{ "cells": [ { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "
\n", "\n", "UFF logo\n", "\n", "\n", "IC logo\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "-" } }, "source": [ "# Evolutionary Multi-Objective Optimization\n", "\n", "## Luis Martí, [IC](http://www.ic.uff.br)/[UFF](http://www.uff.br)\n", "\n", "[http://lmarti.com](http://lmarti.com); [lmarti@ic.uff.br](mailto:lmarti@ic.uff.br) \n", "\n", "[Advanced Evolutionary Computation: Theory and Practice](http://lmarti.com/aec-2014) " ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "source": [ "This notebook is better viewed rendered as slides. You can convert it to slides and view them by:\n", "- using [nbconvert](http://ipython.org/ipython-doc/1/interactive/nbconvert.html) with a command like:\n", " ```bash\n", " $ ipython nbconvert --to slides --post serve \n", " ```\n", "- installing [Reveal.js - Jupyter/IPython Slideshow Extension](https://github.com/damianavila/live_reveal)\n", "- using the online [IPython notebook slide viewer](https://slideviewer.herokuapp.com/) (some slides of the notebook might not be properly rendered).\n", "\n", "This and other related IPython notebooks can be found at the course github repository:\n", "* [https://github.com/lmarti/evolutionary-computation-course](https://github.com/lmarti/evolutionary-computation-course)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# In this notebook\n", "\n", "* Present the basic concepts related to evolutionary multi-objective optimization algorithms.\n", "* The Non-dominated Sorting Genetic Algorithm II (NSGA-II).\n", "* Benchmark test problems.\n", "* Experiment design and results comparison." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## How can we handle multiple conflicting objectives?\n", "\n", "Even choosing a fruit implies dealing with conflicting objectives.\n", "\n", "
\n", "taken from http://xkcd.com/388/
" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# [Multi-objective optimization](http://en.wikipedia.org/wiki/Multi-objective_optimization)\n", "\n", "* Most -*if not all*- optimization problems involve more than one objective function to be optimized simultaneously.\n", "* For example, you must optimize a given feature of an object while keeping under control the resources needed to elaborate that object.\n", "* Sometimes those other objectives are converted to constraints or fixed to default values, but that does not means that they are there.\n", "* Multi-objective optimization is also known as *multi-objective programming*, *vector optimization*, *multicriteria optimization*, *multiattribute optimization* or *Pareto optimization* (and probably by other names, depending on the field).\n", "* Multi-objective optimization has been applied in [many fields of science](http://en.wikipedia.org/wiki/Multi-objective_optimization#Examples_of_multi-objective_optimization_applications), including engineering, economics and logistics (see the section on applications for detailed examples) where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## A Multi-objective Optimization Problem (MOP)\n", "\n", "$$\n", "\\renewcommand{\\vec}[1]{\\mathbf{#1}}\n", "\\newcommand{\\set}[1]{\\mathcal{#1}}\n", "\\newcommand{\\dom}{\\preccurlyeq}\n", "\\left.\n", "\\begin{array}{rl}\n", "\\mathrm{minimize} & \\vec{F}(\\vec{x})=\\langle f_1(\\vec{x}),\\ldots,f_M(\\vec{x})\\rangle\\,,\\\\ \n", "\\mathrm{subject}\\ \\mathrm{to} & c_1(\\vec{x}),\\ldots,c_C(\\vec{x})\\le 0\\,,\\\\\n", "\t\t\t\t\t\t\t & d_1(\\vec{x}),\\ldots,d_D(\\vec{x})= 0\\,,\\\\\n", "& \\text{with}\\ \\vec{x}\\in\\set{D}\\,,\n", "\\end{array}\\right\\}\n", "$$\n", "\n", "* $\\mathcal{D}$ is known as the *decision set* or *search set*.\n", "* functions $f_1(\\mathbf{x}),\\ldots,f_M(\\mathbf{x})$ are the *objective functions*. If $M=1$ the problem reduces to a single-objective optimization problem. \n", "* Image set, $\\set{O}$, result of the projection of $\\set{D}$ via $f_1(\\vec{x}),\\ldots,f_M(\\vec{x})$ is called *objective set* ($\\vec{F}:\\set{D}\\rightarrow\\set{O}$).\n", "* $c_1(\\vec{x}),\\ldots,c_C(\\vec{x})\\le 0$ and $d_1(\\vec{x}),\\ldots,d_D(\\vec{x})= 0$ express the constraints imposed on the values of $\\vec{x}$.