 504.95 P 3.37 (ference between an) 432.34 504.95 P 4.34 (individual\325) 135.65 490.95 P 4.34 (s actual and expected selection probability) 187.63 490.95 P 4.34 (. Optimal zero bias is) 412.04 490.95 P 1.03 (therefore achieved when an individual\325) 135.65 476.95 P 1.03 (s selection probability equals its expected) 326.95 476.95 P (number of trials.) 135.65 462.95 T -0.05 (Spread is the range in the possible number of trials that an individual may achieve.) 135.65 436.95 P 0.71 (If) 135.65 422.95 P 0 F 0.71 (f\050i\051) 147.34 422.95 P 2 F 0.71 ( is the actual number of trials that individual) 162 422.95 P 0 F 0.71 (i) 383.91 422.95 P 2 F 0.71 ( receives, then the \322minimum) 387.24 422.95 P (spread\323 is the smallest spread that theoretically permits zero bias, i.e.) 135.65 408.95 T 0.3 (where) 135.65 321.65 P 0 F 0.3 (et\050i\051) 168.24 321.65 P 2 F 0.3 ( is the expected number of trials of individual) 188.23 321.65 P 0 F 0.3 (i) 412.42 321.65 P 2 F 0.3 (,) 415.76 321.65 P 0.3 ( is the \337oor of) 463.16 321.65 P 1.64 (et\050i\051 and) 135.65 307.65 P 1.64 ( is the ceil. Thus, while bias is an indication of accuracy) 223.32 307.65 P 1.64 (, the) 509.36 307.65 P (spread of a selection method measures its consistency) 135.65 293.65 T (.) 393.02 293.65 T 0.88 (The desire for ef) 135.65 267.65 P 0.88 (\336cient selection methods is motivated by the need to maintain a) 217.67 267.65 P 1.72 (GAs overall time complexity) 135.65 253.65 P 1.72 (. It has been shown in the literature that the other) 279.61 253.65 P 4.96 (phases of a GA \050excluding the actual objective function evaluations\051 are) 135.65 239.65 P 1 (O\050L) 135.65 225.65 P 2 10 Q 0.83 (ind) 155.63 222.65 P 2 12 Q 1 (.N) 168.4 225.65 P 2 10 Q 0.83 (ind) 180.06 222.65 P 2 12 Q 1 (\051 or better time complexity) 192.83 225.65 P 1 (, where L) 324.64 225.65 P 2 10 Q 0.83 (ind) 372.27 222.65 P 2 12 Q 1 ( is the length of an individual) 385.05 225.65 P 0.71 (and N) 135.65 211.65 P 2 10 Q 0.59 (ind) 165.33 208.65 P 2 12 Q 0.71 ( is the population size. The selection algorithm should thus achieve zero) 178.1 211.65 P 1.51 (bias whilst maintaining a minimum spread and not contributing to an increased) 135.65 197.65 P (time complexity of the GA.) 135.65 183.65 T 1 14 Q (Roulette Wheel Selection Methods) 135.65 156.31 T 2 12 Q 8.61 (Many selection techniques employ a \322roulette wheel\323 mechanism to) 135.65 129.65 P -0.14 (probabilistically select individuals based on some measure of their performance. A) 135.65 115.65 P 2.72 (real-valued interval,) 135.65 101.65 P 0 F 2.72 (Sum) 240.67 101.65 P 2 F 2.72 (, is determined as either the sum of the individuals\325) 261.32 101.65 P 261.26 343.65 406.04 390.95 C 0 12 Q 0 X 0 K (f) 262.26 364.71 T (i) 273.4 364.71 T 4 F (\050) 268.3 364.71 T (\051) 277.34 364.71 T 0 F (e) 312.75 365.19 T (t) 318.78 365.19 T (i) 329.92 365.19 T 4 F (\050) 324.82 365.19 T (\051) 333.86 365.19 T 0 F (e) 357.85 365.19 T (t) 363.89 365.19 T (i) 375.03 365.19 T 4 F (\050) 369.92 365.19 T (\051) 378.97 365.19 T (,) 345.86 365.19 T (\376) 394.67 350.05 T (\375) 394.67 362.17 T (\374) 394.67 374.29 T (\356) 299.88 350.05 T (\355) 299.88 362.17 T (\354) 299.88 374.29 T (\316) 286.33 364.71 T 307.75 362.2 307.75 373.4 2 L 0.33 H 0 Z N 307.75 362.2 310.75 362.2 2 L N 343.86 362.2 343.86 373.4 2 L N 343.86 362.2 340.86 362.2 2 L N 352.85 362.2 352.85 373.4 2 L N 352.85 373.4 355.85 373.4 2 L N 388.96 362.2 388.96 373.4 2 L N 388.96 373.4 385.96 373.4 2 L N -8.35 24.95 603.65 816.95 C 422.05 316.65 463.16 330.85 C 0 12 Q 0 X 0 K (e) 429.05 321.65 T (t) 435.08 321.65 T (i) 446.23 321.65 T 4 F (\050) 441.12 321.65 T (\051) 450.17 321.65 T 424.05 318.65 424.05 329.85 2 L 0.33 H 0 Z N 424.05 318.65 427.05 318.65 2 L N 460.16 318.65 460.16 329.85 2 L N 460.16 318.65 457.16 318.65 2 L N -8.35 24.95 603.65 816.95 C 182.22 302.65 223.32 316.85 C 0 12 Q 0 X 0 K (e) 189.22 307.65 T (t) 195.25 307.65 T (i) 206.39 307.65 T 4 F (\050) 201.29 307.65 T (\051) 210.33 307.65 T 184.22 304.65 184.22 315.85 2 L 0.33 H 0 Z N 184.22 315.85 187.22 315.85 2 L N 220.32 304.65 220.32 315.85 2 L N 220.32 315.85 217.32 315.85 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "10" 11 %%Page: "11" 11 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-11) 513.33 61.29 T 2 12 Q 1.17 (expected selection probabilities or the sum of the raw \336tness values over all the) 135.65 736.95 P 0.26 (individuals in the current population. Individuals are then mapped one-to-one into) 135.65 722.95 P 1.69 (contiguous intervals in the range [0,) 135.65 708.95 P 0 F 1.69 (Sum) 321.33 708.95 P 2 F 1.69 (]. The size of each individual interval) 341.98 708.95 P -0.14 (corresponds to the \336tness value of the associated individual. For example, in Fig. 2) 135.65 694.95 P 1.38 (the circumference of the roulette wheel is the sum of all six individual\325) 135.65 680.95 P 1.38 (s \336tness) 491.95 680.95 P 1.76 (values. Individual 5 is the most \336t individual and occupies the lar) 135.65 666.95 P 1.76 (gest interval,) 467.93 666.95 P 1.97 (whereas individuals 6 and 4 are the least \336t and have correspondingly smaller) 135.65 652.95 P 1.31 (intervals within the roulette wheel. T) 135.65 638.95 P 1.31 (o select an individual, a random number is) 318.59 638.95 P 1.88 (generated in the interval [0,) 135.65 624.95 P 0 F 1.88 (Sum) 280.29 624.95 P 2 F 1.88 (] and the individual whose segment spans the) 300.94 624.95 P 1.11 (random number is selected. This process is repeated until the desired number of) 135.65 610.95 P (individuals have been selected.) 135.65 596.95 T -0.04 (The basic roulette wheel selection method is stochastic sampling with replacement) 135.65 570.95 P 4.89 (\050SSR\051. Here, the segment size and selection probability remain the same) 135.65 556.95 P 3.36 (throughout the selection phase and individuals are selected according to the) 135.65 542.95 P 0.48 (procedure outlined above. SSR gives zero bias but a potentially unlimited spread.) 135.65 528.95 P (Any individual with a segment size > 0 could entirely \336ll the next population.) 135.65 514.95 T 3.91 (Stochastic sampling with partial replacement \050SSPR\051 extends upon SSR by) 135.65 271.94 P 3.1 (resizing an individual\325) 135.65 257.94 P 3.1 (s segment if it is selected. Each time an individual is) 249.12 257.94 P 1.33 (selected, the size of its segment is reduced by 1.0. If the segment size becomes) 135.65 243.94 P 2.15 (negative, then it is set to 0.0. This provides an upper bound on the spread of) 135.65 229.94 P -0.2 (. However) 176.76 215.94 P -0.2 (, the lower bound is zero and the bias is higher than that of SSR.) 226.02 215.94 P 1.29 (Remainder sampling methods involve two distinct phases. In the integral phase,) 135.65 189.94 P 2.36 (individuals are selected deterministically according to the integer part of their) 135.65 175.94 P 0.4 (expected trials. The remaining individuals are then selected probabilistically from) 135.65 161.94 P 3.95 (the fractional part of the individuals expected values. Remainder stochastic) 135.65 147.94 P 1.82 (sampling with replacement \050RSSR\051 uses roulette wheel selection to sample the) 135.65 133.94 P 3.42 (individual not assigned deterministically) 135.65 119.94 P 3.42 (. During the roulette wheel selection) 340.02 119.94 P 3.29 (phase, individual\325) 135.65 105.94 P 3.29 (s fractional parts remain unchanged and, thus, compete for) 224.22 105.94 P 63.65 96.95 531.65 744.95 C 133.38 293.94 531.65 510.95 C 0.5 H 2 Z 0 X 0 K 90 450 70.87 70.87 332.51 420.22 A 332.51 491.09 332.51 420.22 2 L N 332.51 420.22 282.91 370.61 2 L N 332.51 420.22 384.95 466.76 2 L N 332.51 420.22 394.88 389.74 2 L N 2 12 Q (1) 358.18 462.39 T 90 450 7.09 7.09 361.18 466.48 A (3) 350.03 366.22 T 90 450 7.09 7.09 353.03 370.31 A (2) 382.66 416.22 T 90 450 7.09 7.09 385.66 420.31 A (4) 299.18 370.87 T 90 450 7.09 7.09 302.18 374.96 A 332.51 420.22 303.38 484.74 2 L N (5) 278.18 428.87 T 90 450 7.09 7.09 281.18 432.96 A 332.38 418.74 305.38 355.74 2 L N (6) 319.18 469.89 T 90 450 7.09 7.09 322.18 473.98 A 5 F (Figure 2: Roulette Wheel Selection) 245.56 316.24 T 146.49 303.24 518.54 501.66 R N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C 135.65 210.95 176.75 225.15 C 0 12 Q 0 X 0 K (e) 142.65 215.94 T (t) 148.68 215.94 T (i) 159.82 215.94 T 4 F (\050) 154.72 215.94 T (\051) 163.76 215.94 T 137.65 212.95 137.65 224.15 2 L 0.33 H 0 Z N 137.65 224.15 140.65 224.15 2 L N 173.76 212.95 173.76 224.15 2 L N 173.76 224.15 170.76 224.15 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "11" 12 %%Page: "12" 12 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-12) 513.33 61.29 T 2 12 Q 2.99 (selection between \322spins\323. RSSR provides zero bias and the spread is lower) 135.65 736.95 P 0.55 (bounded. The upper bound is limited only by the number of fractionally assigned) 135.65 722.95 P 2.87 (samples and the size of the integral part of an individual. For example, any) 135.65 708.95 P -0.04 (individual with a fractional part > 0 could win all the samples during the fractional) 135.65 694.95 P 2.65 (phase. Remainder stochastic sampling without replacement \050RSSWR\051 sets the) 135.65 680.95 P 0.02 (fractional part of an individual\325) 135.65 666.95 P 0.02 (s expected values to zero if it is sampled during the) 285.62 666.95 P 2.51 (fractional phase. This gives RSSWR minimum spread, although this selection) 135.65 652.95 P (method is biased in favour of smaller fractions.) 135.65 638.95 T 1 14 Q (Stochastic Universal Sampling) 135.65 611.62 T 2 12 Q 1.84 (Stochastic universal sampling \050SUS\051 is a single-phase sampling algorithm with) 135.65 584.95 P 0.05 (minimum spread and zero bias. Instead of the single selection pointer employed in) 135.65 570.95 P 2.58 (roulette wheel methods, SUS uses) 135.65 556.95 P 0 F 2.58 (N) 315.09 556.95 P 2 F 2.58 ( equally spaced pointers, where) 323.09 556.95 P 0 F 2.58 (N) 489.84 556.95 P 2 F 2.58 ( is the) 497.84 556.95 P 1.13 (number of selections required. The population is shuf) 135.65 542.95 P 1.13 (\337ed randomly and a single) 399.86 542.95 P 1.43 (random number in the range [0) 135.65 528.95 P 0 F 1.43 (Sum) 296.11 528.95 P 2 F 1.43 (/) 316.77 528.95 P 0 F 1.43 (N) 320.1 528.95 P 2 F 1.43 (] is generated,) 328.1 528.95 P 0 F 1.43 (ptr) 402.99 528.95 P 2 F 1.43 (. The) 416.33 528.95 P 0 F 1.43 (N) 446.84 528.95 P 2 F 1.43 ( individuals are) 454.84 528.95 P -0.2 (then chosen by generating the) 135.65 514.95 P 0 F -0.2 (N) 280.87 514.95 P 2 F -0.2 ( pointers spaced by 1, [) 288.87 514.95 P 0 F -0.2 (ptr) 399.13 514.95 P 2 F -0.2 (,) 412.64 514.95 P 0 F -0.2 (ptr) 418.44 514.95 P 2 F -0.2 (+1, ...,) 432.44 514.95 P 0 F -0.2 (ptr) 465.79 514.95 P 2 F -0.2 (+) 479.78 514.95 P 0 F -0.2 (N) 486.55 514.95 P 2 F -0.2 (-1], and) 494.55 514.95 P 1.84 (selecting the individuals whose \336tnesses span the positions of the pointers. An) 135.65 500.95 P 0.78 (individual is thus guaranteed to be selected a minimum of) 135.65 486.95 P 0.78 ( times and no) 465.02 486.95 P 1.34 (more than) 135.65 472.95 P 1.34 (, thus achieving minimum spread. In addition, as individuals) 230.74 472.95 P (are selected entirely on their position in the population, SUS has zero bias.) 135.65 458.95 T 3.69 (The roulette wheel selection methods can all be implemented as O\050NlogN\051) 135.65 432.95 P 0.4 (although SUS is a simpler algorithm and has time complexity O\050N\051. The T) 135.65 418.95 P 0.4 (oolbox) 498.33 418.95 P 4.7 (supplies a stochastic universal sampling function,) 135.65 404.95 P 3 F 11.28 (sus) 404.69 404.95 P 2 F 4.7 (, and the stochastic) 426.28 404.95 P (sampling with replacement algorithm,) 135.65 390.95 T 3 F (rws) 321.2 390.95 T 2 F (.) 342.79 390.95 T 1 16 Q (Cr) 135.65 362.29 T (ossover \050Recombination\051) 154.01 362.29 T 2 12 Q -0.08 (The basic operator for producing new chromosomes in the GA is that of crossover) 135.65 334.95 P -0.08 (.) 528.65 334.95 P 0.39 (Like its counterpart in nature, crossover produces new individuals that have some) 135.65 320.95 P 1.05 (parts of both parent\325) 135.65 306.95 P 1.05 (s genetic material. The simplest form of crossover is that of) 235.72 306.95 P 3.04 (single-point crossover) 135.65 292.95 P 3.04 (, described in the Overview of GAs. In this Section, a) 244.47 292.95 P 1.75 (number of variations on crossover are described and discussed and the relative) 135.65 278.95 P (merits of each reviewed.) 135.65 264.95 T 1 14 Q (Multi-point Cr) 135.65 237.62 T (ossover) 224.4 237.62 T 2 12 Q 0.7 (For multi-point crossover) 135.65 210.95 P 0.7 (,) 259.16 210.95 P 0 F 0.7 (m) 265.86 210.95 P 2 F 0.7 ( crossover positions,) 274.52 210.95 P 0.7 (, where) 483.85 210.95 P 0 F 0.7 (k) 523.54 210.95 P 0 10 Q 0.58 (i) 528.87 207.95 P 2 12 Q 2.14 (are the crossover points and) 135.65 196.95 P 0 F 2.14 (l) 283.23 196.95 P 2 F 2.14 ( is the length of the chromosome, are chosen at) 286.57 196.95 P 0.08 (random with no duplicates and sorted into ascending order) 135.65 182.95 P 0.08 (. Then, the bits between) 416.75 182.95 P -0.18 (successive crossover points are exchanged between the two parents to produce two) 135.65 168.95 P 423.91 481.96 465.02 496.16 C 0 12 Q 0 X 0 K (e) 430.91 486.95 T (t) 436.94 486.95 T (i) 448.08 486.95 T 4 F (\050) 442.98 486.95 T (\051) 452.02 486.95 T 425.91 483.96 425.91 495.16 2 L 0.33 H 0 Z N 425.91 483.96 428.91 483.96 2 L N 462.02 483.96 462.02 495.16 2 L N 462.02 483.96 459.02 483.96 2 L N -8.35 24.95 603.65 816.95 C 189.63 467.96 230.74 482.16 C 0 12 Q 0 X 0 K (e) 196.63 472.95 T (t) 202.66 472.95 T (i) 213.8 472.95 T 4 F (\050) 208.7 472.95 T (\051) 217.74 472.95 T 191.63 469.96 191.63 481.16 2 L 0.33 H 0 Z N 191.63 481.16 194.63 481.16 2 L N 227.74 469.96 227.74 481.16 2 L N 227.74 481.16 224.74 481.16 2 L N -8.35 24.95 603.65 816.95 C 377.89 204.32 483.85 220.16 C 0 12 Q 0 X 0 K (k) 378.89 210.95 T 0 9 Q (i) 384.68 207.17 T 2 12 Q (1) 410.59 210.95 T (2) 422.58 210.95 T 4 F (\274) 434.58 210.95 T 0 F (l) 452.57 210.95 T 2 F (1) 468.49 210.95 T 4 F (-) 458.91 210.95 T (,) 416.59 210.95 T (,) 428.58 210.95 T (,) 446.57 210.95 T ({) 403.73 210.95 T (}) 475.09 210.95 T (\316) 390.17 210.95 T -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "12" 13 %%Page: "13" 13 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-13) 513.33 61.29 T 2 12 Q 0.51 (new of) 135.65 736.95 P 0.51 (fspring. The section between the \336rst allele position and the \336rst crossover) 168.91 736.95 P (point is not exchanged between individuals. This process is illustrated in Fig. 3.) 135.65 722.95 T 0.94 (The idea behind multi-point, and indeed many of the variations on the crossover) 135.65 557.78 P 0.7 (operator) 135.65 543.78 P 0.7 (, is that the parts of the chromosome representation that contribute to the) 175.13 543.78 P 4.05 (most to the performance of a particular individual may not necessarily be) 135.65 529.78 P 0.41 (contained in adjacent substrings [16]. Further) 135.65 515.78 P 0.41 (, the disruptive nature of multi-point) 355.05 515.78 P 1.73 (crossover appears to encourage the exploration of the search space, rather than) 135.65 501.78 P 0.29 (favoring the conver) 135.65 487.78 P 0.29 (gence to highly \336t individuals early in the search, thus making) 229.93 487.78 P (the search more robust [17].) 135.65 473.78 T 1 14 Q (Uniform Cr) 135.65 446.44 T (ossover) 206.51 446.44 T 2 12 Q 0.42 (Single and multi-point crossover de\336ne cross points as places between loci where) 135.65 419.78 P 1.9 (a chromosome can be split. Uniform crossover [18] generalises this scheme to) 135.65 405.78 P 0.75 (make every locus a potential crossover point. A crossover mask, the same length) 135.65 391.78 P 0.26 (as the chromosome structures is created at random and the parity of the bits in the) 135.65 377.78 P 1.13 (mask indicates which parent will supply the of) 135.65 363.78 P 1.13 (fspring with which bits. Consider) 366.88 363.78 P (the following two parents, crossover mask and resulting of) 135.65 349.78 T (fspring:) 416.9 349.78 T 3 F (P) 143.73 323.78 T 3 10 Q (1) 150.92 320.78 T 3 12 Q (= 1 0 1 1 0 0 0 1 1 1) 186.25 323.78 T (P) 143.73 305.78 T 3 10 Q (2) 150.92 302.78 T 3 12 Q (= 0 0 0 1 1 1 1 0 0 0) 186.25 305.78 T (Mask) 143.73 287.78 T (= 0 0 1 1 0 0 1 1 0 0) 186.25 287.78 T (O) 143.73 269.78 T 3 10 Q (1) 150.92 266.78 T 3 12 Q (= 0 0 1 1 1 1 0 1 0 0) 186.25 269.78 T (O) 143.73 251.78 T 3 10 Q (2) 150.92 248.78 T 3 12 Q (= 1 0 0 1 0 0 1 0 1 1) 186.25 251.78 T 2 F 3.65 (Here, the \336rst of) 135.65 221.78 P 3.65 (fspring,) 224.98 221.78 P 3 F 8.75 (O) 268.6 221.78 P 3 10 Q 7.29 (1) 275.79 218.78 P 2 12 Q 3.65 (, is produced by taking the bit from) 281.79 221.78 P 3 F 8.75 (P) 483.18 221.78 P 3 10 Q 7.29 (1) 490.38 218.78 P 2 12 Q 3.65 ( if the) 496.38 221.78 P 0.5 (corresponding mask bit is 1 or the bit from) 135.65 207.78 P 3 F 1.21 (P) 348.37 207.78 P 3 10 Q 1 (2) 355.57 204.78 P 2 12 Q 0.5 ( if the corresponding mask bit is 0.) 