\n", "\n", "*Note:* In case you are -still- wondering, a maximization problem can be posed as the minimization one: $\\min\\ -\\vec{F}(\\vec{x})$." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Example: A two variables and two objectives MOP\n", "" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## MOP (optimal) solutions\n", "\n", "Usually, there is not a unique solution that minimizes all objective functions simultaneously, but, instead, a set of equally good *trade-off* solutions.\n", "\n", "* *Optimality* can be defined in terms of the [*Pareto dominance*](https://en.wikipedia.org/wiki/Pareto_efficiency) relation. That is, having $\\vec{x},\\vec{y}\\in\\set{D}$, $\\vec{x}$ is said to dominate $\\vec{y}$ (expressed as $\\vec{x}\\dom\\vec{y}$) iff $\\forall f_j$, $f_j(\\vec{x})\\leq f_j(\\vec{y})$ and $\\exists f_i$ such that $f_i(\\vec{x})< f_i(\\vec{y})$.\n", "* Having the set $\\set{A}$. $\\set{A}^\\ast$, the *non-dominated subset* of $\\set{A}$, is defined as\n", "\n", "$$\n", "\\set{A}^\\ast=\\left\\{ \\vec{x}\\in\\set{A} \\left|\\not\\exists\\vec{y}\\in\\set{A}:\\vec{y}\\dom\\vec{x}\\right.\\right\\}.\n", "$$\n", "\n", "* The *Pareto-optimal set*, $\\set{D}^{\\ast}$, is the solution of the problem. It is the subset of non-dominated elements of $\\set{D}$. It is also known as the *efficient set*.\n", "* It consists of solutions that cannot be improved in any of the objectives without degrading at least one of the other objectives.\n", "* Its image in objective set is called the *Pareto-optimal front*, $\\set{O}^\\ast$.\n", "* Evolutionary algorithms generally yield a set of non-dominated solutions, $\\set{P}^\\ast$, that approximates $\\set{D}^{\\ast}$.\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "As usual, we need some initialization and configuration." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "internals": {}, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import time, array, random, copy, math\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n", "plt.rc('text', usetex=True)\n", "plt.rc('font', family='serif')\n", "plt.rcParams['text.latex.preamble'] ='\\\\usepackage{libertine}\\n\\\\usepackage[utf8]{inputenc}'\n", "\n", "import seaborn\n", "seaborn.set(style='whitegrid')\n", "seaborn.set_context('notebook')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from deap import algorithms, base, benchmarks, tools, creator" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "subslide" } }, "source": [ "Planting a constant seed to always have the same results (and avoid surprises in class). -*you should not do this in a real-world case!*" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "random.seed(a=42)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "# Visualizing the Pareto dominance relation\n", "\n", "* To start, lets have a visual example of the Pareto dominance relationship in action.\n", "* In this notebook we will deal with two-objective problems in order to simplify visualization. \n", "* Therefore, we can create:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "creator.create(\"FitnessMin\", base.Fitness, weights=(-1.0,-1.0))\n", "creator.create(\"Individual\", array.array, typecode='d', \n", " fitness=creator.FitnessMin)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Let's use an illustrative MOP problem: Dent\n", "\n", "$$\n", "\\begin{array}{rl}\n", "\\text{minimize} & f_1(\\vec{x}),f_2(\\vec{x}) \\\\\n", "\\text{such that} & f_1(\\vec{x}) = \\frac{1}{2}\\left( \\sqrt{1 + (x_1 + x_2)^2} \\sqrt{1 + (x_1 - x_2)^2} + x_1 -x_2\\right) + d,\\\\\n", " & f_2(\\vec{x}) = \\frac{1}{2}\\left( \\sqrt{1 + (x_1 + x_2)^2} \\sqrt{1 + (x_1 - x_2)^2} - x_1 -x_2\\right) + d,\\\\\n", "\\text{with}& d = \\lambda e^{-\\left(x_1-x_2\\right)^2}\\ (\\text{generally }\\lambda=0.85) \\text{ and } \\vec{x}\\in \\left[-1.5,1.5\\right]^2.\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Implementing the Dent problem" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def dent(individual, lbda = 0.85):\n", " \"\"\" \n", " Implements the test problem Dent\n", " Num. variables = 2; bounds in [-1.5, 1.5]; num. objetives = 2.