361.57 207.78 P -0.28 (Of) 135.65 193.78 P -0.28 (fspring) 148.09 193.78 P 3 F -0.67 (O) 184.78 193.78 P 3 10 Q -0.56 (2) 191.98 190.78 P 2 12 Q -0.28 ( is created using the inverse of the mask or) 197.97 193.78 P -0.28 (, equivalently) 399.82 193.78 P -0.28 (, swapping) 464.05 193.78 P 3 F -0.67 (P) 518.46 193.78 P 3 10 Q -0.56 (1) 525.65 190.78 P 2 12 Q (and) 135.65 179.78 T 3 F (P) 155.96 179.78 T 3 10 Q (2) 163.16 176.78 T 2 12 Q (.) 169.16 179.78 T 0.08 (Uniform crossover) 135.65 153.78 P 0.08 (, like multi-point crossover) 225.51 153.78 P 0.08 (, has been claimed to reduce the bias) 355.21 153.78 P 2.24 (associated with the length of the binary representation used and the particular) 135.65 139.78 P 0.79 (coding for a given parameter set. This helps to overcome the bias in single-point) 135.65 125.78 P 0.58 (crossover towards short substrings without requiring precise understanding of the) 135.65 111.78 P 63.65 96.95 531.65 744.95 C 124.27 579.78 531.65 718.95 C 151.07 674.97 307.83 682.06 R 8 X 0 K V 0.5 H 2 Z 0 X N 151.07 646.62 307.83 653.71 R 4 X V 0 X N 164.13 689.14 164.13 639.54 2 L N 190.26 689.14 190.26 639.54 2 L N 242.51 689.14 242.51 639.54 2 L N 278.44 689.14 278.44 639.54 2 L N 301.3 689.14 301.3 639.54 2 L N 360.08 674.97 373.15 682.06 R 8 X V 0 X N 373.15 646.62 399.28 653.71 R 8 X V 0 X N 399.27 674.97 451.53 682.06 R 8 X V 0 X N 451.53 646.62 487.45 653.71 R 8 X V 0 X N 487.45 674.97 510.32 682.06 R 8 X V 0 X N 510.32 646.62 516.85 653.71 R 8 X V 0 X N 373.15 674.97 399.28 682.06 R 4 X V 0 X N 451.53 674.97 487.45 682.06 R 4 X V 0 X N 510.32 674.97 516.85 682.06 R 4 X V 0 X N 360.08 646.62 373.15 653.71 R 4 X V 0 X N 399.27 646.62 451.53 653.71 R 4 X V 0 X N 487.45 646.62 510.32 653.71 R 4 X V 0 X N 335.49 667.65 347.02 664.34 335.49 661.03 335.49 664.34 4 Y V 320.89 664.34 335.49 664.34 2 L N 5 12 Q (Figure 3: Multi-point Crossover \050m=5\051) 237.91 612.02 T 138 594.44 529.92 704.29 R N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "13" 14 %%Page: "14" 14 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-14) 513.33 61.29 T 2 12 Q 1.26 (signi\336cance of individual bits in the chromosome representation. Spears and De) 135.65 736.95 P 1.96 (Jong [19] have demonstrated how uniform crossover may be parameterised by) 135.65 722.95 P 0.09 (applying a probability to the swapping of bits. This extra parameter can be used to) 135.65 708.95 P 0.56 (control the amount of disruption during recombination without introducing a bias) 135.65 694.95 P 1.78 (towards the length of the representation used. When uniform crossover is used) 135.65 680.95 P (with real-valued alleles, it is usually referred to as) 135.65 666.95 T 0 F (discr) 378.13 666.95 T (ete r) 401.67 666.95 T (ecombination) 422.88 666.95 T 2 F (.) 488.17 666.95 T 1 14 Q (Other Cr) 135.65 639.62 T (ossover Operators) 190.96 639.62 T 2 12 Q -0.05 (A related crossover operator is that of) 135.65 612.95 P 0 F -0.05 (shuf\337e) 319.45 612.95 P 2 F -0.05 ( [20]. A single cross-point is selected,) 350.77 612.95 P -0.24 (but before the bits are exchanged, they are randomly shuf) 135.65 598.95 P -0.24 (\337ed in both parents. After) 409.03 598.95 P -0.15 (recombination, the bits in the of) 135.65 584.95 P -0.15 (fspring are unshuf) 287.92 584.95 P -0.15 (\337ed. This too removes positional) 374.67 584.95 P (bias as the bits are randomly reassigned each time crossover is performed.) 135.65 570.95 T 0.72 (The) 135.65 544.95 P 0 F 0.72 (r) 158.02 544.95 P 0.72 (educed surr) 162.24 544.95 P 0.72 (ogate) 219.47 544.95 P 2 F 0.72 ( operator [16] constrains crossover to always produce new) 246.12 544.95 P 2.89 (individuals wherever possible. Usually) 135.65 530.95 P 2.89 (, this is implemented by restricting the) 330.08 530.95 P 2.18 (location of crossover points such that crossover points only occur where gene) 135.65 516.95 P (values dif) 135.65 502.95 T (fer) 182.4 502.95 T (.) 195.05 502.95 T 1 14 Q (Intermediate Recombination) 135.65 475.62 T 2 12 Q 5.99 (Given a real-valued encoding of the chromosome structure, intermediate) 135.65 448.95 P 0.54 (recombination is a method of producing new phenotypes around and between the) 135.65 434.95 P 1.68 (values of the parents phenotypes [21]. Of) 135.65 420.95 P 1.68 (fspring are produced according to the) 343.71 420.95 P (rule,) 135.65 406.95 T (,) 391.24 379.75 T 2.92 (where) 135.65 351.04 P 4 F 2.92 (a) 170.87 351.04 P 2 F 2.92 ( is a scaling factor chosen uniformly at random over some interval,) 178.43 351.04 P 3.3 (typically [-0.25, 1.25] and) 135.65 337.04 P 0 F 3.3 (P) 277.1 337.04 P 0 10 Q 2.75 (1) 284.42 334.04 P 2 12 Q 3.3 ( and) 289.42 337.04 P 0 F 3.3 (P) 319.34 337.04 P 0 10 Q 2.75 (2) 326.67 334.04 P 2 12 Q 3.3 ( are the parent chromosomes \050see, for) 331.67 337.04 P 2.82 (example, [21]\051. Each variable in the of) 135.65 323.04 P 2.82 (fspring is the result of combining the) 337.52 323.04 P -0.04 (variables in the parents according to the above expression with a new) 135.65 309.04 P 4 F -0.04 (a) 470.88 309.04 P 2 F -0.04 ( chosen for) 478.45 309.04 P 3.03 (each pair of parent genes. In geometric terms, intermediate recombination is) 135.65 295.04 P 273.05 373.04 391.24 388.95 C 0 12 Q 0 X 0 K (O) 274.05 379.75 T 2 9 Q (1) 283.17 375.99 T 0 12 Q (P) 306.25 379.75 T 2 9 Q (1) 314.04 375.99 T 4 12 Q (a) 331.12 379.75 T 0 F (P) 346.49 379.75 T 2 9 Q (2) 354.28 375.99 T 0 12 Q (P) 371.36 379.75 T 2 9 Q (1) 379.15 375.99 T 4 12 Q (-) 361.78 379.75 T (\050) 341.39 379.75 T (\051) 384.25 379.75 T (\264) 321.53 379.75 T (=) 293.67 379.75 T -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "14" 15 %%Page: "15" 15 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-15) 513.33 61.29 T 2 12 Q 1.47 (capable of producing new variables within a slightly lar) 135.65 736.95 P 1.47 (ger hypercube than that) 414.33 736.95 P (de\336ned by the parents but constrained by the range of) 135.65 722.95 T 4 F (a) 396.12 722.95 T 2 F (. as shown in Fig 4.) 403.69 722.95 T 1 14 Q (Line Recombination) 135.65 481.79 T 2 12 Q 0.13 (Line recombination [21] is similar to intermediate recombination, except that only) 135.65 455.12 P 0.29 (one value of) 135.65 441.12 P 4 F 0.29 (a) 198.79 441.12 P 2 F 0.29 ( is used in the recombination. Fig. 5 shows how line recombination) 206.36 441.12 P 0.88 (can generate any point on the line de\336ned by the parents within the limits of the) 135.65 427.12 P (perturbation,) 135.65 413.12 T 4 F (a,) 200.27 413.12 T 2 F (for a recombination in two variables.) 213.83 413.12 T 1 14 Q (Discussion) 135.65 165.83 T 2 12 Q 2.58 (The binary operators discussed in this Section have all, to some extent, used) 135.65 139.16 P 0.03 (disruption in the representation to help improve exploration during recombination.) 135.65 125.16 P 1.99 (Whilst these operators may be used with real-valued populations, the resulting) 135.65 111.16 P 63.65 96.95 531.65 744.95 C 133.38 505.12 531.65 718.95 C 205.79 685.03 209.1 696.57 212.41 685.03 209.1 685.03 4 Y 0 X 0 K V 209.1 565.46 209.1 685.03 2 L 0.5 H 2 Z N 1 X 90 450 5.32 5.32 249.85 655.82 G 0 X 90 450 5.32 5.32 249.85 655.82 A 230.36 590.27 315.4 675.31 R 8 X N 325.12 572.18 336.66 568.87 325.12 565.56 325.12 568.87 4 Y 0 X V 205.56 568.87 325.12 568.87 2 L N 1 X 90 450 5.32 5.32 295.91 609.75 G 0 X 90 450 5.32 5.32 295.91 609.75 A 4 X 90 450 5.32 5.32 271.11 662.9 G 0 X 90 450 5.32 5.32 271.11 662.9 A 4 X 90 450 5.32 5.32 260.48 631.01 G 0 X 90 450 5.32 5.32 260.48 631.01 A 4 X 90 450 5.32 5.32 242.76 602.67 G 0 X 90 450 5.32 5.32 242.76 602.67 A 4 X 90 450 5.32 5.32 285.28 641.64 G 0 X 90 450 5.32 5.32 285.28 641.64 A 1 X 90 450 5.32 5.32 356.15 634.56 G 0 X 90 450 5.32 5.32 356.15 634.56 A 4 X 90 450 5.32 5.32 356.15 609.75 G 0 X 90 450 5.32 5.32 356.15 609.75 A 2 12 Q (Gene1) 255.46 553.89 T (Gene 2) 0 -270 197.02 611.53 TF (Parents) 368.55 630.47 T (Potential of) 368.55 605.66 T (fspring) 423.97 605.66 T (Area of possible of) 350.83 656.65 T (fspring) 442.21 656.65 T 330.48 657.43 318.94 660.74 330.48 664.05 330.48 660.74 4 Y V 347.29 660.74 330.48 660.74 2 L N 5 F (Figure 4: Geometric Ef) 186.7 529.94 T (fect of Intermediate Recombination) 302.75 529.94 T 141.18 514.6 523.85 709.48 R N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C 63.65 96.95 531.65 744.95 C 133.38 189.16 531.65 409.12 C 196.34 372.12 199.64 383.66 202.95 372.12 199.64 372.12 4 Y 0 X 0 K V 199.64 252.55 199.64 372.12 2 L 0.5 H 2 Z N 1 X 90 450 5.32 5.32 228.24 352.09 G 0 X 90 450 5.32 5.32 228.24 352.09 A 315.67 259.27 327.2 255.96 315.67 252.65 315.67 255.96 4 Y V 196.1 255.96 315.67 255.96 2 L N 1 X 90 450 5.32 5.32 299.08 281.22 G 0 X 90 450 5.32 5.32 299.08 281.22 A 4 X 90 450 5.32 5.32 221.15 359.14 G 0 X 90 450 5.32 5.32 221.15 359.14 A 4 X 90 450 5.32 5.32 255.87 324.45 G 0 X 90 450 5.32 5.32 255.87 324.45 A 4 X 90 450 5.32 5.32 239.55 340.03 G 0 X 90 450 5.32 5.32 239.55 340.03 A 1 X 90 450 5.32 5.32 346.69 321.65 G 0 X 90 450 5.32 5.32 346.69 321.65 A 4 X 90 450 5.32 5.32 346.69 296.85 G 0 X 90 450 5.32 5.32 346.69 296.85 A 2 12 Q (Gene1) 246 240.98 T (Gene 2) 0 -270 187.56 298.62 TF (Parents) 359.09 317.56 T (Potential of) 359.09 292.76 T (fspring) 414.51 292.76 T 5 F (Figure 5: Geometric Ef) 197.57 217.03 T (fect of Line Recombination) 313.62 217.03 T 141.18 201.7 523.85 396.58 R N 4 X 90 450 5.32 5.32 270.76 309.57 G 0 X 90 450 5.32 5.32 270.76 309.57 A 4 X 90 450 5.32 5.32 286.33 293.94 G 0 X 90 450 5.32 5.32 286.33 293.94 A 4 X 90 450 5.32 5.32 306.88 273.42 G 0 X 90 450 5.32 5.32 306.88 273.42 A 4 X 90 450 5.32 5.32 314.68 265.62 G 0 X 90 450 5.32 5.32 314.68 265.62 A 4 X 90 450 5.32 5.32 214.04 366.26 G 0 X 90 450 5.32 5.32 214.04 366.26 A 213.69 366.6 312.9 267.39 2 L V 8 X N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "15" 16 %%Page: "16" 16 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-16) 513.33 61.29 T 2 12 Q 0.19 (changes in the genetic material after recombination would not extend to the actual) 135.65 736.95 P 0.54 (values of the decision variables, although of) 135.65 722.95 P 0.54 (fspring may) 350.19 722.95 P 0.54 (, of course, contain genes) 407.58 722.95 P 1.14 (from either parent. The intermediate and line recombination operators overcome) 135.65 708.95 P 3.39 (this limitation by acting on the decision variables themselves. Like uniform) 135.65 694.95 P -0.23 (crossover) 135.65 680.95 P -0.23 (, the real-valued operators may also be parameterised to provide a control) 181.13 680.95 P 4.94 (over the level of disruption introduced into of) 135.65 666.95 P 4.94 (fspring. For discrete-valued) 388.87 666.95 P -0.07 (representations, variations on the recombination operators may be used that ensure) 135.65 652.95 P (that only valid values are produced as a result of crossover [22].) 135.65 638.95 T 1.04 (The GA T) 135.65 612.95 P 1.04 (oolbox provides a number of crossover routines incorporating most of) 186.18 612.95 P 0.24 (the methods described above. Single-point, double-point and shuf) 135.65 598.95 P 0.24 (\337e crossover are) 452.58 598.95 P 0.73 (implemented in the T) 135.65 584.95 P 0.73 (oolbox functions) 239.92 584.95 P 3 F 1.74 (xovsp) 325.33 584.95 P 2 F 0.73 (,) 361.31 584.95 P 3 F 1.74 (xovdp) 368.03 584.95 P 2 F 0.73 ( and) 404.01 584.95 P 3 F 1.74 (xovsh) 428.77 584.95 P 2 F 0.73 (, respectively) 464.76 584.95 P 0.73 (,) 528.65 584.95 P 0.56 (and can operate on any chromosome representation. Reduced surrogate crossover) 135.65 570.95 P 3.17 (is supported with both single-point,) 135.65 556.95 P 3 F 7.62 (xovsprs) 324.77 556.95 P 2 F 3.17 (, and double-point,) 375.14 556.95 P 3 F 7.62 (xovdprs) 478.28 556.95 P 2 F 3.17 (,) 528.65 556.95 P 2.17 (crossover and with shuf) 135.65 542.95 P 2.17 (\337e crossover) 256.2 542.95 P 2.17 (,) 318.85 542.95 P 3 F 5.22 (xovshrs) 327.02 542.95 P 2 F 2.17 (. A further general multi-point) 377.39 542.95 P 1.09 (crossover routine,) 135.65 528.95 P 3 F 2.61 (xovmp) 226.75 528.95 P 2 F 1.09 (, is also provided. T) 262.73 528.95 P 1.09 (o support real-valued chromosome) 361.51 528.95 P 1.62 (representations, discrete, intermediate and line recombination operators are also) 135.65 514.95 P 1.57 (included. The discrete recombination operator) 135.65 500.95 P 1.57 (,) 362.95 500.95 P 3 F 3.77 (recdis) 370.52 500.95 P 2 F 1.57 (, performs crossover on) 413.69 500.95 P 1.86 (real-valued individuals in a similar manner to the uniform crossover operators.) 135.65 486.95 P 0.37 (Line and intermediate recombination are supported by the functions) 135.65 472.95 P 3 F 0.9 (reclin) 467.78 472.95 P 2 F 0.37 ( and) 510.96 472.95 P 3 F 0.26 (recint) 135.65 458.95 P 2 F 0.11 ( respectively) 178.82 458.95 P 0.11 (. A high-level entry function to all of the crossover operators) 239.1 458.95 P (is provided by the function) 135.65 444.95 T 3 F (recombin) 267.9 444.95 T 2 F (.) 325.47 444.95 T 1 16 Q (Mutation) 135.65 416.29 T 2 12 Q 1.09 (In natural evolution, mutation is a random process where one allele of a gene is) 135.65 388.95 P 2.75 (replaced by another to produce a new genetic structure. In GAs, mutation is) 135.65 374.95 P 0.53 (randomly applied with low probability) 135.65 360.95 P 0.53 (, typically in the range 0.001 and 0.01, and) 322.21 360.95 P 3.36 (modi\336es elements in the chromosomes. Usually considered as a background) 135.65 346.95 P 2.57 (operator) 135.65 332.95 P 2.57 (, the role of mutation is often seen as providing a guarantee that the) 175.13 332.95 P 0.45 (probability of searching any given string will never be zero and acting as a safety) 135.65 318.95 P 3.12 (net to recover good genetic material that may be lost through the action of) 135.65 304.95 P (selection and crossover [1].) 135.65 290.95 T 2.61 (The ef) 135.65 264.95 P 2.61 (fect of mutation on a binary string is illustrated in Fig. 6 for a 10-bit) 169.01 264.95 P 0.05 (chromosome representing a real value decoded over the interval [0, 10] using both) 135.65 250.95 P 1.59 (standard and Gray coding and a mutation point of 3 in the binary string. Here,) 135.65 236.95 P 1.41 (binary mutation \337ips the value of the bit at the loci selected to be the mutation) 135.65 222.95 P -0.23 (point. Given that mutation is generally applied uniformly to an entire population of) 135.65 208.95 P FMENDPAGE %%EndPage: "16" 17 %%Page: "17" 17 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-17) 513.33 61.29 T 2 12 Q 0.82 (strings, it is possible that a given binary string may be mutated at more than one) 135.65 736.95 P (point.) 135.65 722.95 T 2.23 (W) 135.65 580.82 P 2.23 (ith non-binary representations, mutation is achieved by either perturbing the) 146.49 580.82 P 0.87 (gene values or random selection of new values within the allowed range. W) 135.65 566.82 P 0.87 (right) 508.99 566.82 P -0 ([8] and Janikow and Michalewicz [23] demonstrate how real-coded GAs may take) 135.65 552.82 P 0.21 (advantage of higher mutation rates than binary-coded GAs, increasing the level of) 135.65 538.82 P 5.94 (possible exploration of the search space without adversely af) 135.65 524.82 P 5.94 (fecting the) 474.74 524.82 P 1.62 (conver) 135.65 510.82 P 1.62 (gence characteristics. Indeed, T) 168.07 510.82 P 1.62 (ate and Smith [24] ar) 323.63 510.82 P 1.62 (gue that for codings) 431.17 510.82 P -0.22 (more complex than binary) 135.65 496.82 P -0.22 (, high mutation rates can be both desirable and necessary) 260.46 496.82 P 0.57 (and show how) 135.65 482.82 P 0.57 (, for a complex combinatorial optimization problem, high mutation) 205.29 482.82 P 0.62 (rates and non-binary coding yielded signi\336cantly better solutions than the normal) 135.65 468.82 P (approach.) 135.65 454.82 T 2.89 (Many variations on the mutation operator have been proposed. For example,) 135.65 428.82 P 0.6 (biasing the mutation towards individuals with lower \336tness values to increase the) 135.65 414.82 P -0.25 (exploration in the search without losing information from the \336tter individuals [25]) 135.65 400.82 P 2.48 (or parameterising the mutation such that the mutation rate decreases with the) 135.65 386.82 P 0.13 (population conver) 135.65 372.82 P 0.13 (gence [26]. M\237hlenbein [21] has introduced a mutation operator) 222.5 372.82 P 0.5 (for the real-coded GA that uses a non-linear term for the distribution of the range) 135.65 358.82 P 0.38 (of mutation applied to gene values. It is claimed that by biasing mutation towards) 135.65 344.82 P 3.96 (smaller changes in gene values, mutation can be used in conjunction with) 135.65 330.82 P 0.7 (recombination as a foreground search process. Other mutation operations include) 135.65 316.82 P 2.66 (that of) 135.65 302.82 P 0 F 2.66 (trade mutation) 174.94 302.82 P 2 F 2.66 ( [7], whereby the contribution of individual genes in a) 248.57 302.82 P 3.95 (chromosome is used to direct mutation towards weaker terms, and) 135.65 288.82 P 0 F 3.95 (r) 495.89 288.82 P 3.95 (eor) 500.12 288.82 P 3.95 (der) 515.66 288.82 P 0.71 (mutation) 135.65 274.82 P 2 F 0.71 ( [7], that swaps the positions of bits or genes to increase diversity in the) 178.3 274.82 P (decision variable space.) 