\n", " @author Cesar Revelo\n", " \"\"\"\n", " d = lbda * math.exp(-(individual[0] - individual[1]) ** 2) \n", " f1 = 0.5 * (math.sqrt(1 + (individual[0] + individual[1]) ** 2) + \\\n", " math.sqrt(1 + (individual[0] - individual[1]) ** 2) + \\\n", " individual[0] - individual[1]) + d\n", " f2 = 0.5 * (math.sqrt(1 + (individual[0] + individual[1]) ** 2) + \\\n", " math.sqrt(1 + (individual[0] - individual[1]) ** 2) - \\\n", " individual[0] + individual[1]) + d\n", " return f1, f2" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Preparing a DEAP `toolbox` with Dent." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox = base.Toolbox()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "BOUND_LOW, BOUND_UP = -1.5, 1.5\n", "NDIM = 2\n", "# toolbox.register(\"evaluate\", lambda ind: benchmarks.dtlz2(ind, 2))\n", "toolbox.register(\"evaluate\", dent)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "Defining attributes, individuals and population." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def uniform(low, up, size=None):\n", " try:\n", " return [random.uniform(a, b) for a, b in zip(low, up)]\n", " except TypeError:\n", " return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n", "\n", "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n", "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n", "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Creating an example population distributed as a mesh." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "num_samples = 50\n", "limits = [np.arange(BOUND_LOW, BOUND_UP, (BOUND_UP - BOUND_LOW)/num_samples)] * NDIM\n", "sample_x = np.meshgrid(*limits)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "flat = []\n", "for i in range(len(sample_x)):\n", " x_i = sample_x[i]\n", " flat.append(x_i.reshape(num_samples**NDIM))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "example_pop = toolbox.population(n=num_samples**NDIM)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "for i, ind in enumerate(example_pop):\n", " for j in range(len(flat)):\n", " ind[j] = flat[j][i]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "fitnesses = toolbox.map(toolbox.evaluate, example_pop)\n", "for ind, fit in zip(example_pop, fitnesses):\n", " ind.fitness.values = fit" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "We also need `a_given_individual`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "a_given_individual = toolbox.population(n=1)[0]\n", "a_given_individual[0] = 0.5\n", "a_given_individual[1] = 0.5" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "a_given_individual.fitness.values = toolbox.evaluate(a_given_individual)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Implementing the Pareto dominance relation between two individulas." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def pareto_dominance(ind1,ind2):\n", " 'Returns `True` if `ind1` dominates `ind2`.'\n", " extrictly_better = False\n", " for item1 in ind1.fitness.values:\n", " for item2 in ind2.fitness.values:\n", " if item1 > item2:\n", " return False\n", " if not extrictly_better and item1 < item2:\n", " extrictly_better = True\n", " return extrictly_better" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "*Note:* Bear in mind that DEAP comes with a Pareto dominance relation that probably is more efficient than this implementation.\n", "```python\n", "def pareto_dominance(x,y):\n", " return tools.emo.isDominated(x.fitness.values, y.fitness.values)\n", "```" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Lets compute the set of individuals that are `dominated` by `a_given_individual`, the ones that dominate it (its `dominators`) and the remaining ones." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "dominated = [ind for ind in example_pop if pareto_dominance(a_given_individual, ind)]\n", "dominators = [ind for ind in example_pop if pareto_dominance(ind, a_given_individual)]\n", "others = [ind for ind in example_pop if not ind in dominated and not ind in dominators]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def plot_dent():\n", " 'Plots the points in decision and objective spaces.'\n", " plt.figure(figsize=(10,5))\n", " plt.subplot(1,2,1)\n", " for ind in dominators: plt.plot(ind[0], ind[1], 'r.')\n", " for ind in dominated: plt.plot(ind[0], ind[1], 'g.')