135.65 260.82 T 1.82 (Binary and integer mutation are provided in the T) 135.65 234.82 P 1.82 (oolbox by the function) 387.85 234.82 P 3 F 4.36 (mut) 507.06 234.82 P 2 F 1.82 (.) 528.65 234.82 P 0.54 (Real-valued mutation is available using the function) 135.65 220.82 P 3 F 1.29 (mutbga) 392.92 220.82 P 2 F 0.54 (. A high-level entry) 436.1 220.82 P (function to the mutation operators is provided by the function) 135.65 206.82 T 3 F (mutate) 434.13 206.82 T 2 F (.) 477.3 206.82 T 63.65 96.95 531.65 744.95 C 133.42 602.82 531.65 718.95 C 5 12 Q 0 X 0 K (Figure 6: Binary Mutation) 266.07 625.61 T 141.21 613.74 523.89 708.01 R 0.5 H 2 Z N 2 F ( Original string -) 170.1 671.56 T ( Mutated string -) 170.1 653.69 T (binary) 413.58 689.43 T (Gray) 466.52 689.43 T 3 F (0 0 0 1 1 0 0 0 1 0) 255.14 671.91 T (0 0 1 1 1 0 0 0 1 0) 255.14 654.04 T 2 F (0.9659) 412.41 671.56 T (2.2146) 412.41 653.69 T (0.6634) 462.02 671.56 T (1.8439) 462.02 653.69 T 281.81 650.83 291.75 681.92 R 8 X N 0 X (mutation point) 172.34 690.39 T 279.39 694.94 285.77 684.78 274.98 690.02 277.19 692.48 4 Y V 248.93 693.96 275.26 694.21 277.19 692.48 3 L N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "17" 18 %%Page: "18" 18 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-18) 513.33 61.29 T 1 16 Q (Reinsertion) 135.65 734.29 T 2 12 Q 2.42 (Once a new population has been produced by selection and recombination of) 135.65 706.95 P 2.66 (individuals from the old population, the \336tness of the individuals in the new) 135.65 692.95 P 7.66 (population may be determined. If fewer individuals are produced by) 135.65 678.95 P 4.52 (recombination than the size of the original population, then the fractional) 135.65 664.95 P 1.26 (dif) 135.65 650.95 P 1.26 (ference between the new and old population sizes is termed a generation gap) 148.76 650.95 P -0.08 ([27]. In the case where the number of new individuals produced at each generation) 135.65 636.95 P 0.43 (is one or two, the GA is said to be steady-state [28] or incremental [29]. If one or) 135.65 622.95 P 0.6 (more of the most \336t individuals is deterministically allowed to propagate through) 135.65 608.95 P (successive generations then the GA is said to use an) 135.65 594.95 T 0 F (elitist strategy) 388.13 594.95 T 2 F (.) 455.66 594.95 T 1.67 (T) 135.65 568.95 P 1.67 (o maintain the size of the original population, the new individuals have to be) 142.14 568.95 P -0.07 (reinserted into the old population. Similarly) 135.65 554.95 P -0.07 (, if not all the new individuals are to be) 344.4 554.95 P 0.46 (used at each generation or if more of) 135.65 540.95 P 0.46 (fspring are generated than the size of the old) 314.82 540.95 P 0.17 (population then a reinsertion scheme must be used to determine which individuals) 135.65 526.95 P 2.22 (are to exist in the new population. An important feature of not creating more) 135.65 512.95 P 5.28 (of) 135.65 498.95 P 5.28 (fspring than the current population size at each generation is that the) 145.42 498.95 P 1.12 (generational computational time is reduced, most dramatically in the case of the) 135.65 484.95 P 2.39 (steady-state GA, and that the memory requirements are smaller as fewer new) 135.65 470.95 P (individuals need to be stored while of) 135.65 456.95 T (fspring are produced.) 315.98 456.95 T 0.19 (When selecting which members of the old population should be replaced the most) 135.65 430.95 P 0.23 (apparent strategy is to replace the least \336t members deterministically) 135.65 416.95 P 0.23 (. However) 466.39 416.95 P 0.23 (, in) 516.09 416.95 P 2.7 (studies, Fogarty [30] has shown that no signi\336cant dif) 135.65 402.95 P 2.7 (ference in conver) 415.24 402.95 P 2.7 (gence) 503.68 402.95 P 2.15 (characteristics was found when the individuals selected for replacement where) 135.65 388.95 P 0.69 (chosen with inverse proportional selection or deterministically as the least \336t. He) 135.65 374.95 P 0.01 (further asserts that replacing the least \336t members ef) 135.65 360.95 P 0.01 (fectively implements an elitist) 386.69 360.95 P 5.91 (strategy as the most \336t will probabilistically survive through successive) 135.65 346.95 P -0.23 (generations. Indeed, the most successful replacement scheme was one that selected) 135.65 332.95 P -0.23 (the oldest members of a population for replacement. This is reported as being more) 135.65 318.95 P 0.03 (in keeping with generational reproduction as every member of the population will,) 135.65 304.95 P 4.87 (at some time, be replaced. Thus, for an individual to survive successive) 135.65 290.95 P 5.74 (generations, it must be suf) 135.65 276.95 P 5.74 (\336ciently \336t to ensure propagation into future) 284.66 276.95 P (generations.) 135.65 262.95 T -0.23 (The GA T) 135.65 236.95 P -0.23 (oolbox provides a function for reinserting individuals into the population) 183.63 236.95 P 1.89 (after recombination,) 135.65 222.95 P 3 F 4.55 (reins) 239.69 222.95 P 2 F 1.89 (. Optional input parameters allow the use of either) 275.67 222.95 P 0.3 (uniform random or \336tness-based reinsertion. Additionally) 135.65 208.95 P 0.3 (, this routine can also be) 413.54 208.95 P (selected to reinsert fewer of) 135.65 194.95 T (fspring than those produced at recombination.) 268.64 194.95 T 1 16 Q (T) 135.65 166.29 T (ermination of the GA) 144.84 166.29 T 2 12 Q 1.32 (Because the GA is a stochastic search method, it is dif) 135.65 138.95 P 1.32 (\336cult to formally specify) 408.77 138.95 P -0.06 (conver) 135.65 124.95 P -0.06 (gence criteria. As the \336tness of a population may remain static for a number) 168.07 124.95 P 5.99 (of generations before a superior individual is found, the application of) 135.65 110.95 P FMENDPAGE %%EndPage: "18" 19 %%Page: "19" 19 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-19) 513.33 61.29 T 2 12 Q 1.07 (conventional termination criteria becomes problematic. A common practice is to) 135.65 736.95 P 2.19 (terminate the GA after a prespeci\336ed number of generations and then test the) 135.65 722.95 P 0.17 (quality of the best members of the population against the problem de\336nition. If no) 135.65 708.95 P -0.22 (acceptable solutions are found, the GA may be restarted or a fresh search initiated.) 135.65 694.95 P FMENDPAGE %%EndPage: "19" 20 %%Page: "20" 20 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-20) 513.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Data Structur) 63.65 732.95 T (es) 170.74 732.95 T 2 12 Q 1.25 (M) 135.65 694.95 P 2 10 Q 1.04 (A) 146.31 694.95 P 1.04 (TLAB) 152.42 694.95 P 2 12 Q 1.25 ( essentially supports only one data type, a rectangular matrix of real or) 178.51 694.95 P 1.93 (complex numeric elements. The main data structures in the Genetic Algorithm) 135.65 680.95 P (toolbox are:) 135.65 666.95 T (\245) 157.25 640.95 T (chromosomes) 171.65 640.95 T (\245) 157.25 620.95 T (phenotypes) 171.65 620.95 T (\245) 157.25 600.95 T (objective function values) 171.65 600.95 T (\245) 157.25 580.95 T (\336tness values) 171.65 580.95 T (These data structures are discussed in the following subsections.) 135.65 560.95 T 1 16 Q (Chr) 135.65 532.29 T (omosomes) 162.9 532.29 T 2 12 Q 1.24 (The chromosome data structure stores an entire population in a single matrix of) 135.65 504.95 P 1.17 (size) 135.65 490.95 P 3 F 2.81 (Nind) 158.47 490.95 P 4 F 1.17 (\264) 191.42 490.95 P 3 F 2.81 (Lind) 202.18 490.95 P 2 F 1.17 (, where) 230.96 490.95 P 3 F 2.81 (Nind) 271.6 490.95 P 2 F 1.17 ( is the number of individuals in the population) 300.39 490.95 P 0.48 (and) 135.65 476.95 P 3 F 1.16 (Lind) 156.45 476.95 P 2 F 0.48 ( is the length of the genotypic representation of those individuals. Each) 185.23 476.95 P -0.26 (row corresponds to an individual\325) 135.65 462.95 P -0.26 (s genotype, consisting of base-) 295.83 462.95 P 0 F -0.26 (n) 442.34 462.95 P 2 F -0.26 (, typically binary) 448.34 462.95 P -0.26 (,) 528.65 462.95 P (values.) 135.65 448.95 T (An example of the chromosome data structure is shown below) 135.65 422.95 T (.) 434.32 422.95 T 1 (This data representation does not force a structure on the chromosome structure,) 135.65 262.48 P 4.56 (only requiring that all chromosomes are of equal length. Thus, structured) 135.65 248.48 P 2.9 (populations or populations with varying genotypic bases may be used in the) 135.65 234.48 P 1.08 (Genetic Algorithm T) 135.65 220.48 P 1.08 (oolbox provided that a suitable decoding function, mapping) 237.58 220.48 P 0.48 (chromosomes onto phenotypes, is employed. The role of the decoding function is) 135.65 206.48 P (described below) 135.65 192.48 T (.) 213.14 192.48 T 1 16 Q (Phenotypes) 135.65 163.81 T 2 12 Q 1.57 (The decision variables, or phenotypes, in the genetic algorithm are obtained by) 135.65 136.48 P 2.06 (applying some mapping from the chromosome representation into the decision) 135.65 122.48 P 0.9 (variable space. Here, each string contained in the chromosome structure decodes) 135.65 108.48 P 154.05 284.48 513.25 404.95 C 3 12 Q 0 X 0 K (C) 155.05 341.98 T (h) 162.95 341.98 T (r) 170.85 341.98 T (o) 178.76 341.98 T (m) 186.66 341.98 T 0 F (g) 224.47 376.28 T 2 9 Q (1) 230.93 372.52 T (1) 239.92 372.52 T 4 F (,) 235.43 372.52 T 0 12 Q (g) 263.48 376.28 T 2 9 Q (1) 269.94 372.52 T (2) 278.93 372.52 T 4 F (,) 274.44 372.52 T 0 12 Q (g) 304.29 376.28 T 2 9 Q (1) 310.75 372.52 T (3) 319.74 372.52 T 4 F (,) 315.25 372.52 T 4 12 Q (\274) 337.57 376.28 T 0 F (g) 362.89 376.28 T 2 9 Q (1) 369.35 372.52 T 3 F (L) 378.34 372.52 T (i) 384.27 372.52 T (n) 390.19 372.52 T (d) 396.11 372.52 T 4 F (,) 373.85 372.52 T 0 12 Q (g) 224.47 358.37 T 2 9 Q (2) 230.93 354.6 T (1) 239.92 354.6 T 4 F (,) 235.43 354.6 T 0 12 Q (g) 263.48 358.37 T 2 9 Q (2) 269.94 354.6 T (2) 278.93 354.6 T 4 F (,) 274.44 354.6 T 0 12 Q (g) 304.29 358.37 T 2 9 Q (2) 310.75 354.6 T (3) 319.74 354.6 T 4 F (,) 315.25 354.6 T 4 12 Q (\274) 337.57 358.37 T 0 F (g) 362.89 358.37 T 2 9 Q (2) 369.35 354.6 T 3 F (L) 378.34 354.6 T (i) 384.27 354.6 T (n) 390.19 354.6 T (d) 396.11 354.6 T 4 F (,) 373.85 354.6 T 0 12 Q (g) 224.47 340.45 T 2 9 Q (3) 230.93 336.69 T (1) 239.92 336.69 T 4 F (,) 235.43 336.69 T 0 12 Q (g) 263.48 340.45 T 2 9 Q (3) 269.94 336.69 T (2) 278.93 336.69 T 4 F (,) 274.44 336.69 T 0 12 Q (g) 304.29 340.45 T 2 9 Q (3) 310.75 336.69 T (3) 319.74 336.69 T 4 F (,) 315.25 336.69 T 4 12 Q (\274) 337.57 340.45 T 0 F (g) 362.89 340.45 T 2 9 Q (3) 369.35 336.69 T 3 F (L) 378.34 336.69 T (i) 384.27 336.69 T (n) 390.19 336.69 T (d) 396.11 336.69 T 4 F (,) 373.85 336.69 T 2 12 Q (.) 232.45 322.56 T (.) 271.46 322.56 T (.) 312.27 322.56 T 4 F (\274) 337.57 322.56 T 2 F (.) 380.2 322.56 T 0 F (g) 216.94 306.36 T 2 9 Q (N) 223.4 302.6 T (i) 230.41 302.6 T (n) 233.44 302.6 T (d) 238.47 302.6 T (1) 247.46 302.6 T 4 F (,) 242.96 302.6 T 0 12 Q (g) 255.95 306.36 T 2 9 Q (N) 262.41 302.6 T (i) 269.43 302.6 T (n) 272.45 302.6 T (d) 277.48 302.6 T (2) 286.47 302.6 T 4 F (,) 281.97 302.6 T 0 12 Q (g) 294.96 306.36 T 3 9 Q (N) 301.42 302.6 T (i) 307.34 302.6 T (n) 313.26 302.6 T (d) 319.19 302.6 T 2 F (3) 329.08 302.6 T 4 F (,) 324.58 302.6 T 4 12 Q (\274) 337.57 306.36 T 0 F (g) 353.56 306.36 T 3 9 Q (N) 360.02 302.74 T (i) 365.94 302.74 T (n) 371.86 302.74 T (d) 377.79 302.74 T (L) 387.67 302.74 T (i) 393.6 302.74 T (n) 399.52 302.74 T (d) 405.44 302.74 T 4 F (,) 383.18 302.74 T 2 12 Q (i) 432.35 376.89 T (n) 435.68 376.89 T (d) 441.68 376.89 T (i) 447.67 376.89 T (v) 451.01 376.89 T (i) 457 376.89 T (d) 460.34 376.89 T (u) 466.33 376.89 T (a) 472.33 376.89 T (l) 477.66 376.89 T (\021) 480.99 376.89 T (1) 483.99 376.89 T (i) 432.35 359.09 T (n) 435.68 359.09 T (d) 441.68 359.09 T (i) 447.67 359.09 T (v) 451.01 359.09 T (i) 457 359.09 T (d) 460.34 359.09 T (u) 466.33 359.09 T (a) 472.33 359.09 T (l) 477.66 359.09 T (\021) 480.99 359.09 T (2) 483.99 359.09 T (i) 432.35 341.29 T (n) 435.68 341.29 T (d) 441.68 341.29 T (i) 447.67 341.29 T (v) 451.01 341.29 T (i) 457 341.29 T (d) 460.34 341.29 T (u) 466.33 341.29 T (a) 472.33 341.29 T (l) 477.66 341.29 T (\021) 480.99 341.29 T (3) 483.99 341.29 T (.) 459.67 323.49 T (i) 419.54 305.69 T (n) 422.87 305.69 T (d) 428.87 305.69 T (i) 434.87 305.69 T (v) 438.2 305.69 T (i) 444.2 305.69 T (d) 447.53 305.69 T (u) 453.53 305.69 T (a) 459.52 305.69 T (l) 464.85 305.69 T (\021) 468.18 305.69 T 3 F (N) 472.89 305.69 T (i) 480.79 305.69 T (n) 488.69 305.69 T (d) 496.6 305.69 T 4 F (=) 199.85 341.98 T 218.44 300.65 214.44 300.65 2 L 0.33 H 0 Z N 214.44 300.65 214.44 388.49 2 L N 214.44 388.49 218.44 388.49 2 L N 408.33 300.65 412.33 300.65 2 L N 412.33 300.65 412.33 388.49 2 L N 412.33 388.49 408.33 388.49 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "20" 21 %%Page: "21" 21 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-21) 513.33 61.29 T 2 12 Q 1.97 (to a row vector of order) 135.65 736.95 P 3 F 4.73 (Nvar) 264.05 736.95 P 2 F 1.97 (, according to the number of dimensions in the) 292.35 736.95 P (search space and corresponding to the decision variable vector value.) 135.65 722.95 T 1.7 (The decision variables are stored in a numerical matrix of size) 135.65 696.95 P 3 F 4.08 (Nind) 455.76 696.95 P 4 F 1.7 (\264) 489.24 696.95 P 3 F 4.08 (Nvar) 500.52 696.95 P 2 F 1.7 (.) 528.65 696.95 P 0.96 (Again, each row corresponds to a particular individual\325) 135.65 682.95 P 0.96 (s phenotype. An example) 406.85 682.95 P -0.11 (of the phenotype data structure is given below) 135.65 668.95 P -0.11 (, where) 355.59 668.95 P 3 F -0.27 (DECODE) 393.66 668.95 P 2 F -0.11 ( is used to represent) 436.83 668.95 P 0.25 (an arbitrary function, possibly from the GA T) 135.65 654.95 P 0.25 (oolbox, mapping the genotypes onto) 355.74 654.95 P (the phenotypes.) 135.65 640.95 T 0.29 (The actual mapping between the chromosome representation and their phenotypic) 135.65 456.66 P 0.39 (values depends upon the) 135.65 442.66 P 3 F 0.94 (DECODE) 257.8 442.66 P 2 F 0.39 ( function used. It is perfectly feasible using this) 300.98 442.66 P 4.22 (representation to have vectors of decision variables of dif) 135.65 428.66 P 4.22 (ferent types. For) 444.28 428.66 P 2.81 (example, it is possible to mix integer) 135.65 414.66 P 2.81 (, real-valued and alphanumeric decision) 328.91 414.66 P (variables in the same) 135.65 400.66 T 3 F (Phen) 239.57 400.66 T 2 F ( data structure.) 268.36 400.66 T 1 16 Q (Objective function values) 135.65 372 T 2 12 Q 0.05 (An objective function is used to evaluate the performance of the phenotypes in the) 135.65 344.66 P 3.4 (problem domain. Objective function values can be scalar or) 135.65 330.66 P 3.4 (, in the case of) 448.45 330.66 P 2.36 (multiobjective problems, vectorial. Note that objective function values are not) 135.65 316.66 P (necessarily the same as the \336tness values.) 135.65 302.66 T 0.47 (Objective function values are stored in a numerical matrix of size) 135.65 276.66 P 3 F 1.12 (Nind) 457.56 276.66 P 4 F 0.47 (\264) 489.81 276.66 P 3 F 1.12 (Nobj) 499.86 276.66 P 2 F 0.47 (,) 528.65 276.66 P 1.65 (where) 135.65 262.66 P 3 F 3.96 (Nobj) 169.6 262.66 P 2 F 1.65 ( is the number of objectives. Each row corresponds to a particular) 198.38 262.66 P 1.86 (individual\325) 135.65 248.66 P 1.86 (s objective vector) 187.63 248.66 P 1.86 (. An example of the objective function values data) 275.29 248.66 P 3.98 (structure is shown below) 135.65 234.66 P 3.98 (, with) 266.4 234.66 P 3 F 9.56 (OBJFUN) 304.68 234.66 P 2 F 3.98 ( representing an arbitrary objective) 347.86 234.66 P (function.) 135.65 220.66 T 144.97 478.66 522.32 622.95 C 3 12 Q 0 X 0 K (P) 146.97 613.96 T (h) 153.87 613.96 T (e) 161.78 613.96 T (n) 169.68 613.96 T (D) 195.46 613.96 T (E) 203.36 613.96 T (C) 211.26 613.96 T (O) 219.16 613.96 T (D) 227.07 613.96 T (E) 234.97 613.96 T (C) 249.97 613.96 T (h) 257.87 613.96 T (r) 265.77 613.96 T (o) 273.68 613.96 T (m) 281.58 613.96 T 4 F (\050) 244.87 613.96 T (\051) 289.38 613.96 T 3 F (%) 309.08 613.96 T (\021) 316.28 613.96 T (M) 323.47 613.96 T (a) 330.67 613.96 T (p) 337.86 613.96 T (\021) 345.06 613.96 T (G) 352.26 613.96 T (e) 359.45 613.96 T (n) 366.65 613.96 T (o) 373.85 613.96 T (t) 381.04 613.96 T (y) 388.24 613.96 T (p) 395.43 613.96 T (e) 402.63 613.96 T (\021) 409.83 613.96 T (t) 417.02 613.96 T (o) 424.22 613.96 T (\021) 431.41 613.96 T (P) 438.61 613.96 T (h) 445.81 613.96 T (e) 453 613.96 T (n) 460.2 613.96 T (o) 467.39 613.96 T (t) 474.59 613.96 T (y) 481.79 613.96 T (p) 488.98 613.96 T (e) 496.18 613.96 T 4 F (=) 182.87 613.96 T 0 F (x) 207.38 568.27 T 2 9 Q (1) 213.17 564.51 T (1) 222.16 564.51 T 4 F (,) 217.67 564.51 T 0 12 Q (x) 249.32 568.27 T 2 9 Q (1) 255.11 564.51 T (2) 264.1 564.51 T 4 F (,) 259.6 564.51 T 0 12 Q (x) 291.26 568.27 T 2 9 Q (1) 297.04 564.51 T (3) 306.03 564.51 T 4 F (,) 301.54 564.51 T 4 12 Q (\274) 323.86 568.27 T 0 F (x) 349.18 568.27 T 2 9 Q (1) 354.97 564.51 T 3 F (N) 363.96 564.51 T (v) 369.88 564.51 T (a) 375.8 564.51 T (r) 381.73 564.51 T 4 F (,) 359.46 564.51 T 0 12 Q (x) 207.38 550.35 T 2 9 Q (2) 213.17 546.59 T (1) 222.16 546.59 T 4 F (,) 217.67 546.59 T 0 12 Q (x) 249.32 550.35 T 2 9 Q (2) 255.11 546.59 T (2) 264.1 546.59 T 4 F (,) 259.6 546.59 T 0 12 Q (x) 291.26 550.35 T 2 9 Q (2) 297.04 546.59 T (3) 306.03 546.59 T 4 F (,) 301.54 546.59 T 4 12 Q (\274) 323.86 550.35 T 0 F (x) 349.18 550.35 T 2 9 Q (2) 354.97 546.59 T 3 F (N) 363.96 546.59 T (v) 369.88 546.59 T (a) 375.8 546.59 T (r) 381.73 546.59 T 4 F (,) 359.46 546.59 T 0 12 Q (x) 207.38 532.44 T 2 9 Q (3) 213.17 528.68 T (1) 222.16 528.68 T 4 F (,) 217.67 528.68 T 0 12 Q (x) 249.32 532.44 T 2 9 Q (3) 255.11 528.68 T (2) 264.1 528.68 T 4 F (,) 259.6 528.68 T 0 12 Q (x) 291.26 532.44 T 2 9 Q (3) 297.04 528.68 T (3) 306.03 528.68 T 4 F (,) 301.54 528.68 T 4 12 Q (\274) 323.86 532.44 T 0 F (x) 349.18 532.44 T 2 9 Q (3) 354.97 528.68 T 3 F (N) 363.96 528.68 T (v) 369.88 528.68 T (a) 375.8 528.68 T (r) 381.73 528.68 T 4 F (,) 359.46 528.68 T 2 12 Q (.) 215.02 514.55 T (.) 256.96 514.55 T (.) 298.89 514.55 T 4 F (\274) 323.86 514.55 T 2 F (.) 366.15 514.55 T 0 F (x) 198.05 498.35 T 3 9 Q (N) 203.84 494.59 T (i) 209.76 494.59 T (n) 215.68 494.59 T (d) 221.6 494.59 T 2 F (1) 231.49 494.59 T 4 F (,) 227 494.59 T 0 12 Q (x) 239.99 498.35 T 3 9 Q (N) 245.77 494.59 T (i) 251.7 494.59 T (n) 257.62 494.59 T (d) 263.54 494.59 T 2 F (2) 273.43 494.59 T 4 F (,) 268.93 494.59 T 0 12 Q (x) 281.92 498.35 T 3 9 Q (N) 287.71 494.59 T (i) 293.63 494.59 T (n) 299.55 494.59 T (d) 305.48 494.59 T 2 F (3) 315.36 494.59 T 4 F (,) 310.87 494.59 T 4 12 Q (\274) 323.86 498.35 T 0 F (x) 339.85 498.35 T 3 9 Q (N) 345.64 494.73 T (i) 351.56 494.73 T (n) 357.48 494.73 T (d) 363.4 494.73 T (N) 373.29 494.73 T (v) 379.21 494.73 T (a) 385.14 494.73 T (r) 391.06 494.73 T 4 F (,) 368.8 494.73 T 2 12 Q (i) 417.96 568.88 T (n) 421.3 568.88 T (d) 427.29 568.88 T (i) 433.29 568.88 T (v) 436.62 568.88 T (i) 442.62 568.88 T (d) 445.96 568.88 T (u) 451.95 568.88 T (a) 457.95 568.88 T (l) 463.27 568.88 T (\021) 466.61 568.88 T (1) 469.61 568.88 T (i) 417.96 551.08 T (n) 421.3 551.08 T (d) 427.29 551.08 T (i) 433.29 551.08 T (v) 436.62 551.08 T (i) 442.62 551.08 T (d) 445.96 551.08 T (u) 451.95 551.08 T (a) 457.95 551.08 T (l) 463.27 551.08 T (\021) 466.61 551.08 T (2) 469.61 551.08 T (i) 417.96 533.28 T (n) 421.3 533.28 T (d) 427.29 533.28 T (i) 433.29 533.28 T (v) 436.62 533.28 T (i) 442.62 533.28 T (d) 445.96 533.28 T (u) 451.95 533.28 T (a) 457.95 533.28 T (l) 463.27 533.28 T (\021) 466.61 533.28 T (3) 469.61 533.28 T (.) 445.28 515.48 T (i) 405.16 497.68 T (n) 408.49 497.68 T (d) 414.49 497.68 T (i) 420.48 497.68 T (v) 423.82 497.68 T (i) 429.82 497.68 T (d) 433.15 497.68 T (u) 439.15 497.68 T (a) 445.14 497.68 T (l) 450.47 497.68 T (\021) 453.8 497.68 T 3 F (N) 458.51 497.68 T (i) 466.41 497.68 T (n) 474.31 497.68 T (d) 482.21 497.68 T 4 F (=) 180.97 533.96 T 199.55 492.64 195.55 492.64 2 L 0.33 H 0 Z N 195.55 492.64 195.55 580.48 2 L N 195.55 580.48 199.55 580.48 2 L N 393.95 492.64 397.95 492.64 2 L N 397.95 492.64 397.95 580.48 2 L N 397.95 580.48 393.95 580.48 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "21" 22 %%Page: "22" 22 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-22) 513.33 61.29 T 1 16 Q (Fitness values) 135.65 577.51 T 2 12 Q 2.12 (Fitness values are derived from objective function values through a scaling or) 135.65 550.18 P 2.59 (ranking function. Fitnesses are non-negative scalars and are stored in column) 135.65 536.18 P 0.07 (vectors of length) 135.65 522.18 P 3 F 0.17 (Nind) 219.46 522.18 P 2 F 0.07 (, an example of which is shown below) 248.25 522.18 P 0.07 (. Again, FITNESS is) 431.82 522.18 P (an arbitrary \336tness function.) 135.65 508.18 T 1.6 (Note that for multiobjective functions, the \336tness of a particular individual is a) 135.65 335.63 P 2.33 (function of a vector of objective function values. Multiobjective problems are) 135.65 321.62 P 2.49 (characterised by having no single unique solution, but a family of equally \336t) 135.65 307.62 P 2.42 (solutions with dif) 135.65 293.62 P 2.42 (ferent values of decision variables. Care should therefore be) 224.23 293.62 P 0.26 (taken to adopt some mechanism to ensure that the population is able to evolve the) 135.65 279.62 P 1.35 (set of Pareto optimal solutions, for example by using \336tness sharing [31] in the) 135.65 265.62 P -0.04 (selection method. Although not supported in this version of the Genetic Algorithm) 135.65 251.62 P 1.73 (T) 135.65 237.62 P 1.73 (oolbox, it is planned that multiobjective search will be implemented in future) 142.14 237.62 P (versions.) 135.65 223.62 T 152.42 602.18 514.87 744.95 C 3 12 Q 0 X 0 K (O) 162.01 735.96 T (b) 169.91 735.96 T (j) 177.82 735.96 T (V) 185.72 735.96 T (O) 211.5 735.96 T (B) 219.4 735.96 T (J) 227.3 735.96 T (F) 235.2 735.96 T (U) 243.1 735.96 T (N) 251.01 735.96 T (P) 266.01 735.96 T (h) 273.91 735.96 T (e) 281.81 735.96 T (n) 289.72 735.96 T 4 F (\050) 260.91 735.96 T (\051) 297.52 735.96 T 3 F (%) 317.22 735.96 T (\021) 324.42 735.96 T (O) 331.61 735.96 T (b) 338.81 735.96 T (j) 346 735.96 T (e) 353.2 735.96 T (c) 360.39 735.96 T (t) 367.59 735.96 T (i) 374.79 735.96 T (v) 381.98 735.96 T (e) 389.18 735.96 T (\021) 396.38 735.96 T (F) 403.57 735.96 T (u) 410.77 735.96 T (n) 417.96 735.96 T (c) 425.16 735.96 T (t) 432.36 735.96 T (i) 439.55 735.96 T (o) 446.75 735.96 T (n) 453.94 735.96 T 4 F (=) 198.91 735.96 T 0 F (y) 223.43 690.27 T 2 9 Q (1) 229.21 686.51 T (1) 238.2 686.51 T 4 F (,) 233.71 686.51 T 0 12 Q (y) 265.36 690.27 T 2 9 Q (1) 271.15 686.51 T (2) 280.14 686.51 T 4 F (,) 275.64 686.51 T 0 12 Q (y) 307.3 690.27 T 2 9 Q (1) 313.08 686.51 T (3) 322.07 686.51 T 4 F (,) 317.58 686.51 T 4 12 Q (\274) 339.9 690.27 T 0 F (y) 365.22 690.27 T 2 9 Q (1) 371.01 686.51 T 3 F (N) 380 686.51 T (v) 385.92 686.51 T (a) 391.85 686.51 T (r) 397.77 686.51 T 4 F (,) 375.5 686.51 T 0 12 Q (y) 223.43 672.36 T 2 9 Q (2) 229.21 668.59 T (1) 238.2 668.59 T 4 F (,) 233.71 668.59 T 0 12 Q (y) 265.36 672.36 T 2 9 Q (2) 271.15 668.59 T (2) 280.14 668.59 T 4 F (,) 275.64 668.59 T 0 12 Q (y) 307.3 672.36 T 2 9 Q (2) 313.08 668.59 T (3) 322.07 668.59 T 4 F (,) 317.58 668.59 T 4 12 Q (\274) 339.9 672.36 T 0 F (y) 365.22 672.36 T 2 9 Q (2) 371.01 668.59 T 3 F (N) 380 668.59 T (v) 385.92 668.59 T (a) 391.85 668.59 T (r) 397.77 668.59 T 4 F (,) 375.5 668.59 T 0 12 Q (y) 223.43 654.44 T 2 9 Q (3) 229.21 650.68 T (1) 238.2 650.68 T 4 F (,) 233.71 650.68 T 0 12 Q (y) 265.36 654.44 T 2 9 Q (3) 271.15 650.68 T (2) 280.14 650.68 T 4 F (,) 275.64 650.68 T 0 12 Q (y) 307.3 654.44 T 2 9 Q (3) 313.08 650.68 T (3) 322.07 650.68 T 4 F (,) 317.58 650.68 T 4 12 Q (\274) 339.9 654.44 T 0 F (y) 365.22 654.44 T 2 9 Q (3) 371.01 650.68 T 3 F (N) 380 650.68 T (v) 385.92 650.68 T (a) 391.85 650.68 T (r) 397.77 650.68 T 4 F (,) 375.5 650.68 T 2 12 Q (.) 231.06 636.55 T (.) 273 636.55 T (.) 314.93 636.55 T 4 F (\274) 339.9 636.55 T 2 F (.) 382.19 636.55 T 0 F (y) 214.09 620.35 T 3 9 Q (N) 219.88 616.59 T (i) 225.8 616.59 T (n) 231.72 616.59 T (d) 237.65 616.59 T 2 F (1) 247.53 616.59 T 4 F (,) 243.04 616.59 T 0 12 Q (y) 256.03 620.35 T 3 9 Q (N) 261.82 616.59 T (i) 267.74 616.59 T (n) 273.66 616.59 T (d) 279.58 616.59 T 2 F (2) 289.47 616.59 T 4 F (,) 284.97 616.59 T 0 12 Q (y) 297.96 620.35 T 3 9 Q (N) 303.75 616.59 T (i) 309.67 616.59 T (n) 315.59 616.59 T (d) 321.52 616.59 T 2 F (3) 331.4 616.59 T 4 F (,) 326.91 616.59 T 4 12 Q (\274) 339.9 620.35 T 0 F (y) 355.89 620.35 T 3 9 Q (N) 361.68 616.73 T (i) 367.6 616.73 T (n) 373.52 616.73 T (d) 379.44 616.73 T (N) 389.33 616.73 T (v) 395.26 616.73 T (a) 401.18 616.73 T (r) 407.1 616.73 T 4 F (,) 384.84 616.73 T 2 12 Q (i) 434 690.88 T (n) 437.34 690.88 T (d) 443.33 690.88 T (i) 449.33 690.88 T (v) 452.66 690.88 T (i) 458.66 690.88 T (d) 461.99 690.88 T (u) 467.99 690.88 T (a) 473.99 690.88 T (l) 479.31 690.88 T (\021) 482.65 690.88 T (1) 485.65 690.88 T (i) 434 673.08 T (n) 437.34 673.08 T (d) 443.33 673.08 T (i) 449.33 673.08 T (v) 452.66 673.08 T (i) 458.66 673.08 T (d) 461.99 673.08 T (u) 467.99 673.08 T (a) 473.99 673.08 T (l) 479.31 673.08 T (\021) 482.65 673.08 T (2) 485.65 673.08 T (i) 434 655.28 T (n) 437.34 655.28 T (d) 443.33 655.28 T (i) 449.33 655.28 T (v) 452.66 655.28 T (i) 458.66 655.28 T (d) 461.99 655.28 T (u) 467.99 655.28 T (a) 473.99 655.28 T (l) 479.31 655.28 T (\021) 482.65 655.28 T (3) 485.65 655.28 T (.) 461.32 637.48 T (i) 421.2 619.68 T (n) 424.53 619.68 T (d) 430.53 619.68 T (i) 436.52 619.68 T (v) 439.86 619.68 T (i) 445.86 619.68 T (d) 449.19 619.68 T (u) 455.19 619.68 T (a) 461.18 619.68 T (l) 466.51 619.68 T (\021) 469.84 619.68 T 3 F (N) 474.55 619.68 T (i) 482.45 619.68 T (n) 490.35 619.68 T (d) 498.25 619.68 T 4 F (=) 197.01 655.96 T 215.59 614.64 211.59 614.64 2 L 0.33 H 0 Z N 211.59 614.64 211.59 702.48 2 L N 211.59 702.48 215.59 702.48 2 L N 409.99 614.64 413.99 614.64 2 L N 413.99 614.64 413.99 702.48 2 L N 413.99 702.48 409.99 702.48 2 L N -8.35 24.95 603.65 816.95 C 182.59 357.63 484.7 488.74 C 3 12 Q 0 X 0 K (F) 195.87 479.75 T (i) 203.77 479.75 T (t) 211.68 479.75 T (n) 219.58 479.75 T (F) 245.36 479.75 T (I) 253.26 479.75 T (T) 261.16 479.75 T (N) 269.07 479.75 T (E) 276.97 479.75 T (S) 284.87 479.75 T (S) 292.77 479.75 T (O) 307.77 479.75 T (b) 315.68 479.75 T (j) 323.58 479.75 T (V) 331.48 479.75 T 4 F (\050) 302.67 479.75 T (\051) 339.28 479.75 T 3 F (\021) 345.98 479.75 T (%) 353.18 479.75 T (\021) 360.37 479.75 T (F) 367.57 479.75 T (i) 374.77 479.75 T (t) 381.96 479.75 T (n) 389.16 479.75 T (e) 396.36 479.75 T (s) 403.55 479.75 T (s) 410.75 479.75 T (\021) 417.94 479.75 T (F) 425.14 479.75 T (u) 432.33 479.75 T (n) 439.53 479.75 T (c) 446.73 479.75 T (t) 453.92 479.75 T (i) 461.12 479.75 T (o) 468.32 479.75 T (n) 475.51 479.75 T 4 F (=) 232.77 479.75 T 0 F (f) 259.74 442.24 T 2 9 Q (1) 263.54 438.48 T 0 12 Q (f) 259.74 424.33 T 2 9 Q (2) 263.54 420.56 T 0 12 Q (f) 259.74 406.41 T 2 9 Q (3) 263.54 402.65 T 2 12 Q (.) 261.89 388.52 T 0 F (f) 250.41 373.71 T 3 9 Q (N) 254.2 370.09 T (i) 260.13 370.09 T (n) 266.05 370.09 T (d) 271.97 370.09 T 2 12 Q (i) 298.32 442.15 T (n) 301.65 442.15 T (d) 307.64 442.15 T (i) 313.64 442.15 T (v) 316.98 442.15 T (i) 322.97 442.15 T (d) 326.31 442.15 T (u) 332.3 442.15 T (a) 338.3 442.15 T (l) 343.63 442.15 T (\021) 346.96 442.15 T (1) 349.96 442.15 T (i) 298.32 424.35 T (n) 301.65 424.35 T (d) 307.64 424.35 T (i) 313.64 424.35 T (v) 316.98 424.35 T (i) 322.97 424.35 T (d) 326.31 424.35 T (u) 332.3 424.35 T (a) 338.3 424.35 T (l) 343.63 424.35 T (\021) 346.96 424.35 T (2) 349.96 424.35 T (i) 298.32 406.55 T (n) 301.65 406.55 T (d) 307.64 406.55 T (i) 313.64 406.55 T (v) 316.98 406.55 T (i) 322.97 406.55 T (d) 326.31 406.55 T (u) 332.3 406.55 T (a) 338.3 406.55 T (l) 343.63 406.55 T (\021) 346.96 406.55 T (3) 349.96 406.55 T (.) 328.11 388.75 T (i) 286.07 373.97 T (n) 289.4 373.97 T (d) 295.4 373.97 T (i) 301.39 373.97 T (v) 304.73 373.97 T (i) 310.73 373.97 T (d) 314.06 373.97 T (u) 320.06 373.97 T (a) 326.05 373.97 T (l) 331.38 373.97 T (\021) 334.71 373.97 T 3 F (N) 339.42 373.97 T (i) 346.61 373.97 T (n) 353.81 373.97 T (d) 361.01 373.97 T 4 F (=) 233.32 408.75 T 251.91 368.23 247.91 368.23 2 L 0.33 H 0 Z N 247.91 368.23 247.91 454.45 2 L N 247.91 454.45 251.91 454.45 2 L N 274.86 368.23 278.86 368.23 2 L N 278.86 368.23 278.86 454.45 2 L N 278.86 454.45 274.86 454.45 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "22" 23 %%Page: "23" 23 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-23) 513.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Support for Multiple Populations) 63.65 732.95 T 2 12 Q 0.49 (The GA T) 135.65 694.95 P 0.49 (oolbox provides support for multiple subpopulations through the use of) 185.09 694.95 P 2.44 (high-level genetic operator functions and a routine for exchanging individuals) 135.65 680.95 P 0.12 (between subpopulations. In the literature, the use of multiple populations has been) 135.65 666.95 P 1.48 (shown, in most cases, to improve the quality of the results obtained using GAs) 135.65 652.95 P (compared to the single population GA \050see, for example, [32] and [33]\051.) 135.65 638.95 T 0.36 (The GA T) 135.65 612.95 P 0.36 (oolbox supports the use of a single population divided into a number of) 184.83 612.95 P 3.75 (subpopulations or) 135.65 598.95 P 0 F 3.75 (demes) 231.76 598.95 P 2 F 3.75 ( by modifying the use of data structures such that) 261.74 598.95 P 4.05 (subpopulations are stored in contiguous blocks within a single matrix. For) 135.65 584.95 P 5.76 (example, the chromosome data structure,) 135.65 570.95 P 3 F 13.81 (Chrom) 364.61 570.95 P 2 F 5.76 (, composed of) 400.59 570.95 P 3 F 13.81 (SUBPOP) 488.47 570.95 P 2 F (subpopulations each of length) 135.65 556.95 T 3 F (N) 282.22 556.95 T 2 F ( individuals is stored as:) 289.42 556.95 T 2.16 (This is known as the) 135.65 242.2 P 0 F 2.16 (Migration) 248.04 242.2 P 2 F 2.16 (, or) 296.69 242.2 P 0 F 2.16 (Island) 319.99 242.2 P 2 F 2.16 (, model [34]. Each subpopulation is) 349.97 242.2 P 1.3 (evolved over generations by a traditional GA and from time to time individuals) 135.65 228.2 P 5.19 (migrate from one subpopulation to another) 135.65 214.2 P 5.19 (. The amount of migration of) 366.46 214.2 P 3.82 (individuals and the pattern of that migration determines how much genetic) 135.65 200.2 P (diversity can occur) 135.65 186.2 T (.) 226.25 186.2 T 2.83 (T) 135.65 160.2 P 2.83 (o allow the T) 142.14 160.2 P 2.83 (oolbox routines to operate independently on subpopulations, a) 213.4 160.2 P -0.29 (number of high-level entry functions are provided that accept an optional ar) 135.65 146.2 P -0.29 (gument) 495.67 146.2 P 1.24 (that determines the number of subpopulations contained in a data structure. The) 135.65 132.2 P 0.5 (low-level routines are then called independently) 135.65 118.2 P 0.5 (, in turn, with each subpopulation) 368.22 118.2 P 238.13 264.2 429.16 548.95 C 3 12 Q 0 X 0 K (C) 239.13 402.93 T (h) 246.33 402.93 T (r) 253.52 402.93 T (o) 260.72 402.93 T (m) 267.92 402.93 T (I) 317.18 515.29 T (n) 324.38 515.29 T (d) 331.58 515.29 T (1) 340.23 509.8 T (S) 349.14 515.29 T (u) 356.33 515.29 T (b) 363.53 515.29 T (P) 370.73 515.29 T (o) 377.92 515.29 T (p) 385.12 515.29 T (1) 393.77 509.8 T (I) 317.68 495.33 T (n) 324.88 495.33 T (d) 332.08 495.33 T (2) 340.73 489.85 T (S) 348.64 495.33 T (u) 355.83 495.33 T (b) 363.03 495.33 T (P) 370.23 495.33 T (o) 377.42 495.33 T (p) 384.62 495.33 T (1) 393.27 489.85 T 4 F (\274) 353.58 475.38 T 3 F (I) 317.18 459.4 T (n) 324.38 459.4 T (d) 331.58 459.4 T (N) 340.23 453.92 T (S) 349.14 459.4 T (u) 356.33 459.4 T (b) 363.53 459.4 T (P) 370.73 459.4 T (o) 377.92 459.4 T (p) 385.12 459.4 T (1) 393.77 453.92 T (I) 317.68 439.45 T (n) 324.88 439.45 T (d) 332.08 439.45 T (1) 340.73 433.96 T (S) 349.64 439.45 T (u) 356.83 439.45 T (b) 364.03 439.45 T (P) 371.23 439.45 T (o) 378.42 439.45 T (p) 385.62 439.45 T (2) 394.27 433.96 T (I) 317.68 419.49 T (n) 324.88 419.49 T (d) 332.08 419.49 T (2) 340.73 414.01 T (S) 348.64 419.49 T (u) 355.83 419.49 T (b) 363.03 419.49 T (P) 370.23 419.49 T (o) 377.42 419.49 T (p) 384.62 419.49 T (2) 393.27 414.01 T 4 F (\274) 353.58 399.54 T 3 F (I) 317.18 383.56 T (n) 324.38 383.56 T (d) 331.58 383.56 T (N) 340.23 378.07 T (S) 349.14 383.56 T (u) 356.33 383.56 T (b) 363.53 383.56 T (P) 370.73 383.56 T (o) 377.92 383.56 T (p) 385.12 383.56 T (2) 393.77 378.07 T 4 F (\274) 353.58 363.6 T 3 F (I) 299.2 347.62 T (n) 306.39 347.62 T (d) 313.59 347.62 T (1) 322.24 342.14 T (S) 331.15 347.62 T (u) 338.34 347.62 T (b) 345.54 347.62 T (P) 352.73 347.62 T (o) 359.93 347.62 T (p) 367.13 347.62 T (S) 375.79 342.14 T (U) 382.98 342.14 T (B) 390.18 342.14 T (P) 397.37 342.14 T (O) 404.57 342.14 T (P) 411.77 342.14 T (I) 299.7 327.67 T (n) 306.89 327.67 T (d) 314.09 327.67 T (2) 322.74 322.18 T (S) 330.65 327.67 T (u) 337.84 327.67 T (b) 345.04 327.67 T (P) 352.23 327.67 T (o) 359.43 327.67 T (p) 366.63 327.67 T (S) 375.29 322.18 T (U) 382.48 322.18 T (B) 389.68 322.18 T (P) 396.87 322.18 T (O) 404.07 322.18 T (P) 411.27 322.18 T 4 F (\274) 353.58 307.72 T 3 F (I) 299.2 291.73 T (n) 306.39 291.73 T (d) 313.59 291.73 T (N) 322.24 286.25 T (S) 331.15 291.73 T (u) 338.34 291.73 T (b) 345.54 291.73 T (P) 352.73 291.73 T (o) 359.93 291.73 T (p) 367.13 291.73 T (S) 375.79 286.25 T (U) 382.98 286.25 T (B) 390.18 286.25 T (P) 397.37 286.25 T (O) 404.57 286.25 T (P) 411.77 286.25 T 2 F (.) 