\n", " for ind in others: plt.plot(ind[0], ind[1], 'k.', ms=3)\n", " plt.plot(a_given_individual[0], a_given_individual[1], 'bo', ms=6);\n", " plt.xlabel('$x_1$');plt.ylabel('$x_2$');\n", " plt.title('Decision space');\n", " plt.subplot(1,2,2)\n", " for ind in dominators: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'r.', alpha=0.7)\n", " for ind in dominated: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'g.', alpha=0.7)\n", " for ind in others: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', alpha=0.7, ms=3)\n", " plt.plot(a_given_individual.fitness.values[0], a_given_individual.fitness.values[1], 'bo', ms=6);\n", " plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');\n", " plt.xlim((0.5,3.6));plt.ylim((0.5,3.6));\n", " plt.title('Objective space');\n", " plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Having `a_given_individual` (blue dot) we can now plot those that are dominated by it (in green), those that dominate it (in red) and those that are uncomparable." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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Dg4OanZ0tub3E0lgAAAA8xQKxTa+99ppmZmZWXM9kMiwQAwDqSmom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\nVqyAz+fj0rtNq4uPTPesZH6zZvFfV6XVxUemz+869Dox1n/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UNVcrr43AVwMI/nUQB791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\nX8fevXuxd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AOY/NlnwPvvh8eOeDfyc50pBw9iSmvr2Isi2vZ2ILKWubkYFwphyr/+K6ZM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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 348, "width": 708 } }, "output_type": "display_data" } ], "source": [ "plot_dent()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Obtaining the nondominated front." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "non_dom = tools.sortNondominated(example_pop, k=len(example_pop), first_front_only=True)[0]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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XjHINA7k0xM/ucP36dUxPT2NubjZSikSf3SERIyNUzQyW4KgnIsomqXw5ZXaN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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 316, "width": 313 } }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(5,5))\n", "for ind in example_pop:\n", " plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', ms=3, alpha=0.5)\n", "for ind in non_dom:\n", " plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'bo', alpha=0.74, ms=5)\n", "plt.title('Pareto-optimal front')" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# The Non-dominated Sorting Genetic Algorithm (NSGA-II)\n", "\n", "* NSGA-II algorithm is one of the pillars of the EMO field.\n", " * Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., *A fast and elitist multiobjective genetic algorithm: NSGA-II*, IEEE Transactions on Evolutionary Computation, vol.6, no.2, pp.182,197, Apr 2002 doi: [10.1109/4235.996017](http://dx.doi.org/10.1109/4235.996017).\n", "* Fitness assignment relies on the Pareto dominance relation:\n", " 1. Rank individuals according the dominance relations established between them. \n", " 2. Individuals with the same domination rank are then compared using a local crowding distance." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## NSGA-II fitness in detail\n", "\n", "* The first step consists in classifying the individuals in a series of categories $\\mathcal{F}_1,\\ldots,\\mathcal{F}_L$. \n", "* Each of these categories store individuals that are only dominated by the elements of the previous categories,\n", "$$\n", "\\begin{array}{rl}\n", "\t\\forall \\vec{x}\\in\\set{F}_i: &\\exists \\vec{y}\\in\\set{F}_{i-1} \\text{ such that } \\vec{y}\\dom\\vec{x},\\text{ and }\\\\ \n", "\t &\\not\\exists\\vec{z}\\in \\set{P}_t\\setminus\\left( \\set{F}_1\\cup\\ldots\\cup\\set{F}_{i-1}\n", "\t \\right)\\text{ that }\\vec{z}\\dom\\vec{x}\\,;\n", "\\end{array}\n", "$$\n", "with $\\mathcal{F}_1$ equal to $\\mathcal{P}_t^\\ast$, the set of non-dominated individuals of $\\mathcal{P}_t$.\n", "\n", "* After all individuals are ranked a local crowding distance is assigned to them. \n", "* The use of this distance primes individuals more isolated with respect to others. " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Crowding distance\n", "\n", "The assignment process goes as follows,\n", "\n", "* for each category set $\\set{F}_l$, having $f_l=|\\set{F}_l|$,\n", " * for each individual $\\vec{x}_i\\in\\set{F}_l$, set $d_{i}=0$.