424.17 402.93 T 4 F (=) 282.11 402.93 T 300.7 283.77 296.7 283.77 2 L 0.33 H 0 Z N 296.7 283.77 296.7 527.27 2 L N 296.7 527.27 300.7 527.27 2 L N 417.46 283.77 421.46 283.77 2 L N 421.46 283.77 421.46 527.27 2 L N 421.46 527.27 417.46 527.27 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "23" 24 %%Page: "24" 24 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-24) 513.33 61.29 T 2 12 Q 0.1 (to perform functions such as selection, crossover and reinsertion. These high-level) 135.65 736.95 P (functions are listed in the T) 135.65 722.95 T (able below) 266.39 722.95 T (.) 317.9 722.95 T 1 F (Note:) 135.65 570.95 T 2 F ( As currently implemented, all subpopulations must be of equal size.) 163.62 570.95 T 0.04 (The transfer of individuals between subpopulations is implemented in the T) 135.65 544.95 P 0.04 (oolbox) 498.33 544.95 P 0.57 (function) 135.65 530.95 P 3 F 1.37 (migrate) 179.19 530.95 P 2 F 0.57 (. A single scalar is used to determine the amount of migration) 229.56 530.95 P 3.62 (of individuals from one subpopulation to another) 135.65 516.95 P 3.62 (. Thus, given a population) 391.9 516.95 P 1.6 (comprised of a number of subpopulations, the same number of individuals will) 135.65 502.95 P 1.86 (always be transferred from a subpopulation as the number it will receive from) 135.65 488.95 P 0.15 (another subpopulation. A second parameter to the function) 135.65 474.95 P 3 F 0.37 (migrate) 421.67 474.95 P 2 F 0.15 ( controls the) 472.05 474.95 P 3.59 (manner in which individuals are selected for migration, either uniformly or) 135.65 460.95 P 4.25 (according to \336tness. Uniform selection picks individuals for migration and) 135.65 446.95 P 2.52 (replaces individuals in a subpopulation with immigrants in a random manner) 135.65 432.95 P 2.52 (.) 528.65 432.95 P 2.4 (Fitness-based migration selects individuals according to their \336tness level, the) 135.65 418.95 P 0.08 (most \336t individuals being the ones selected for migration, and replaces individuals) 135.65 404.95 P (in a subpopulation uniformly at random.) 135.65 390.95 T 1.09 (A further parameter speci\336es the population topology over which migration will) 135.65 364.95 P -0.26 (take place. Fig. 7 shows the most basic migration paths implemented in) 135.65 350.95 P 3 F -0.63 (migrate) 478.28 350.95 P 2 F -0.26 (,) 528.65 350.95 P 0.71 (the ring topology) 135.65 336.95 P 0.71 (. Here individuals are transferred between directionally adjacent) 218.92 336.95 P 1.69 (subpopulations. For example, individuals from subpopulation 6 migrate only to) 135.65 322.95 P 6.65 (subpopulation 1 and individuals from subpopulation 1 only migrate to) 135.65 308.95 P (subpopulation 2.) 135.65 294.95 T (SUBPOPULA) 222.4 690.95 T (TION SUPPOR) 291.04 690.95 T (T FUNCTIONS) 367.28 690.95 T 3 F (mutate) 141.65 666.95 T 2 F (mutation operators) 249.65 666.95 T 3 F (recombin) 141.65 644.95 T 2 F (crossover and recombination operators) 249.65 644.95 T 3 F (reins) 141.65 622.95 T 2 F (uniform random and \336tness-based reinsertion) 249.65 622.95 T 3 F (select) 141.65 600.95 T 2 F (independent subpopulation selection) 249.65 600.95 T 135.65 706.7 135.65 593.2 2 L V 0.5 H 0 Z N 243.65 679.45 243.65 592.7 2 L V N 531.65 706.7 531.65 593.2 2 L V N 135.4 706.95 531.9 706.95 2 L V N 135.9 682.2 531.4 682.2 2 L V N 135.9 679.7 531.4 679.7 2 L V N 135.4 592.95 531.9 592.95 2 L V N 63.65 96.95 531.65 744.95 C 133.38 126.4 531.65 290.95 C 314.34 259.94 354.02 279.78 9.92 RR 7 X 0 K V 0.5 H 2 Z 0 X N 2 9 Q (SubPop 1) 316.82 266.16 T 373.86 190.49 413.55 210.33 9.92 RR 7 X V 0 X N (SubPop 3) 376.35 196.71 T 254.81 190.49 294.49 210.33 9.92 RR 7 X V 0 X N (SubPop 5) 257.3 196.71 T 254.81 230.17 294.49 250.02 9.92 RR 7 X V 0 X N (SubPop 6) 257.3 236.4 T 373.86 230.17 413.55 250.02 9.92 RR 7 X V 0 X N (SubPop 2) 376.35 236.4 T 314.34 160.72 354.02 180.57 9.92 RR 7 X V 0 X N (SubPop 4) 316.82 166.95 T 308.7 272.85 314.34 269.86 308.93 266.48 308.81 269.67 4 Y V 98 180 39.68 19.84 314.34 250.02 A 395.27 255.94 393.69 250.02 389.35 254.35 392.31 255.15 4 Y V 15 90 39.68 19.84 354.02 250.02 A 273.07 184.57 274.65 190.49 278.99 186.17 276.03 185.37 4 Y V 195 270 39.68 19.84 314.34 190.49 A 359.65 167.65 354.02 170.65 359.43 174.03 359.54 170.84 4 Y V 278 360 39.68 19.84 354.02 190.49 A 396.7 215.53 393.7 210.33 390.7 215.53 393.7 215.53 4 Y V 393.7 230.17 393.7 215.53 2 L N 271.65 224.98 274.65 230.17 277.65 224.98 274.65 224.98 4 Y V 274.65 210.33 274.65 224.98 2 L N 5 12 Q (Figure 7: Ring Migration T) 246.77 143.55 T (opology) 382.95 143.55 T 142.84 130.96 525.52 287.44 R N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "24" 25 %%Page: "25" 25 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-25) 513.33 61.29 T 2 12 Q 1.18 (A similar strategy to the ring topology is the neighbourhood migration of Fig.8.) 135.65 736.95 P 3.3 (Like the ring topology) 135.65 722.95 P 3.3 (, migration is made only between nearest neighbours,) 252.38 722.95 P 2.19 (however) 135.65 708.95 P 2.19 (, migration may occur in either direction between subpopulations. For) 176.46 708.95 P 2.73 (each subpopulation, the possible immigrants are determined, according to the) 135.65 694.95 P 0.13 (desired selection method, from adjacent subpopulations and a \336nal selection made) 135.65 680.95 P 0.07 (from this pool of individuals. This ensures that individuals will not migrate from a) 135.65 666.95 P (subpopulation to the same subpopulation.) 135.65 652.95 T -0.1 (The most general migration strategy supported by) 135.65 458.75 P 3 F -0.25 (migrate) 377.1 458.75 P 2 F -0.1 ( is that of unrestricted) 427.47 458.75 P 3.36 (migration, Fig. 9. Here, individuals may migrate from any subpopulation to) 135.65 444.75 P 2.16 (another) 135.65 430.75 P 2.16 (. For each subpopulation, a pool of potential immigrants is constructed) 170.96 430.75 P 3.58 (from the other subpopulations. The individual migrants are then determined) 135.65 416.75 P (according to the appropriate selection strategy) 135.65 402.75 T (.) 356.36 402.75 T 0.63 (An example of a GA with multiple subpopulations is considered in the) 135.65 215.11 P 0 F 0.63 (Examples) 485.02 215.11 P 2 F (Section.) 135.65 201.11 T 63.65 96.95 531.65 744.95 C 133.38 470.75 531.65 648.95 C 312.67 609.34 352.35 629.18 9.92 RR 7 X 0 K V 0.5 H 0 Z 0 X N 2 9 Q (SubPop 1) 315.16 615.56 T 372.2 539.9 411.88 559.74 9.92 RR 7 X V 0 X N (SubPop 3) 374.68 546.12 T 253.14 539.9 292.83 559.74 9.92 RR 7 X V 0 X N (SubPop 5) 255.63 546.12 T 253.14 579.58 292.83 599.42 9.92 RR 7 X V 0 X N (SubPop 6) 255.63 585.8 T 372.2 579.58 411.88 599.42 9.92 RR 7 X V 0 X N (SubPop 2) 374.68 585.8 T 312.67 510.13 352.35 529.97 9.92 RR 7 X V 0 X N (SubPop 4) 315.16 516.35 T 277.32 603.75 272.98 599.42 271.4 605.35 274.36 604.55 4 Y V 307.04 622.26 312.67 619.26 307.26 615.88 307.15 619.07 4 Y V 98 165 39.68 19.84 312.67 599.42 A 357.77 615.88 352.36 619.26 357.99 622.26 357.88 619.07 4 Y V 393.6 605.35 392.03 599.42 387.68 603.75 390.64 604.55 4 Y V 15 82 39.68 19.84 352.35 599.42 A 307.26 523.43 312.67 520.05 307.04 517.06 307.15 520.25 4 Y V 271.4 533.98 272.98 539.9 277.32 535.57 274.36 534.77 4 Y V 195 262 39.68 19.84 312.67 539.9 A 387.68 535.57 392.03 539.9 393.6 533.98 390.64 534.77 4 Y V 357.99 517.06 352.36 520.05 357.77 523.43 357.88 520.25 4 Y V 278 345 39.68 19.84 352.35 539.9 A 389.04 574.38 392.04 579.58 395.04 574.38 392.04 574.38 4 Y V 395.04 564.93 392.04 559.74 389.04 564.93 392.04 564.93 4 Y V 392.04 574.38 392.04 564.93 2 L N 275.99 564.93 272.99 559.74 269.99 564.93 272.99 564.93 4 Y V 269.99 574.38 272.99 579.58 275.99 574.38 272.99 574.38 4 Y V 272.99 564.93 272.99 574.38 2 L N 5 12 Q (Figure 8: Neighbourhood Migration T) 218.12 492.95 T (opology) 408.27 492.95 T 141.18 481.15 523.85 638.55 R 2 Z N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C 63.65 96.95 531.65 744.95 C 133.38 227.11 531.65 398.75 C 311.25 362.42 353.77 382.26 9.92 RR 7 X 0 K V 0.5 H 0 Z 0 X N 2 9 Q (SubPop 1) 315.16 369.28 T 382.12 291.56 424.64 311.4 9.92 RR 7 X V 0 X N (SubPop 3) 386.02 298.41 T 311.25 263.21 353.77 283.05 9.92 RR 7 X V 0 X N (SubPop 4) 315.16 270.07 T 240.39 334.08 282.91 353.92 9.92 RR 7 X V 0 X N (SubPop 6) 244.29 340.93 T 382.12 334.08 424.64 353.92 9.92 RR 7 X V 0 X N (SubPop 2) 386.02 340.93 T 240.39 291.56 282.91 311.4 9.92 RR 7 X V 0 X N (SubPop 5) 244.29 298.41 T 288.1 339.74 282.91 342.74 288.1 345.74 288.1 342.74 4 Y V 376.92 345.74 382.12 342.74 376.92 339.74 376.92 342.74 4 Y V 288.1 342.74 376.92 342.74 2 L N 288.1 297.22 282.91 300.22 288.1 303.22 288.1 300.22 4 Y V 376.92 303.22 382.12 300.22 376.92 297.22 376.92 300.22 4 Y V 288.1 300.22 376.92 300.22 2 L N 259.27 328.82 262.45 333.91 265.27 328.61 262.27 328.72 4 Y V 264.83 316.48 261.64 311.4 258.83 316.7 261.83 316.59 4 Y V 262.27 328.71 261.83 316.59 2 L N 400.7 328.77 403.79 333.91 406.69 328.66 403.69 328.71 4 Y V 406.47 316.54 403.38 311.4 400.47 316.65 403.47 316.59 4 Y V 403.7 328.71 403.48 316.59 2 L N 335.55 288.23 332.51 283.05 329.55 288.27 332.55 288.25 4 Y V 330.08 357.4 333.12 362.57 336.08 357.36 333.08 357.38 4 Y V 332.55 288.25 333.08 357.38 2 L N 265.7 357.93 261.12 353.91 259.92 359.88 262.81 358.91 4 Y V 304.36 376.57 310.45 373.24 304.52 369.63 304.44 373.1 4 Y V 97 165 49.33 19.33 310.46 353.91 A 358.95 369.45 353.79 372.57 359.07 375.49 359.01 372.47 4 Y V 404.8 360.17 403.78 353.91 398.86 357.93 401.83 359.05 4 Y V 16 84 50 18.67 353.79 353.91 A 398.23 287.21 403.12 291.24 404.17 284.99 401.2 286.1 4 Y V 359.87 269.25 353.78 272.58 359.71 276.19 359.79 272.72 4 Y V 277 344 49.33 18.67 353.79 291.24 A 305.19 275.53 311.12 271.91 305.02 268.58 305.11 272.05 4 Y V 260.59 285.27 261.79 291.24 266.36 287.22 263.48 286.24 4 Y V 195 263 49.33 19.33 311.12 291.24 A 377.29 310.28 382.45 306.58 376.66 303.96 376.97 307.12 4 Y V 339.96 356.6 343.12 362.57 346.72 356.84 343.34 356.72 4 Y V 186 262 39.33 56 382.46 362.57 A 314.84 356.76 318.45 362.57 321.68 356.54 318.26 356.65 4 Y V 289.05 303.42 283.12 305.91 288.24 309.8 288.64 306.61 4 Y V 279 354 35.33 56.67 283.12 362.57 A 286.86 334.27 281.79 337.91 287.48 340.48 287.17 337.37 4 Y V 323.54 289.08 320.45 283.24 316.94 288.83 320.24 288.96 4 Y V 6 82 38.67 54.67 281.79 283.24 A 343.9 289.35 340.45 283.91 337.47 289.62 340.69 289.49 4 Y V 378.27 339.89 383.78 337.24 378.73 333.79 378.5 336.84 4 Y V 97 174 43.33 53.33 383.79 283.91 A 5 12 Q (Figure 9: Unrestricted Migration T) 226.45 246.03 T (opology) 399.93 246.03 T 141.18 238.52 523.85 387.34 R 2 Z N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "25" 26 %%Page: "26" 26 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-26) 513.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Examples) 63.65 732.95 T 2 12 Q 2.91 (This Section contains two detailed examples using the GA T) 135.65 694.95 P 2.91 (oolbox to solve) 451.86 694.95 P (optimization problems:) 135.65 680.95 T (\245) 157.25 654.95 T (A simple binary GA to solve De Jong\325) 171.65 654.95 T (s \336rst test function [13].) 355.87 654.95 T (\245) 157.25 634.95 T (A real-valued multi-population GA to solve the Harvest problem [9].) 171.65 634.95 T 1 16 Q (The Simple GA) 135.65 598.29 T 2 12 Q 1.33 (This example demonstrates how a simple GA can be constructed using routines) 135.65 570.95 P 0.28 (from the GA T) 135.65 556.95 P 0.28 (oolbox to solve an optimization problem. The objective function to) 207.28 556.95 P (be minimized is an extended version of De Jong\325) 135.65 542.95 T (s \336rst test function [13]:) 370.15 542.95 T (,) 315.32 503.13 T 0.97 (where) 135.65 463.88 P 0 F 0.97 (n) 168.91 463.88 P 2 F 0.97 ( de\336nes the number of dimensions of the problem. For this example, we) 174.91 463.88 P (choose) 135.65 449.88 T 0 F (n) 171.95 449.88 T 2 F ( = 20. The minimum of this function is, of course, located at) 177.95 449.88 T 0 F (x) 469.87 449.88 T 0 10 Q (i) 475.19 446.88 T 2 12 Q ( = 0.) 477.97 449.88 T 1 (The computational element of the M) 135.65 423.88 P 2 10 Q 0.84 (A) 316.21 423.88 P 0.84 (TLAB) 322.32 423.88 P 2 12 Q 1 ( objective function is encapsulated in) 348.42 423.88 P (the code segment below) 135.65 409.88 T (.) 250.45 409.88 T 3 F (function ObjVal = objfun1\050 Phen \051) 171.65 383.88 T (ObjVal = sum\050\050Phen .* Phen\051\325\051\325;) 171.65 363.88 T 2 F 1.32 (An m-\336le implementing this objective function,) 135.65 337.88 P 3 F 3.15 (objfun1) 375.74 337.88 P 2 F 1.32 (, is included with the) 426.11 337.88 P (GA T) 135.65 323.88 T (oolbox software.) 162.45 323.88 T 1.92 (Having written an m-\336le for the objective function, the GA code may now be) 135.65 297.88 P -0.07 (constructed. This can be done directly from the M) 135.65 283.88 P 2 10 Q -0.06 (A) 375.22 283.88 P -0.06 (TLAB) 381.33 283.88 P 2 12 Q -0.07 ( command line, in a script) 407.42 283.88 P 2.05 (\336le or as a M) 135.65 269.88 P 2 10 Q 1.71 (A) 207.13 269.88 P 1.71 (TLAB) 213.24 269.88 P 2 12 Q 2.05 ( function. Fig. 10 shows an outline of the script \336le) 239.33 269.88 P 3 F 4.92 (sga) 510.06 269.88 P 2 F (supplied with the toolbox that implements a simple GA to solve this problem.) 135.65 255.88 T 3.3 (The \336rst \336ve lines describe the major variables of the GA. The number of) 135.65 229.88 P 1.5 (individuals is set to) 135.65 215.88 P 3 F 3.6 (NIND = 40) 237.61 215.88 P 2 F 1.5 ( and the number of generations) 309.58 215.88 P 3 F 3.6 (MAXGEN =) 470.48 215.88 P -0.31 (300) 135.65 201.88 P 2 F -0.13 (. The number of variables used is) 157.24 201.88 P 3 F -0.31 (NVAR = 20) 318.87 201.88 P 2 F -0.13 ( and each variable uses a 20 bit) 383.01 201.88 P 1.58 (representation,) 135.65 187.88 P 3 F 3.8 (PRECI = 20) 211.17 187.88 P 2 F 1.58 (. This example uses a generation gap,) 290.73 187.88 P 3 F 3.8 (GGAP =) 484.67 187.88 P 4.4 (0.9) 135.65 173.88 P 2 F 1.83 (, and \336tness-based reinsertion to implement an elitist strategy whereby the) 157.24 173.88 P 2.92 (four most \336t individuals always propagate through to successive generations.) 135.65 159.88 P (Thus, 36 \050) 135.65 145.88 T 3 F (NIND) 184.62 145.88 T 4 F (\264) 216.4 145.88 T 3 F (GGAP) 225.98 145.88 T 2 F (\051 new individuals are produced at each generation.) 254.77 145.88 T 237.51 485.88 315.32 524.95 C 0 12 Q 0 X 0 K (f) 238.51 503.13 T 2 9 Q (1) 242.31 499.36 T 0 12 Q (x) 254.61 503.13 T 4 F (\050) 249.51 503.13 T (\051) 260.54 503.13 T 0 F (x) 304.04 503.13 T 0 9 Q (i) 309.83 499.35 T 2 F (2) 309.83 509.24 T 0 F (i) 285.12 488.83 T 2 F (1) 298.55 488.83 T 4 F (=) 290.62 488.83 T 0 F (n) 291.83 517.81 T 4 18 Q (\345) 287.67 499.93 T 4 12 Q (=) 272.53 503.13 T -8.35 24.95 603.65 816.95 C 351.3 496.49 429.79 512.33 C 2 12 Q 0 X 0 K (5) 359.35 503.13 T (1) 365.35 503.13 T (2) 371.34 503.13 T 4 F (-) 352.3 503.13 T 0 F (x) 389.92 503.13 T 0 9 Q (i) 395.71 499.35 T 2 12 Q (5) 410.8 503.13 T (1) 416.79 503.13 T (2) 422.79 503.13 T 4 F (\243) 380.34 503.13 T (\243) 401.21 503.13 T -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "26" 27 %%Page: "27" 27 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-27) 513.33 61.29 T 2 12 Q 1.06 (The \336eld descriptor is constructed using the matrix replication function,) 135.65 178.42 P 3 F 2.54 (rep) 493.67 178.42 P 2 F 1.06 (, to) 515.26 178.42 P 3.96 (build the matrix,) 135.65 164.42 P 3 F 9.51 (FieldD) 230.16 164.42 P 2 F 3.96 (, describing the chromosomes\325 representation and) 273.34 164.42 P -0.2 (interpretation. In this case,) 135.65 150.42 P 3 F -0.49 (FieldD) 265.41 150.42 P 2 F -0.2 ( describes 20 variables, each Gray coded using) 308.59 150.42 P 0.35 (20 bits over the interval [-512, 512]. An initial population is then created with the) 135.65 136.42 P (function) 135.65 122.42 T 3 F (crtbp) 178.62 122.42 T 2 F ( thus,) 214.6 122.42 T 63.65 96.95 531.65 744.95 C 136.44 200.42 531.65 732.95 C 142.71 234 525.38 722.98 R 7 X 0 K V 3 12 Q 0 X (NIND = 40;) 142.71 714.98 T (% Number of individuals) 305.86 714.98 T (MAXGEN = 300;) 142.71 700.98 T (% Maximum no. of generations) 305.86 700.98 T (NVAR = 20;) 142.71 686.98 T (% No. of variables) 305.86 686.98 T (PRECI = 20;) 142.71 672.98 T (% Precision of variables) 305.86 672.98 T (GGAP = 0.9;) 142.71 658.98 T (% Generation gap) 305.86 658.98 T (% Build f) 142.71 639.98 T (ield descriptor) 207.47 639.98 T (FieldD = [rep\050[PRECI],[1,NVAR]\051;...) 142.71 625.98 T (rep\050[-512;512],[1,NVAR]\051; rep\050[1;0;1;1],[1,NVAR]\051];) 157.1 611.98 T (% Initialise population) 142.71 592.98 T (Chrom = crtbp\050NIND, NVAR*PRECI\051;) 142.71 578.98 T (gen = 0;) 142.71 559.98 T (% Counter) 305.86 559.98 T (% Evaluate initial population) 142.71 540.98 T (ObjV = objfun1\050bs2rv\050Chrom,FieldD\051\051;) 142.71 526.98 T (% Generational loop) 142.71 507.98 T (while gen < MAXGEN,) 142.71 493.98 T (% Assign f) 167.91 474.98 T (itness values to entire population) 239.87 474.98 T (FitnV = ranking\050ObjV\051;) 167.91 460.98 T (% Select individuals for breeding) 167.91 441.98 T (SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 167.91 427.98 T (% Recombine individuals \050crossover\051) 167.91 408.98 T (SelCh = recombin\050\325xovsp\325,SelCh,0.7\051;) 167.91 394.98 T (% Apply mutation) 167.91 375.98 T (SelCh = mut\050SelCh\051;) 167.91 361.98 T (% Evaluate offspring, call objective function) 167.91 342.98 T (ObjVSel = objfun1\050bs2rv\050SelCh,FieldD\051\051;) 167.91 328.98 T (% Reinsert offspring into population) 167.91 309.98 T ([Chrom ObjV]=reins\050Chrom,SelCh,1,1,ObjV,ObjVSel\051;) 167.91 295.98 T (% Increment counter) 167.91 276.98 T (gen = gen+1;) 167.91 262.98 T (end) 142.71 243.98 T 139.16 204.48 528.92 728.89 R 0.5 H 2 Z N 5 F (Figure 10: The Simple GA in M) 238.91 212.83 T 5 10 Q (A) 397.51 212.83 T (TLAB) 403.63 212.83 T 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "27" 28 %%Page: "28" 28 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-28) 513.33 61.29 T 3 12 Q (Chrom = crtbp\050NIND, NVAR*PRECI\051;) 171.65 736.95 T 2 F 0.14 (producing a matrix,) 135.65 710.95 P 3 F 0.35 (Chrom) 233.35 710.95 P 2 F 0.14 (, of) 269.33 710.95 P 3 F 0.35 (NIND) 288.6 710.95 P 2 F 0.14 ( uniformly distributed random binary strings) 317.39 710.95 P (of length) 135.65 696.95 T 3 F (NVAR) 181.62 696.95 T 4 F (\264) 213.4 696.95 T 3 F (PRECI) 222.98 696.95 T 2 F (.) 258.96 696.95 T 0.86 (The generation counter) 135.65 670.95 P 0.86 (,) 248.12 670.95 P 3 F 2.06 (gen) 254.98 670.95 P 2 F 0.86 (, is set to zero. The following line then converts the) 276.57 670.95 P 0.12 (binary strings to real-values using the function) 135.65 656.95 P 3 F 0.28 (bs2rv) 362.64 656.95 P 2 F 0.12 ( and evaluates the objective) 398.62 656.95 P 1.26 (function,) 135.65 642.95 P 3 F 3.03 (objfun1) 182.88 642.95 P 2 F 1.26 (, for all of the individuals in the initial population as shown) 233.25 642.95 P (below) 135.65 628.95 T (.) 164.18 628.95 T 3 F (ObjV = objfun1\050bs2rv\050Chrom, FieldD\051\051;) 171.65 602.95 T 2 F 2.08 (The function) 135.65 576.95 P 3 F 4.98 (bs2rv) 204.42 576.95 P 2 F 2.08 ( converts the binary strings in the matrix) 240.4 576.95 P 3 F 4.98 (Chrom) 454.22 576.95 P 2 F 2.08 ( to real-) 490.2 576.95 P 1.74 (values according to the \336eld descriptor) 135.65 562.95 P 1.74 (,) 330.07 562.95 P 3 F 4.18 (FieldD) 337.81 562.95 P 2 F 1.74 (, and returns a matrix of real-) 380.99 562.95 P 1.05 (valued phenotypes. The return value matrix of) 135.65 548.95 P 3 F 2.52 (bs2rv) 368.17 548.95 P 2 F 1.05 ( is then passed directly as) 404.15 548.95 P 4.34 (the input ar) 135.65 534.95 P 4.34 (gument to the objective function,) 198.74 534.95 P 3 F 10.41 (objfun1) 382.32 534.95 P 2 F 4.34 (, and the resulting) 432.69 534.95 P 0.18 (objective function values are returned in the matrix) 135.65 520.95 P 3 F 0.44 (ObjV) 385.59 520.95 P 2 F 0.18 (. The GA then enters the) 412.83 520.95 P (generational) 135.65 506.95 T 3 F (while) 197.93 506.95 T 2 F ( loop.) 233.91 506.95 T 1.49 (The \336rst step in the generational loop is the assignment of \336tness values to the) 135.65 480.95 P 3.02 (individuals. In this example, rank-based \336tness assignment is used as shown) 135.65 466.95 P (below) 135.65 452.95 T (,) 164.18 452.95 T 3 F (FitnV = ranking\050ObjV\051;) 171.65 426.95 T 2 F 2.36 (Here, the objective function values, ObjV) 135.65 400.95 P 2.36 (, are passed to the T) 346.1 400.95 P 2.36 (oolbox function) 452.99 400.95 P 3 F 1.32 (ranking) 135.65 386.95 P 2 F 0.55 ( with no other ar) 186.02 386.95 P 0.55 (guments. The default setting for the ranking algorithm) 267.29 386.95 P -0.1 (assume a selective pressure of 2 and linear ranking, giving the most \336t individual a) 135.65 372.95 P 1.62 (\336tness value of 2 and the least \336t individual a \336tness value of 0. Note that the) 135.65 358.95 P 1.78 (ranking algorithm assumes that the objective function is to be) 135.65 344.95 P 1 F 1.78 (minimised) 451.91 344.95 P 2 F 1.78 (. The) 505.22 344.95 P (resulting \336tness values are returned in the vector) 135.65 330.95 T 3 F (FitnV) 371.47 330.95 T 2 F (.) 405.91 330.95 T 2.13 (The selection stage uses the high-level function) 135.65 304.95 P 3 F 5.1 (select) 381.37 304.95 P 2 F 2.13 ( to call the low-level) 424.55 304.95 P (stochastic universal sampling routine,) 135.65 290.95 T 3 F (sus) 319.87 290.95 T 2 F (, as follows,) 341.45 290.95 T 3 F (SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 171.65 264.95 T 2 F 2.64 (After selection,) 135.65 238.95 P 3 F 6.33 (SelCh) 217.86 238.95 P 2 F 2.64 ( contains) 253.84 238.95 P 3 F 6.33 (GGAP) 305.09 238.95 P 4 F 2.64 (\264) 339.51 238.95 P 3 F 6.33 (NIND) 351.73 238.95 P 2 F 2.64 ( individuals from the original) 380.51 238.95 P 1.73 (population) 135.65 224.95 P 3 F 4.16 (Chrom) 191.68 224.95 P 2 F 1.73 (. These individuals are now recombined using the high-level) 227.67 224.95 P (function) 135.65 210.95 T 3 F (recombin) 178.62 210.95 T 2 F ( as shown below) 236.19 210.95 T (.) 315.02 210.95 T 3 F (SelCh = recombin\050\325xovsp\325, SelCh, 0.7\051;) 171.65 184.95 T 1.76 (recombin) 135.65 158.95 P 2 F 0.73 ( takes the individuals selected for reproduction,) 193.22 158.95 P 3 F 1.76 (SelCh) 428.85 158.95 P 2 F 0.73 (, and uses the) 464.83 158.95 P -0.27 (single-point crossover routine,) 135.65 144.95 P 3 F -0.65 (xovsp) 284.07 144.95 P 2 F -0.27 (, to perform crossover with probability) 320.05 144.95 P -0.27 (,) 503.78 144.95 P 0 F -0.27 (Px) 509.5 144.95 P 2 F -0.27 ( =) 522.16 144.95 P -0.21 (0.7. The individuals in the input matrix) 135.65 130.95 P 3 F -0.51 (SelCh) 325.06 130.95 P 2 F -0.21 ( are ordered such that individuals in) 361.04 130.95 P 2.9 (odd numbered positions are crossed with the individual in the adjacent even) 135.65 116.95 P 1.66 (numbered position. If the number of individuals in) 135.65 102.95 P 3 F 3.98 (SelCh) 394.43 102.95 P 2 F 1.66 ( is odd then the last) 430.41 102.95 P FMENDPAGE %%EndPage: "28" 29 %%Page: "29" 29 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-29) 513.33 61.29 T 2 12 Q 0.28 (individual is always returned uncrossed. The of) 135.65 736.95 P 0.28 (fspring produced by this crossover) 364.63 736.95 P -0.05 (are returned in the same matrix,) 135.65 722.95 P 3 F -0.13 (SelCh) 290.87 722.95 P 2 F -0.05 (. The actual crossover routine used may be) 326.85 722.95 P 5.34 (changed by supplying a dif) 135.65 708.95 P 5.34 (ferent function name in the string passed to) 286.72 708.95 P 3 F (recombin) 135.65 694.95 T 2 F (.) 193.22 694.95 T 2.79 (Having produced a set of of) 135.65 668.95 P 2.79 (fspring, mutation may now be applied using the) 282.93 668.95 P (mutation function) 135.65 654.95 T 3 F (mut) 224.27 654.95 T 2 F (:) 245.85 654.95 T 3 F (SelCh = mut\050SelCh\051;) 171.65 628.95 T 2 F 2.71 (Again, the of) 135.65 602.95 P 2.71 (fspring are returned in the matrix) 203.8 602.95 P 3 F 6.49 (SelCh) 381.91 602.95 P 2 F 2.71 (. As no probability of) 417.89 602.95 P -0.08 (mutation has been speci\336ed in the function call, the default value of) 135.65 588.95 P 0 F -0.08 (Pm) 462.74 588.95 P 2 F -0.08 ( = 0.7/) 478.73 588.95 P 0 F -0.08 (Lind) 509.65 588.95 P 2 F (= 0.0017, where) 135.65 574.95 T 0 F (Lind) 216.69 574.95 T 2 F ( is the length of an individual, is assumed.) 238.68 574.95 T -0.02 (The objective function values for the of) 135.65 548.95 P -0.02 (fspring,) 325.16 548.95 P 3 F -0.05 (ObjVSel) 365.12 548.95 P 2 F -0.02 (, may now be calculated) 415.49 548.95 P (thus:) 135.65 534.95 T 3 F (ObjVSel = objfun1\050bs2rv\050SelCh, FieldD\051\051;) 171.65 508.95 T 2 F 0.92 (Because we have used a generation gap, the number of of) 135.65 482.95 P 0.92 (fspring is less than the) 420.71 482.95 P 1.1 (size of the population. Therefore, we must reinsert the of) 135.65 468.95 P 1.1 (fspring into the current) 418.1 468.95 P (population. This is achieved using the reinsertion function,) 135.65 454.95 T 3 F (reins) 420.8 454.95 T 2 F (, as follows:) 456.78 454.95 T 3 F ([Chrom,ObjV]=reins\050Chrom, SelCh,1,1,ObjV,ObjVSel\051;) 171.65 428.95 T 2 F 0.57 (Here,) 135.65 402.95 P 3 F 1.37 (Chrom) 165.52 402.95 P 2 F 0.57 ( and) 201.5 402.95 P 3 F 1.37 (SelCh) 225.95 402.95 P 2 F 0.57 ( are matrices containing the original population and the) 261.93 402.95 P 1.36 (resulting of) 135.65 388.95 P 1.36 (fspring. The two occurrences of the numeral) 191.76 388.95 P 3 F 3.26 (1) 417.09 388.95 P 2 F 1.36 ( indicate that a single) 424.28 388.95 P 2.69 (population is used and that \336tness-based reinsertion be applied. Fitness-based) 135.65 374.95 P 3.38 (reinsertion replaces the least \336t members of) 135.65 360.95 P 3 F 8.12 (Chrom) 371.51 360.95 P 2 F 3.38 ( with the individuals in) 407.49 360.95 P 3 F 2.11 (SelCh) 135.65 346.95 P 2 F 0.88 (. The objective function values of the original population,) 171.63 346.95 P 3 F 2.11 (ObjV) 459.02 346.95 P 2 F 0.88 (, are thus) 486.26 346.95 P 2.41 (required as a parameter to) 135.65 332.95 P 3 F 5.79 (reins) 275.25 332.95 P 2 F 2.41 (. In addition, so that the objective function) 311.23 332.95 P 1.58 (values of the new population can be returned without having to re-evaluate the) 135.65 318.95 P 0.74 (objective function for the entire population, the objective values of the of) 135.65 304.95 P 0.74 (fspring,) 494.67 304.95 P 3 F -0.64 (ObjVSel) 135.65 290.95 P 2 F -0.27 (, are also supplied.) 186.02 290.95 P 3 F -0.64 (reins) 277.56 290.95 P 2 F -0.27 ( returns the new population with the of) 313.54 290.95 P -0.27 (fspring) 497.67 290.95 P (inserted,) 135.65 276.95 T 3 F (Chrom) 179.62 276.95 T 2 F (, and the objective function values for this population,) 215.6 276.95 T 3 F (ObjV) 477.76 276.95 T 2 F (.) 505 276.95 T 0.09 (Finally) 135.65 250.95 P 0.09 (, the generational counter) 168.86 250.95 P 0.09 (,) 290.54 250.95 P 3 F 0.21 (gen) 296.62 250.95 P 2 F 0.09 (, is incremented. The GA iterates around the) 318.21 250.95 P 0.49 (loop until) 135.65 236.95 P 3 F 1.17 (gen = MAXGEN) 185.94 236.95 P 2 F 0.49 (, in this case 300, and then terminates. The results of) 274.62 236.95 P 1.28 (the genetic optimization are contained in the matrix ObjV and the values of the) 135.65 222.95 P (decision variables may be obtained by:) 135.65 208.95 T 3 F (Phen = bs2rv\050Chrom, FieldD\051;) 171.65 182.95 T FMENDPAGE %%EndPage: "29" 30 %%Page: "30" 30 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-30) 513.33 61.29 T 1 16 Q (A Multi-population GA) 135.65 734.29 T 2 12 Q 3.7 (This example shows how functions from the GA T) 135.65 706.95 P 3.7 (oolbox may be used to) 408.25 706.95 P 1.76 (implement a real-valued, multi-population GA. A M) 135.65 692.95 P 2 10 Q 1.47 (A) 398.07 692.95 P 1.47 (TLAB) 404.18 692.95 P 2 12 Q 1.76 ( m-\336le script) 430.27 692.95 P 3 F 4.24 (mpga) 499.86 692.95 P 2 F 1.76 (,) 528.65 692.95 P 0.49 (supplied with the T) 135.65 678.95 P 0.49 (oolbox, implements the code described in this subsection. The) 229.23 678.95 P 2.82 (objective function chosen is that of the harvest problem [9] which is a one-) 135.65 664.95 P (dimensional equation of growth:) 135.65 650.95 T (,) 378.2 623.75 T (with one equality constraint,) 135.65 595.02 T (,) 353.47 567.81 T 0.35 (where) 135.65 539.1 P 0 F 0.35 (x) 168.29 539.1 P 0 10 Q 0.29 (0) 173.62 536.1 P 2 12 Q 0.35 ( is the initial condition of the state,) 178.62 539.1 P 0 F 0.35 (a) 350.98 539.1 P 2 F 0.35 ( is a scalar constant, and) 356.98 539.1 P 0 F 0.35 (x) 478.65 539.1 P 0 10 Q 0.29 (k) 483.97 536.1 P 4 12 Q 0.35 (\316) 491.76 539.1 P 0 F 0.35 (R) 503.65 539.1 P 2 F 0.35 (and) 514.33 539.1 P 0 F 0.25 (u) 135.65 525.1 P 0 10 Q 0.21 (k) 141.65 522.1 P 4 12 Q 0.25 (\316) 149.33 525.1 P 0 F 0.25 ( R) 157.88 525.1 P 0 10 Q 0.21 (+) 168.46 529.9 P 2 12 Q 0.25 ( are the state and nonnegative control respectively) 175.2 525.1 P 0.25 (. The objective function) 416.31 525.1 P (is de\336ned as:) 135.65 511.1 T (,) 375.47 471.18 T 0.04 (where) 135.65 431.93 P 0 F 0.04 (N) 167.98 431.93 P 2 F 0.04 ( is the number of control steps over which the problem is to be solved. An) 175.98 431.93 P 1.19 (m-\336le implementing this objective function,) 135.65 417.93 P 3 F 2.86 (objharv) 356.16 417.93 P 2 F 1.19 (, is supplied with the GA) 405.75 417.93 P 1.41 (T) 135.65 403.93 P 1.41 (oolbox software. Note that as this is a maximisation problem and the T) 142.14 403.93 P 1.41 (oolbox) 498.33 403.93 P 5.62 (routines are implemented to minimise, the objective function,) 135.65 389.93 P 3 F 13.48 (objharv) 479.06 389.93 P 2 F 5.62 (,) 528.65 389.93 P -0.25 (multiplies) 135.65 375.93 P 0 F -0.25 (J) 186.38 375.93 P 2 F -0.25 ( by -1 to produce a minimisation problem. The initial condition is set to) 191.71 375.93 P 0 F 2.3 (x) 135.65 361.93 P 0 10 Q 1.92 (0) 140.97 358.93 P 2 12 Q 2.3 ( = 100 and the scalar is chosen as) 145.97 361.93 P 0 F 2.3 (a) 329.64 361.93 P 2 F 2.3 ( = 1.1. Additionally) 335.64 361.93 P 2.3 (, the exact optimal) 436.14 361.93 P (solution for this problem can be determined analytically as:) 135.65 347.93 T (.) 384.8 299.39 T 2.08 (The number of control steps for this problem is) 135.65 260.73 P 0 F 2.08 (N) 383.86 260.73 P 2 F 2.08 ( = 20, thus,) 391.86 260.73 P 3 F 4.99 (NVAR = 20) 456.91 260.73 P 2 F 2.9 (decision variables will be used, one for each control input,) 135.65 246.73 P 0 F 2.9 (u) 447.79 246.73 P 0 10 Q 2.42 (k) 453.79 243.73 P 2 12 Q 2.9 (. The decision) 458.23 246.73 P -0.02 (variables are bounded in the range) 135.65 232.73 P 3 F -0.04 (RANGE = [0, 200]) 303.4 232.73 P 2 F -0.02 (, limiting the maximum) 418.41 232.73 P 0.99 (control input, at any time-step, to 200. The \336eld descriptor) 135.65 218.73 P 0.99 (,) 424.54 218.73 P 3 F 2.37 (FieldD) 431.52 218.73 P 2 F 0.99 (, describing) 474.7 218.73 P 1.46 (the decision variables may be constructed using the matrix replication function,) 135.65 204.73 P 3 F (rep) 135.65 190.73 T 2 F (, thus:) 157.24 190.73 T 3 F (NVAR = 20;) 171.65 164.73 T (RANGE = [0; 200];) 171.65 149.73 T (FieldD = rep\050RANGE,[1,NVAR]\051;) 171.65 134.73 T 286.1 617.02 378.2 632.95 C 0 12 Q 0 X 0 K (x) 287.1 623.75 T 0 9 Q (k) 292.89 619.97 T 2 F (1) 306.31 619.97 T 4 F (+) 299.13 619.97 T 0 12 Q (a) 329.39 623.75 T (x) 344.39 623.75 T 4 F (\327) 338.39 623.75 T 0 9 Q (k) 350.17 619.97 T 0 12 Q (u) 366.75 623.75 T 0 9 Q (k) 373.21 619.97 T 4 12 Q (-) 357.16 623.75 T (=) 316.81 623.75 T -8.35 24.95 603.65 816.95 C 310.83 561.1 353.47 577.02 C 0 12 Q 0 X 0 K (x) 311.83 567.81 T 2 9 Q (0) 317.61 564.05 T 0 12 Q (x) 340.69 567.81 T 0 9 Q (N) 346.48 564.03 T 4 12 Q (=) 328.11 567.81 T -8.35 24.95 603.65 816.95 C 288.83 453.93 375.47 493.1 C 0 12 Q 0 X 0 K (J) 289.83 471.18 T 2 F (m) 313.74 471.18 T (a) 323.07 471.18 T (x) 328.39 471.18 T 0 F (u) 364.02 471.18 T 0 9 Q (k) 370.48 467.4 T (k) 336.35 456.88 T 2 F (0) 351.27 456.88 T 4 F (=) 343.34 456.88 T 0 F (N) 336.1 485.95 T 2 F (1) 351.53 485.95 T 4 F (-) 344.34 485.95 T 4 18 Q (\345) 339.64 467.97 T 4 12 Q (=) 301.15 471.18 T 374.47 482.38 364.02 482.38 2 L 0.33 H 0 Z N 364.02 482.38 361.02 467.54 2 L N 361.02 467.54 359.02 471.75 2 L N 359.02 471.75 358.02 469.65 2 L N -8.35 24.95 603.65 816.95 C 279.49 282.73 384.8 329.93 C 0 12 Q 0 X 0 K (J) 280.49 299.39 T 2 9 Q (*) 285.82 305.5 T 0 12 Q (x) 320.47 309.69 T 2 9 Q (0) 326.26 305.93 T 0 12 Q (a) 338.56 309.69 T 0 9 Q (N) 344.56 315.75 T 2 12 Q (1) 363.14 309.69 T 4 F (-) 353.55 309.69 T (\050) 333.46 309.69 T (\051) 369.74 309.69 T 2 9 Q (2) 375.73 319.8 T 0 12 Q (a) 317.9 287.73 T 0 9 Q (N) 323.89 293.83 T 2 F (1) 339.32 293.83 T 4 F (-) 332.14 293.83 T 0 12 Q (a) 351.62 287.73 T 2 F (1) 370.2 287.73 T 4 F (-) 360.62 287.73 T (\050) 346.52 287.73 T (\051) 376.81 287.73 T (=) 297.31 299.39 T 317.9 301.98 382.55 301.98 2 L 0.33 H 0 Z N 383.8 328.93 316.9 328.93 2 L N 316.9 328.93 313.9 285.73 2 L N 313.9 285.73 311.9 297.03 2 L N 311.9 297.03 310.9 291.38 2 L N -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "30" 31 %%Page: "31" 31 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-31) 513.33 61.29 T 2 12 Q 1.59 (The parameters for the GA may be speci\336ed using M) 135.65 736.95 P 2 10 Q 1.32 (A) 405.4 736.95 P 1.32 (TLAB) 411.51 736.95 P 2 12 Q 1.59 ( variables. For this) 437.61 736.95 P (example the following parameters are de\336ned:) 135.65 722.95 T 3 F (% Def) 171.65 696.95 T (ine GA Parameters) 207.63 696.95 T (GGAP = 0.8;) 171.65 681.95 T (% Generation gap) 315.65 681.95 T (XOVR = 1;) 171.65 666.95 T (% Crossover rate) 315.65 666.95 T (MUTR = 1/NVAR;) 171.65 651.95 T (% Mutation rate) 315.65 651.95 T (MAXGEN = 1200;) 171.65 636.95 T (% Maximum no. of generations) 315.65 636.95 T (INSR = 0.9;) 171.65 621.95 T (% Insertion rate) 315.65 621.95 T (SUBPOP = 8;) 171.65 606.95 T (% No. of subpopulations) 315.65 606.95 T (MIGR = 0.2;) 171.65 591.95 T (% Migration rate) 315.65 591.95 T (MIGGEN = 20;) 171.65 576.95 T (% No. of gens / migration) 315.65 576.95 T (NIND = 20;) 171.65 561.95 T (% No. of individuals / subpop) 315.65 561.95 T 2 F 1.04 (As well as the conventional GA parameters, such as generation gap \050) 135.65 535.95 P 3 F 2.5 (GGAP) 477.51 535.95 P 2 F 1.04 (\051 and) 506.3 535.95 P 3.32 (crossover rate \050) 135.65 521.95 P 3 F 7.96 (XOVR) 216.21 521.95 P 2 F 3.32 (\051, a number of other parameters associated with multi-) 244.99 521.95 P 0.71 (population GAs are de\336ned. Here,) 135.65 507.95 P 3 F 1.71 (INSR = 0.9) 306.75 507.95 P 2 F 0.71 ( speci\336es that only 90% of the) 382.13 507.95 P 4.47 (individuals produced at each generation are reinserted into the population,) 135.65 493.95 P 3 F 2.2 (SUBPOP = 8) 135.65 479.95 P 2 F 0.92 ( subpopulations are to be used with a migration rate of) 212.01 479.95 P 3 F 2.2 (MIGR =) 486.27 479.95 P 1.31 (0.2) 135.65 465.95 P 2 F 0.55 (, or 20%, between subpopulations and migration occurring at every) 157.24 465.95 P 3 F 1.31 (MIGGEN) 488.47 465.95 P (= 20) 135.65 451.95 T 2 F (generations. Each subpopulation contains) 171.63 451.95 T 3 F (NIND = 20) 373.83 451.95 T 2 F ( individuals.) 438.59 451.95 T (The functions used by the script-\336le are speci\336ed using M) 135.65 425.95 T 2 10 Q (A) 414.46 425.95 T (TLAB) 420.57 425.95 T 2 12 Q ( strings:) 446.66 425.95 T 3 F (% Specify other functions as strings) 171.65 399.95 T (SEL_F = \325sus\325;) 171.65 384.95 T (% Name of selection function) 315.65 384.95 T (XOV_F = \325recdis\325;) 171.65 369.95 T (% Name of recombination fun.) 315.65 369.95 T (MUT_F = \325mutbga\325;) 171.65 354.95 T (% Name of mutation function) 315.65 354.95 T (OBJ_F = \325objharv\325;) 171.65 339.95 T (% Name of objective function) 315.65 339.95 T 2 F 3.51 (Because we are using discrete recombination,) 135.65 313.95 P 3 F 8.42 (recdis) 378.85 313.95 P 2 F 3.51 (, for the breeding of) 422.03 313.95 P (of) 135.65 299.95 T (fspring, the crossover rate is not used and, hence) 145.42 299.95 T 3 F (XOVR = 1) 381.57 299.95 T 2 F ( above.) 439.14 299.95 T 2.11 (The initial population is created using the function) 135.65 273.95 P 3 F 5.07 (crtrp) 397.73 273.95 P 2 F 2.11 ( and the generation) 433.71 273.95 P (counter) 135.65 259.95 T (,) 171.14 259.95 T 3 F (gen) 177.13 259.95 T 2 F (, set to zero:) 198.72 259.95 T 3 F (Chrom = crtrp\050SUBPOP*NIND,FieldD\051;) 171.65 233.95 T (gen = 0;) 171.65 218.95 T 2 F 4.09 (This will consist of) 135.65 192.95 P 3 F 9.82 (SUBPOP) 247.3 192.95 P 4 F 4.09 (\264) 297.57 192.95 P 3 F 9.82 (NIND) 311.25 192.95 P 2 F 4.09 ( individuals with individual decision) 340.03 192.95 P 2.1 (variables chosen uniformly at random in the range speci\336ed by) 135.65 178.95 P 3 F 5.03 (FieldD) 461.73 178.95 P 2 F 2.1 (. The) 504.9 178.95 P 3 F -0.02 (Chrom) 135.65 164.95 P 2 F -0.01 ( matrix contains all of the subpopulations and the objective function values) 171.63 164.95 P (for all the individuals in all the subpopulations may be calculated directly) 135.65 150.95 T (,) 487.64 150.95 T 3 F (ObjV = feval\050OBJ_F, Chrom\051;) 171.65 124.95 T FMENDPAGE %%EndPage: "31" 32 %%Page: "32" 32 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-32) 513.33 61.29 T 2 12 Q 0 (using the M) 135.65 736.95 P 2 10 Q 0 (A) 192.96 736.95 P 0 (TLAB) 199.07 736.95 P 3 12 Q 0.01 (feval) 228.16 736.95 P 2 F 0 ( command.) 264.14 736.95 P 3 F 0.01 (feval) 320.45 736.95 P 2 F 0 ( performs function evaluation taking) 356.42 736.95 P -0.19 (the \336rst input ar) 135.65 722.95 P -0.19 (gument, in this case the name of our objective function,) 211.15 722.95 P 3 F -0.46 (objharv) 479.06 722.95 P 2 F -0.19 (,) 528.65 722.95 P -0.13 (contained in) 135.65 708.95 P 3 F -0.3 (OBJ_F) 197.35 708.95 P 2 F -0.13 (, as the function to be evaluated and calls that function with all) 232.37 708.95 P (the remaining parameters as its input ar) 135.65 694.95 T (guments. In this case, the function call is:) 324.63 694.95 T 3 F (ObjV = objharv\050Chrom\051;) 171.65 668.95 T 2 F 0.28 (As a real-valued coding is used, there is no need to convert the chromosomes into) 135.65 642.95 P 2.3 (a phenotypic representation. Like the previous example, the GA now enters a) 135.65 628.95 P (generational) 135.65 614.95 T 3 F (while) 197.93 614.95 T 2 F ( loop.) 233.91 614.95 T 0.39 (The M) 135.65 588.95 P 2 10 Q 0.33 (A) 168.35 588.95 P 0.33 (TLAB) 174.46 588.95 P 2 12 Q 0.39 ( code for the generational loop of the multi-population GA is shown) 200.55 588.95 P (in Fig. 1) 135.65 574.95 T (1 below) 175.53 574.95 T (.) 213.05 574.95 T 63.65 96.95 531.65 744.95 C 136.44 123.46 531.65 570.95 C 142.71 164.04 525.38 558 R 7 X 0 K V 3 12 Q 0 X (% Generational loop) 142.71 550 T (while gen < MAXGEN,) 142.71 536 T (% Fitness assignment to whole population) 167.91 514 T (FitnV = ranking\050ObjV,2,SUBPOP\051;) 167.91 500 T (% Select individuals from population) 167.91 478 T -0.39 (SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 167.91 464 P (% Recombine selected individuals) 167.91 442 T (SelCh=recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 167.91 428 T (% Mutate offspring) 167.91 406 T (SelCh = mutate\050MUT_F,SelCh,FieldD,[MUTR],SUBPOP\051;) 167.91 392 T (% Calculate objective function for offsprings) 167.91 370 T (ObjVOff = feval\050OBJ_F,SelCh\051;) 167.91 356 T (% Insert best offspring replacing worst parents) 167.91 334 T ([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP, ...) 167.91 320 T ([1 INSR], ObjV, ObjVOff\051;) 203.89 306 T (% Increment counter) 167.91 284 T (gen=gen+1;) 167.91 270 T (% Migrate individuals between subpopulations) 167.91 248 T (if \050rem\050gen,MIGGEN\051 == 0\051) 167.91 234 T ([Chrom, ObjV] = ...) 189.49 220 T -0.47 (migrate\050Chrom, SUBPOP, [MIGR, 1, 1], ObjV\051;) 218.28 206 P (end) 167.91 192 T (end) 142.71 170 T 139.16 129.55 528.92 564.86 R 0.5 H 2 Z N 5 F (Figure 1) 196.93 138.85 T (1: Generational Loop of a Multipopulation GA) 239.25 138.85 T 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "32" 33 %%Page: "33" 33 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-33) 513.33 61.29 T 2 12 Q 2.91 (The \336rst step of the generational loop is the assignment of \336tness values to) 135.65 736.95 P (individuals:) 135.65 722.95 T 3 F (FitnV = ranking\050ObjV, 2, SUBPOP\051;) 171.65 696.95 T 2 F 1.22 (Because we are using multiple subpopulations,) 135.65 670.95 P 3 F 2.92 (ranking) 371.15 670.95 P 2 F 1.22 ( requires us to specify) 421.52 670.95 P 2.2 (the selective pressure required, here we use a selective pressure of 2, and the) 135.65 656.95 P 0.96 (number of subpopulations,) 135.65 642.95 P 3 F 2.3 (SUBPOP) 269.77 642.95 P 2 F 0.96 (. Each subpopulation\325) 311.62 642.95 P 0.96 (s individuals\325 objective) 417.8 642.95 P 2.68 (values in) 135.65 628.95 P 3 F 6.43 (ObjV) 186.97 628.95 P 2 F 2.68 ( are ranked separately and the resulting sets of \336tness values) 215.76 628.95 P (returned in the vector) 135.65 614.95 T 3 F (FitnV) 241.56 614.95 T 2 F (.) 275.99 614.95 T 1.97 (W) 135.65 588.95 P 1.97 (ithin each subpopulation, individuals are selected for breeding independently) 146.49 588.95 P (using the high-level selection function,) 135.65 574.95 T 3 F (select) 325.53 574.95 T 2 F (:) 368.7 574.95 T 3 F (SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 171.65 548.95 T 5.96 (select) 135.65 522.95 P 2 F 2.48 ( calls the low-level selection function,) 178.82 522.95 P 3 F 5.96 (SEL_F = \325sus\325) 379.26 522.95 P 2 F 2.48 ( for each) 484.73 522.95 P 0.23 (subpopulation and builds the matrix) 135.65 508.95 P 3 F 0.56 (SelCh) 312.38 508.95 P 2 F 0.23 ( containing all the pairs of individuals) 348.36 508.95 P 0.24 (to be recombined. Like the previous example, the generation gap,) 135.65 494.95 P 3 F 0.59 (GGAP = 0.8) 455.52 494.95 P 2 F 0.24 (,) 528.65 494.95 P 2.22 (means that 0.8) 135.65 480.95 P 4 F 2.22 (\264) 214.92 480.95 P 2 F 2.22 ( 20 = 16,) 221.5 480.95 P 3 F 5.32 (GGAP) 276.11 480.95 P 4 F 2.22 (\264) 310.11 480.95 P 3 F 5.32 (NIND) 321.92 480.95 P 2 F 2.22 (, individuals are selected from each) 350.7 480.95 P -0.03 (subpopulation. Thus,) 135.65 466.95 P 3 F -0.07 (SelCh) 239.54 466.95 P 2 F -0.03 ( contains a total of) 275.52 466.95 P 3 F -0.07 (GGAP) 366.98 466.95 P 4 F -0.03 (\264) 398.73 466.95 P 3 F -0.07 (NIND) 408.29 466.95 P 4 F -0.03 (\264) 440.04 466.95 P 3 F -0.07 (SUBPOP) 449.59 466.95 P -0.07 (= 128) 495.74 466.95 P 2 F (individuals.) 135.65 452.95 T 0.04 (In a similar manner) 135.65 426.95 P 0.04 (, the high-level recombination function,) 228.89 426.95 P 3 F 0.1 (recombin) 422.64 426.95 P 2 F 0.04 (, is used to) 480.21 426.95 P (recombine the pairs of individuals within each subpopulation of) 135.65 412.95 T 3 F (SelCh) 445.11 412.95 T 2 F (:) 481.09 412.95 T 3 F (SelCh = recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 171.65 386.95 T 2 F 5.24 (The recombination function,) 135.65 360.95 P 3 F 12.58 (XOV_F = \325recdis\325) 291.28 360.95 P 2 F 5.24 (, performs discrete) 431.57 360.95 P 1.73 (recombination between pairs of individuals for each subpopulation. As discrete) 135.65 346.95 P 0.6 (recombination does not require the speci\336cation of a conventional crossover rate,) 135.65 332.95 P (the variable) 135.65 318.95 T 3 F (XOVR = 1.0) 194.93 318.95 T 2 F ( is used only for compatibility) 266.89 318.95 T (.) 410.37 318.95 T (The of) 135.65 292.95 T (fspring are now mutated:) 167.07 292.95 T 3 F (SelCh = mutate\050MUT_F,SelCh,FieldD,MUTR,SUBPOP\051;) 171.65 266.95 T 2 F 0.16 (Here, the breeder genetic algorithm mutation function,) 135.65 240.95 P 3 F 0.39 (MUT_F = \325mutbga\325) 401.58 240.95 P 2 F 0.16 (, is) 517.49 240.95 P 2 (called using the high-level mutation routine,) 135.65 226.95 P 3 F 4.81 (mutate) 363.2 226.95 P 2 F 2 (, with a mutation rate of) 406.38 226.95 P 3 F 1.94 (MUTR = 1/NIND = 0.05) 135.65 212.95 P 2 F 0.81 (. The breeder genetic algorithm mutation function) 287.31 212.95 P 2.68 (requires the \336eld descriptor) 135.65 198.95 P 2.68 (,) 274.78 198.95 P 3 F 6.43 (FieldD) 283.45 198.95 P 2 F 2.68 (, so that the result of mutation will not) 326.63 198.95 P (produce values outside the bounds of the decision variables.) 135.65 184.95 T 0.23 (The objective values of all the of) 135.65 158.95 P 0.23 (fspring,) 294.7 158.95 P 3 F 0.55 (ObjVOff) 334.9 158.95 P 2 F 0.23 ( may now be calculated, again) 385.28 158.95 P (using) 135.65 144.95 T 3 F (feval) 164.64 144.95 T 2 F (:) 200.62 144.95 T 3 F (ObjVOff = feval\050OBJ_F, SelCh\051;) 171.65 118.95 T FMENDPAGE %%EndPage: "33" 34 %%Page: "34" 34 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-34) 513.33 61.29 T 2 12 Q (Of) 135.65 736.95 T (fspring may now be reinserted into the appropriate subpopulations:) 148.09 736.95 T 3 F ([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP,...) 171.65 710.95 T ([1, INSR], ObjV, ObjVOff\051;) 337.16 695.95 T 2 F 1.72 (Fitness-based reinsertion is used, but the addition of the extra parameter to the) 135.65 669.95 P 1.81 (fourth ar) 135.65 655.95 P 1.81 (gument of) 178.87 655.95 P 3 F 4.34 (reins) 234.46 655.95 P 2 F 1.81 ( speci\336es an insertion rate of) 270.44 655.95 P 3 F 4.34 (INSR = 0.9) 421.87 655.95 P 2 F 1.81 (. This) 502.52 655.95 P 3.04 (means that for each subpopulation the least-\336t 10% of the of) 135.65 641.95 P 3.04 (fspring are not) 455.62 641.95 P (reinserted.) 135.65 627.95 T 4.78 (Individuals in Multi-population GAs migrate between populations at some) 135.65 601.95 P 2.63 (interval. The T) 135.65 587.95 P 2.63 (oolbox routine) 211.69 587.95 P 3 F 6.32 (migrate) 290.25 587.95 P 2 F 2.63 ( is used to swap individuals between) 340.62 587.95 P 1.84 (subpopulations according to some migration strategy) 135.65 573.95 P 1.84 (. In this example, at every) 398.23 573.95 P 3 F (MIGGEN = 20) 135.65 559.95 T 2 F ( generations, migration takes place between subpopulations.) 214.8 559.95 T 3 F (% Migration between subpopulations) 171.65 533.95 T (if\050rem\050gen, MIGGEN\051 == 0\051) 171.65 518.95 T ([Chrom, ObjV] = migrate\050Chrom, SUBPOP, ...) 200.43 503.95 T ([MIGR, 1, 1], ObjV\051;) 380.33 488.95 T (end) 171.65 473.95 T 2 F 1.79 (Here, the most \336t 20%,) 135.65 447.95 P 3 F 4.29 (MIGR = 0.2) 258.85 447.95 P 2 F 1.79 (, of each subpopulation is selected for) 339.39 447.95 P 3.37 (migration. Nearest neighbour subpopulations then exchange these individuals) 135.65 433.95 P 2.79 (amongst their subpopulations, uniformly reinserting the immigrant individuals) 135.65 419.95 P 0.32 (\050see the) 135.65 405.95 P 0 F 0.32 (Support for Multiple Populations) 176.26 405.95 P 2 F 0.32 ( Section\051. The return matrix) 336.83 405.95 P 3 F 0.78 (Chrom) 475.02 405.95 P 2 F 0.32 ( and) 511.01 405.95 P 0.24 (vector) 135.65 391.95 P 3 F 0.58 (ObjV) 168.86 391.95 P 2 F 0.24 ( re\337ect the changes of individuals in the subpopulations as a result of) 197.64 391.95 P (migration.) 135.65 377.95 T 1.39 (The GA iterates around the generational loop until) 135.65 351.95 P 3 F 3.33 (gen = MAXGEN) 391.9 351.95 P 2 F 1.39 ( and then) 484.91 351.95 P 1.41 (terminates. Fig. 12 shows a typical solution of the harvest problem obtained by) 135.65 337.95 P 3 F (mpga) 135.65 323.95 T 2 F (.) 164.43 323.95 T 63.65 96.95 531.65 744.95 C 133.38 101.21 531.65 319.95 C 0 77 211 550 590 191.56 153.49 240.81 153.36 FMBEGINEPSF %%BeginDocument: %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: MATLAB graph %%CreationDate: 04/13/94 22:48:14 %%DocumentFonts: Times-Roman %%DocumentNeededFonts: Times-Roman %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 77 211 550 590 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 120 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc /setrgbcolor ldef /w /setlinewidth ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin % fonts for text, standard numbers and exponents %%IncludeFont: Times-Roman %line width, line cap, and joint spec 0 cap 1 setlinejoin end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 77 211 550 590 MathWorks begin bpage %%EndPageSetup %%BeginObject: graph1 1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 710 260 5677 4549 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sc} bdef /c1 { 1 1 1 sc} bdef /c2 { 1 0 0 sc} bdef /c3 { 0 1 0 sc} bdef /c4 { 0 0 1 sc} bdef /c5 { 1 1 0 sc} bdef /c6 { 1 0 1 sc} bdef /c7 { 0 1 1 sc} bdef /Helvetica 144 FMS c1 0 0 6917 5187 PR 6 w DO 4 w SO 6 w c0 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 4615 mt 899 4615 L 6258 4615 mt 6258 4615 L 899 4615 mt 6258 4615 L 899 4615 mt 899 389 L 899 4615 mt 899 4615 L 899 4615 mt 899 4561 L 899 389 mt 899 443 L 859 4776 mt (0) s 1435 4615 mt 1435 4561 L 1435 389 mt 1435 443 L 1395 4776 mt (2) s 1971 4615 mt 1971 4561 L 1971 389 mt 1971 443 L 1931 4776 mt (4) s 2507 4615 mt 2507 4561 L 2507 389 mt 2507 443 L 2467 4776 mt (6) s 3043 4615 mt 3043 4561 L 3043 389 mt 3043 443 L 3003 4776 mt (8) s 3579 4615 mt 3579 4561 L 3579 389 mt 3579 443 L 3499 4776 mt (10) s 4114 4615 mt 4114 4561 L 4114 389 mt 4114 443 L 4034 4776 mt (12) s 4650 4615 mt 4650 4561 L 4650 389 mt 4650 443 L 4570 4776 mt (14) s 5186 4615 mt 5186 4561 L 5186 389 mt 5186 443 L 5106 4776 mt (16) s 5722 4615 mt 5722 4561 L 5722 389 mt 5722 443 L 5642 4776 mt (18) s 6258 4615 mt 6258 4561 L 6258 389 mt 6258 443 L 6178 4776 mt (20) s 899 4615 mt 953 4615 L 6258 4615 mt 6204 4615 L 792 4668 mt (0) s 899 3911 mt 953 3911 L 6258 3911 mt 6204 3911 L 712 3964 mt (10) s 899 3206 mt 953 3206 L 6258 3206 mt 6204 3206 L 712 3259 mt (20) s 899 2502 mt 953 2502 L 6258 2502 mt 6204 2502 L 712 2555 mt (30) s 899 1798 mt 953 1798 L 6258 1798 mt 6204 1798 L 712 1851 mt (40) s 899 1093 mt 953 1093 L 6258 1093 mt 6204 1093 L 712 1146 mt (50) s 899 389 mt 953 389 L 6258 389 mt 6204 389 L 712 442 mt (60) s 899 4615 mt 6258 4615 L 899 389 mt 6258 389 L 899 4615 mt 899 389 L 6258 4615 mt 6258 389 L 899 389 mt 899 389 L 6258 389 mt 6258 389 L gs 899 389 5360 4227 MR c np 268 -498 268 -691 268 -535 268 -415 268 -274 268 -381 268 -226 268 -159 268 -204 267 -157 268 -95 268 -80 268 -95 268 -56 268 -33 268 -59 268 -34 268 -28 268 -21 1167 4500 20 MP stroke gr gs 0 0 256 192 MR c np end eplot %%EndObject graph 1 epage end showpage %%Trailer %%EOF %%EndDocument FMENDEPSF 0 12 Q 0 X 0 K (u) 334.85 146.66 T 0 10 Q (k) 340.85 143.66 T 0 12 Q (J) 232.65 228.4 T 5 F (Figure 12: Optimal Solution Obtained by) 214.83 124 T 6 F (mpga) 421.42 124 T 137.63 114.44 527.4 313.33 R 0.5 H 2 Z N 63.65 96.95 531.65 744.95 C -8.35 24.95 603.65 816.95 C FMENDPAGE %%EndPage: "34" 35 %%Page: "35" 35 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-35) 513.33 61.29 T 2 12 Q 0.02 (Again, like the previous example, the results of the GA search are contained in the) 135.65 736.95 P 0.13 (matrix) 135.65 722.95 P 3 F 0.31 (ObjV) 170.09 722.95 P 2 F 0.13 (. The objective value and index of the best individual are found using) 197.33 722.95 P (the function) 135.65 708.95 T 3 F (min) 196.27 708.95 T 2 F (, for example:) 217.86 708.95 T 3 F ([Y, I] = min\050ObjV\051) 171.65 682.95 T (Y =) 171.65 667.95 T (-73.2370) 200.43 652.95 T (I =) 171.65 637.95 T (50) 200.43 622.95 T 2 F 0.87 (Remembering that the sign of the objective function has been changed to form a) 135.65 596.95 P 0.99 (minimisation problem, these results correspond to an objective function value of) 135.65 582.95 P 2.46 (73.2370. The exact solution is given as 73.2376. The GA optimal solution is) 135.65 568.95 P 1.59 (therefore accurate within a 10) 135.65 554.95 P 2 10 Q 1.32 (-5) 285.2 559.75 P 2 12 Q 1.59 (error bound on the exact optimal solution. The) 297.35 554.95 P (chromosome values are displayed in Fig. 12 using:) 135.65 540.95 T 3 F (plot\050Chrom\050I,:\051\051) 171.65 514.95 T FMENDPAGE %%EndPage: "35" 36 %%Page: "36" 36 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-36) 513.33 61.29 T 1 16 Q (Demonstration Scripts) 135.65 734.29 T 2 12 Q -0.03 (A number of test functions have been implemented for use with the GA script \336les) 135.65 706.95 P 4.04 (supplied with the T) 135.65 692.95 P 4.04 (oolbox. These test functions are supplied in a separate) 239.87 692.95 P 1.62 (directory) 135.65 678.95 P 1.62 (,) 178.16 678.95 P 3 F 3.89 (test_fns) 185.78 678.95 P 2 F 1.62 (, from the main demonstrations and T) 243.35 678.95 P 1.62 (oolbox routines and) 433.13 678.95 P 1.58 (are accompanied by a postscript \336le,) 135.65 664.95 P 3 F 3.79 (test_fns.ps) 323.33 664.95 P 2 F 1.58 (, giving full details of the) 402.48 664.95 P 1.23 (problems implemented. The T) 135.65 650.95 P 1.23 (able below summarises the test functions supplied) 283.74 650.95 P (with the T) 135.65 636.95 T (oolbox.) 184.11 636.95 T (No.) 179.02 604.95 T (m-\336le name) 232.83 604.95 T (Description) 379.47 604.95 T (1) 163.25 580.95 T 3 F (objfun1) 224.45 580.95 T 2 F (De Jong\325) 310.85 580.95 T (s function 1) 353.82 580.95 T (2) 163.25 558.95 T 3 F (objfun1a) 224.45 558.95 T 2 F (axis parallel hyper) 310.85 558.95 T (-ellipsoid) 399.2 558.95 T (3) 163.25 536.95 T 3 F (objfun1b) 224.45 536.95 T 2 F (rotated hyper) 310.85 536.95 T (-ellipsoid) 374.22 536.95 T (4) 163.25 514.95 T 3 F (objfun2) 224.45 514.95 T 2 F (Rosenbrock\325) 310.85 514.95 T (s valley \050banana function\051) 371.48 514.95 T (5) 163.25 492.95 T 3 F (objfun6) 224.45 492.95 T 2 F (Rastrigin\325) 310.85 492.95 T (s function) 358.16 492.95 T (6) 163.25 470.95 T 3 F (objfun7) 224.45 470.95 T 2 F (Schwefel\325) 310.85 470.95 T (s function) 358.81 470.95 T (7) 163.25 448.95 T 3 F (objfun8) 224.45 448.95 T 2 F (Griewangk\325) 310.85 448.95 T (s function) 367.47 448.95 T (8) 163.25 426.95 T 3 F (objfun9) 224.45 426.95 T 2 F (sum of dif) 310.85 426.95 T (ferent powers) 359.94 426.95 T (9) 163.25 404.95 T 3 F (objdopi) 224.45 404.95 T 2 F (double integrator) 310.85 404.95 T (10) 163.25 382.95 T 3 F (objharv) 224.45 382.95 T 2 F (harvest problem) 310.85 382.95 T (1) 163.25 360.95 T (1) 168.8 360.95 T 3 F (objlinq) 224.45 360.95 T 2 F (discrete linear) 310.85 360.95 T (-quadratic problem) 378.21 360.95 T (12) 163.25 338.95 T 3 F (objlinq2) 224.45 338.95 T 2 F (continuous linear) 310.85 338.95 T (-quadratic problem) 393.55 338.95 T (13) 163.25 316.95 T 3 F (objpush) 224.45 316.95 T 2 F (push-cart problem) 310.85 316.95 T 157.25 620.7 157.25 309.2 2 L V 0.5 H 0 Z N 218.45 621.2 218.45 308.7 2 L V N 304.85 621.2 304.85 308.7 2 L V N 510.05 620.7 510.05 309.2 2 L V N 157 620.95 510.3 620.95 2 L V N 157.5 596.2 509.8 596.2 2 L V N 157.5 593.7 509.8 593.7 2 L V N 157 572.95 510.3 572.95 2 L V N 157 550.95 510.3 550.95 2 L V N 157 528.95 510.3 528.95 2 L V N 157 506.95 510.3 506.95 2 L V N 157 484.95 510.3 484.95 2 L V N 157 462.95 510.3 462.95 2 L V N 157 440.95 510.3 440.95 2 L V N 157 418.95 510.3 418.95 2 L V 2 H N 157 396.95 510.3 396.95 2 L V 0.5 H N 157 374.95 510.3 374.95 2 L V N 157 352.95 510.3 352.95 2 L V N 157 330.95 510.3 330.95 2 L V N 157 308.95 510.3 308.95 2 L V N FMENDPAGE %%EndPage: "36" 37 %%Page: "37" 37 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-37) 513.33 61.29 T 63.65 716.95 531.65 726.95 C 63.65 725.95 531.65 725.95 2 L 1 H 2 Z 0 X 0 K N -8.35 24.95 603.65 816.95 C 1 18 Q 0 X 0 K (Refer) 63.65 732.95 T (ences) 106.27 732.95 T 2 12 Q 2.36 ([1] D. E. Goldber) 135.65 694.95 P 2.36 (g,) 226.77 694.95 P 0 F 2.36 (Genetic Algorithms in Sear) 241.12 694.95 P 2.36 (ch, Optimization and Machine) 378.67 694.95 P (Learning) 150.05 680.95 T 2 F (, Addison W) 194.03 680.95 T (esley Publishing Company) 254.03 680.95 T (, January 1989.) 381.86 680.95 T 1.14 ([2] C. L. Karr) 135.65 658.95 P 1.14 (, \322Design of an Adaptive Fuzzy Logic Controller Using a Genetic) 204.85 658.95 P (Algorithm\323,) 150.05 644.95 T 0 F (Pr) 211.35 644.95 T (oc. ICGA 4) 222.9 644.95 T 2 F (, pp. 450-457, 1991.) 277.19 644.95 T 1.8 ([3] R. B. Holstien,) 135.65 622.95 P 0 F 1.8 (Arti\336cial Genetic Adaptation in Computer Contr) 234.46 622.95 P 1.8 (ol Systems) 476.55 622.95 P 2 F 1.8 (,) 528.65 622.95 P 7.26 (PhD Thesis, Department of Computer and Communication Sciences,) 150.05 608.95 P (University of Michigan, Ann Arbor) 150.05 594.95 T (, 1971.) 320.45 594.95 T 0.67 ([4] R. A. Caruana and J. D. Schaf) 135.65 572.95 P 0.67 (fer) 301.64 572.95 P 0.67 (, \322Representation and Hidden Bias: Gray vs.) 314.47 572.95 P (Binary Coding\323,) 150.05 558.95 T 0 F (Pr) 232.34 558.95 T (oc. 6) 243.88 558.95 T 274.98 562.79 267.2 562.79 2 L V 0.48 H 0 Z N 0 10 Q (th) 267.2 563.75 T 0 12 Q ( Int. Conf. Machine Learning) 274.98 558.95 T 2 F (, pp153-161, 1988.) 415.56 558.95 T 2.14 ([5] W) 135.65 536.95 P 2.14 (. E. Schmitendor) 164.99 536.95 P 2.14 (gf, O. Shaw) 249.67 536.95 P 2.14 (, R. Benson and S. Forrest, \322Using Genetic) 310.46 536.95 P 1.16 (Algorithms for Controller Design: Simultaneous Stabilization and Eigenvalue) 150.05 522.95 P 4.21 (Placement in a Region\323,) 150.05 508.95 P 0 F 4.21 (T) 286.49 508.95 P 4.21 (echnical Report No. CS92-9) 292.05 508.95 P 2 F 4.21 (, Dept. Computer) 439.94 508.95 P (Science, College of Engineering, University of New Mexico, 1992.) 150.05 494.95 T 1.52 ([6] M. F) 135.65 472.95 P 1.52 (. Bramlette, \322Initialization, Mutation and Selection Methods in Genetic) 178.04 472.95 P (Algorithms for Function Optimization\323,) 150.05 458.95 T 0 F (Pr) 344.94 458.95 T (oc ICGA 4) 356.49 458.95 T 2 F (, pp. 100-107, 1991.) 407.79 458.95 T 0.31 ([7] C. B. Lucasius and G. Kateman, \322T) 135.65 436.95 P 0.31 (owards Solving Subset Selection Problems) 324.51 436.95 P 2.37 (with the Aid of the Genetic Algorithm\323, In) 150.05 422.95 P 0 F 2.37 (Parallel Pr) 377.18 422.95 P 2.37 (oblem Solving fr) 433.41 422.95 P 2.37 (om) 516.99 422.95 P 2.89 (Natur) 150.05 408.95 P 2.89 (e 2) 177.6 408.95 P 2 F 2.89 (, R. M\212nner and B. Manderick, \050Eds.\051, pp. 239-247, Amsterdam:) 194.81 408.95 P (North-Holland, 1992.) 150.05 394.95 T 2.88 ([8] A. H. W) 135.65 372.95 P 2.88 (right, \322Genetic Algorithms for Real Parameter Optimization\323, In) 201.41 372.95 P 0 F -0.29 (Foundations of Genetic Algorithms) 150.05 358.95 P 2 F -0.29 (, J. E. Rawlins \050Ed.\051, Mor) 318.74 358.95 P -0.29 (gan Kaufmann, pp.) 440.31 358.95 P (205-218, 1991.) 150.05 344.95 T -0.01 ([9] Z. Michalewicz,) 135.65 322.95 P 0 F -0.01 (Genetic Algorithms + Data Structur) 233.88 322.95 P -0.01 (es = Evolution Pr) 407.41 322.95 P -0.01 (ograms) 492.67 322.95 P 2 F -0.01 (,) 528.65 322.95 P (Springer V) 150.05 308.95 T (erlag, 1992.) 201.68 308.95 T 4.12 ([10] T) 135.65 286.95 P 4.12 (. B\212ck, F) 169.19 286.95 P 4.12 (. Hof) 219.77 286.95 P 4.12 (fmeister and H.-P) 248.32 286.95 P 4.12 (. Schwefel, \322A Survey of Evolution) 340.17 286.95 P (Strategies\323,) 150.05 272.95 T 0 F (Pr) 208.67 272.95 T (oc. ICGA 4) 220.22 272.95 T 2 F (, pp. 2-10, 1991.) 274.52 272.95 T 1.27 ([1) 135.65 250.95 P 1.27 (1] J. J. Grefenstette, \322Incorporating Problem Speci\336c Knowledge into Genetic) 145.2 250.95 P 1.83 (Algorithms\323, In) 150.05 236.95 P 0 F 1.83 (Genetic Algorithms and Simulated Annealing) 232.66 236.95 P 2 F 1.83 (, pp. 42-60, L.) 457.86 236.95 P (Davis \050Ed.\051, Mor) 150.05 222.95 T (gan Kaufmann, 1987.) 231.77 222.95 T 0.89 ([12] D. Whitley) 135.65 200.95 P 0.89 (, K. Mathias and P) 212.93 200.95 P 0.89 (. Fitzhorn, \322Delta Coding: An Iterative Search) 304.45 200.95 P (Strategy for Genetic Algorithms\323,) 150.05 186.95 T 0 F (Pr) 316.27 186.95 T (oc. ICGA 4) 327.81 186.95 T 2 F (, pp. 77-84, 1991.) 382.11 186.95 T 1.8 ([13] K. A. De Jong,) 135.65 164.95 P 0 F 1.8 (Analysis of the Behaviour of a Class of Genetic Adaptive) 242.59 164.95 P 4.64 (Systems) 150.05 150.95 P 2 F 4.64 (, PhD Thesis, Dept. of Computer and Communication Sciences,) 188.02 150.95 P (University of Michigan, Ann Arbor) 150.05 136.95 T (, 1975.) 320.45 136.95 T 2.09 ([14] J. E. Baker) 135.65 114.95 P 2.09 (, \322Adaptive Selection Methods for Genetic Algorithms\323,) 217.03 114.95 P 0 F 2.09 (Pr) 505.78 114.95 P 2.09 (oc.) 517.33 114.95 P (ICGA 1) 150.05 100.95 T 2 F (, pp. 101-1) 187.02 100.95 T (1) 238.55 100.95 T (1, 1985.) 244.1 100.95 T FMENDPAGE %%EndPage: "37" 38 %%Page: "38" 38 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-38) 513.33 61.29 T 2 12 Q -0.08 ([15] J. E. Baker) 135.65 736.95 P -0.08 (, \322Reducing bias and inef) 210.55 736.95 P -0.08 (\336ciency in the selection algorithm\323,) 331.61 736.95 P 0 F -0.08 (Pr) 505.78 736.95 P -0.08 (oc.) 517.33 736.95 P (ICGA 2) 150.05 722.95 T 2 F (, pp. 14-21, 1987.) 187.02 722.95 T 0.71 ([16] L. Booker) 135.65 700.95 P 0.71 (, \322Improving search in genetic algorithms,\323 In) 208.2 700.95 P 0 F 0.71 (Genetic Algorithms) 437.33 700.95 P 4.04 (and Simulated Annealing) 150.05 686.95 P 2 F 4.04 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 279.4 686.95 P 4.04 (gan Kaufmann) 456.66 686.95 P (Publishers, 1987.) 150.05 672.95 T 0 ([17] W) 135.65 650.95 P 0 (. M. Spears and K. A. De Jong, \322An Analysis of Multi-Point Crossover\323, In) 168.85 650.95 P 0 F (Foundations of Genetic Algorithms) 150.05 636.95 T 2 F (, J. E. Rawlins \050Ed.\051, pp. 301-315, 1991.) 319.62 636.95 T 0.66 ([18] G. Syswerda, \322Uniform crossover in genetic algorithms\323, Proc. ICGA 3, pp.) 135.65 614.95 P (2-9, 1989.) 150.05 600.95 T 0.46 ([19] W) 135.65 578.95 P 0.46 (. M. Spears and K. A. De Jong, \322On the V) 169.31 578.95 P 0.46 (irtues of Parameterised Uniform) 375.38 578.95 P (Crossover\323,) 150.05 564.95 T 0 F (Pr) 210 564.95 T (oc. ICGA 4) 221.55 564.95 T 2 F (, pp.230-236, 1991.) 275.85 564.95 T 1.05 ([20] R. A. Caruana, L. A. Eshelman, J. D. Schaf) 135.65 542.95 P 1.05 (fer) 376.42 542.95 P 1.05 (, \322Representation and hidden) 389.25 542.95 P -0.3 (bias II: Eliminating de\336ning length bias in genetic search via shuf) 150.05 528.95 P -0.3 (\337e crossover\323,) 462.67 528.95 P 2.77 (In) 150.05 514.95 P 0 F 2.77 (Eleventh International Joint Confer) 165.81 514.95 P 2.77 (ence on Arti\336cial Intelligence) 345.24 514.95 P 2 F 2.77 (, N. S.) 495.79 514.95 P (Sridharan \050Ed.\051, V) 150.05 500.95 T (ol. 1, pp. 750-755, Mor) 237.1 500.95 T (gan Kaufmann Publishers, 1989.) 348.82 500.95 T 3.24 ([21] H. M\237hlenbein and D. Schlierkamp-V) 135.65 478.95 P 3.24 (oosen, \322Predictive Models for the) 357.14 478.95 P 0.37 (Breeder Genetic Algorithm\323,) 150.05 464.95 P 0 F 0.37 (Evolutionary Computation) 293.72 464.95 P 2 F 0.37 (, V) 422.36 464.95 P 0.37 (ol. 1, No. 1, pp. 25-) 435.84 464.95 P (49, 1993.) 150.05 450.95 T 1.26 ([22] H. Furuya and R. T) 135.65 428.95 P 1.26 (. Haftka, \322Genetic Algorithms for Placing Actuators on) 257.33 428.95 P (Space Structures\323,) 150.05 414.95 T 0 F (Pr) 241.64 414.95 T (oc. ICGA 5) 253.19 414.95 T 2 F (, pp. 536-542, 1993.) 307.48 414.95 T 0.3 ([23] C. Z. Janikow and Z. Michalewicz, \322An Experimental Comparison of Binary) 135.65 392.95 P 0.49 (and Floating Point Representations in Genetic Algorithms\323,) 150.05 378.95 P 0 F 0.49 (Pr) 443.33 378.95 P 0.49 (oc. ICGA 4) 454.89 378.95 P 2 F 0.49 (, pp.) 510.17 378.95 P (31-36, 1991.) 150.05 364.95 T 0.74 ([24] D. M. T) 135.65 342.95 P 0.74 (ate and A. E. Smith, \322Expected Allele Conver) 198.65 342.95 P 0.74 (gence and the Role of) 424.11 342.95 P (Mutation in Genetic Algorithms\323,) 150.05 328.95 T 0 F (Pr) 315.62 328.95 T (oc. ICGA) 327.17 328.95 T 2 F ( 5, pp.31-37, 1993.) 372.47 328.95 T 2.12 ([25] L. Davis, \322Adapting Operator Probabilities in Genetic Algorithms\323,) 135.65 306.95 P 0 F 2.12 (Pr) 505.78 306.95 P 2.12 (oc.) 517.33 306.95 P (ICGA 3) 150.05 292.95 T 2 F (, pp. 61-69, 1989.) 187.02 292.95 T 5.14 ([26] T) 135.65 270.95 P 5.14 (. C. Fogarty) 170.21 270.95 P 5.14 (, \322V) 237.02 270.95 P 5.14 (arying the Probability of Mutation in the Genetic) 260.81 270.95 P (Algorithm\323,) 150.05 256.95 T 0 F (Pr) 211.35 256.95 T (oc. ICGA 3) 222.9 256.95 T 2 F (, pp. 104-109, 1989.) 277.19 256.95 T 0.12 ([27] K. A. De Jong and J. Sarma, \322Generation Gaps Revisited\323, In) 135.65 234.95 P 0 F 0.12 ( Foundations of) 455.43 234.95 P 2.86 (Genetic Algorithms 2) 150.05 220.95 P 2 F 2.86 (, L. D. Whitley \050Ed.\051, Mor) 258.37 220.95 P 2.86 (gan Kaufmann Publishers,) 399.02 220.95 P (1993.) 150.05 206.95 T 2.13 ([28] D. Whitley) 135.65 184.95 P 2.13 (, \322The GENIT) 215.4 184.95 P 2.13 (OR algorithm and selection pressure: why rank-) 288.38 184.95 P 1.7 (based allocations of reproductive trials is best\323,) 150.05 170.95 P 0 F 1.7 ( Pr) 387.77 170.95 P 1.7 (oc. ICGA 3) 404.02 170.95 P 2 F 1.7 (, pp. 1) 461.73 170.95 P 1.7 (16-121,) 494.67 170.95 P (1989.) 150.05 156.95 T 2.82 ([29] R. Huang and T. C. Fogarty, \322Adaptive Classification and Control-Rule) 135.65 134.95 P 1.46 (Optimization Via a Learning Algorithm for Controlling a Dynamic System\323,) 150.05 120.95 P 0 F (Proc. 30th Conf. Decision and Control) 150.05 106.95 T 2 F (, Brighton, England, pp. 867-868, 1991.) 336.95 106.95 T FMENDPAGE %%EndPage: "38" 39 %%Page: "39" 39 595.3 841.9 0 FMBEGINPAGE 0 10 Q 0 X 0 K (Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T (1-39) 513.33 61.29 T 2 12 Q 0.5 ([30] T) 135.65 736.95 P 0.5 (. C. Fogarty) 165.57 736.95 P 0.5 (, \322An Incremental Genetic Algorithm for Real-T) 223.11 736.95 P 0.5 (ime Learning\323,) 458.53 736.95 P 0 F (Pr) 150.05 722.95 T (oc. 6th Int. W) 161.6 722.95 T (orkshop on Machine Learning) 225.45 722.95 T 2 F (, pp. 416-419, 1989.) 371.03 722.95 T 2.13 ([31] D. E. Goldber) 135.65 700.95 P 2.13 (g and J. Richardson, \322Genetic Algorithms with Sharing for) 232.1 700.95 P (Multimodal Function Optimization\323,) 150.05 686.95 T 0 F (Pr) 329.96 686.95 T (oc. ICGA 2) 341.51 686.95 T 2 F (, pp.41-49, 1987.) 395.8 686.95 T 0.39 ([32] H. M\237hlenbein, M. Schomisch and J. Born, \322The Parallel Genetic Algorithm) 135.65 664.95 P (as a Function Optimizer\323,) 150.05 650.95 T 0 F (Parallel Computing) 276.96 650.95 T 2 F (, No. 17, pp. 619-632, 1991.) 372.59 650.95 T -0.14 ([33] T) 135.65 628.95 P -0.14 (. Starkweather) 164.93 628.95 P -0.14 (, D. Whitley and K. Mathias, \322Optimization Using Distributed) 233.59 628.95 P 0.85 (Genetic Algorithms\323,) 150.05 614.95 P 0 F 0.85 (Pr) 258 614.95 P 0.85 (oc. Parallel Pr) 269.55 614.95 P 0.85 (oblem Solving Fr) 342.43 614.95 P 0.85 (om Natur) 426.96 614.95 P 0.85 (e 1) 473.01 614.95 P 2 F 0.85 (, Lecture) 488.18 614.95 P (Notes in Computer Science No. 496, pp. 176-185, Springer) 150.05 600.95 T (-V) 434.29 600.95 T (erlag, 1990.) 445.61 600.95 T 0.22 ([34] M. Geor) 135.65 578.95 P 0.22 (ges-Schleuter) 199.48 578.95 P 0.22 (, \322Comparison of Local Mating Strategies in Massively) 264.28 578.95 P 1.35 (Parallel Genetic Algorithms\323, In) 150.05 564.95 P 0 F 1.35 ( Parallel Pr) 309.98 564.95 P 1.35 (oblem Solving fr) 369.54 564.95 P 1.35 (om Natur) 451.08 564.95 P 1.35 (e 2) 497.64 564.95 P 2 F 1.35 (, R.) 513.3 564.95 P 1.77 (M\212nner and B. Manderick, \050Eds.\051, pp. 553-562, Amsterdam: North-Holland,) 150.05 550.95 P (1992.) 150.05 536.95 T FMENDPAGE %%EndPage: "39" 40 %%Trailer %%BoundingBox: 0 0 595.3 841.9 %%Pages: 39 1 %%DocumentFonts: Times-Italic %%+ Times-Bold %%+ Times-Roman %%+ Courier %%+ Symbol %%+ Times-BoldItalic %%+ Courier-BoldOblique