\n", " * for each objective function $m=1,\\ldots,M$,\n", " * $\\vec{I}=\\mathrm{sort}\\left(\\set{F}_l,m\\right)$ (generate index vector).\n", " * $d_{I_1}^{(l)}=d_{I_{f_l}}^{(l)}=\\infty$.\n", " * for $i=2,\\ldots,f_l-1$,\n", " * Update the remaining distances as,\n", " $$\n", " d_i = d_i + \\frac{f_m\\left(\\vec{x}_{I_{i+1}}\\right)-f_m\\left(\\vec{x}_{I_{i+1}}\\right)}\n", "\t\t\t {f_m\\left(\\vec{x}_{I_{1}}\\right)-f_m\\left(\\vec{x}_{I_{f_l}}\\right)}\\,.\n", " $$\n", "\n", "Here the $\\mathrm{sort}\\left(\\set{F},m\\right)$ function produces an ordered index vector $\\vec{I}$ with respect to objective function $m$. " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "Sorting the population by rank and distance.\n", "\n", "* Having the individual ranks and their local distances they are sorted using the crowded comparison operator, stated as: \n", " * An individual $\\vec{x}_i$ _is better than_ $\\vec{x}_j$ if:\n", " * $\\vec{x}_i$ has a better rank: $\\vec{x}_i\\in\\set{F}_k$, $\\vec{x}_j\\in\\set{F}_l$ and $kd_j$.\n", " \n", "**Now we have key element of the the non-dominated sorting GA.**" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Implementing NSGA-II\n", "\n", "We will deal with [DTLZ3](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/dtlz3/), which is a more difficult test problem.\n", "\n", "* DTLZ problems can be configured to have as many objectives as desired, but as we want to visualize results we will stick to two objectives.\n", "* DTLZ3 is a (more complex) version of [DTLZ2](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/dtlz2/).\n", "* The Pareto-optimal front of DTLZ3 lies in the first [orthant](http://en.wikipedia.org/wiki/Orthant) of a unit (radius 1) hypersphere located at the coordinate origin ($\\vec{0}$).\n", "* It has many local optima that run parallel to the global optima and render the optimization process more complicated.\n", "\n", "
\n", "from Coello Coello, Lamont and Van Veldhuizen (2007) Evolutionary Algorithms for Solving Multi-Objective Problems, Second Edition. Springer [Appendix E](http://www.cs.cinvestav.mx/~emoobook/apendix-e/apendix-e.html).
" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "New `toolbox` instance with the necessary components." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox = base.Toolbox()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define problem domain as $\\vec{x}\\in\\left[0,1\\right]^{30}$ and a two-objective DTLZ3 instance." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "NDIM = 30 \n", "BOUND_LOW, BOUND_UP = 0.0, 1.0\n", "toolbox.register(\"evaluate\", lambda ind: benchmarks.dtlz3(ind, 2))" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "Describing attributes, individuals and population and defining the selection, mating and mutation operators." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n", "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n", "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n", "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n", "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n", "toolbox.register(\"select\", tools.selNSGA2)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "Let's also use the `toolbox` to store other configuration parameters of the algorithm. This will show itself usefull when performing massive experiments." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox.pop_size = 50\n", "toolbox.max_gen = 1000\n", "toolbox.mut_prob = 0.2" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## A compact NSGA-II implementation\n", "\n", "Storing all the required information in the `toolbox` and using DEAP's `algorithms.eaMuPlusLambda` function allows us to create a very compact -albeit not a 100% exact copy of the original- implementation of NSGA-II." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def run_ea(toolbox, stats=None, verbose=False):\n", " pop = toolbox.population(n=toolbox.pop_size)\n", " pop = toolbox.select(pop, len(pop))\n", " return algorithms.eaMuPlusLambda(pop, toolbox, mu=toolbox.pop_size, \n", " lambda_=toolbox.pop_size, \n", " cxpb=1-toolbox.mut_prob,\n", " mutpb=toolbox.mut_prob, \n", " stats=stats, \n", " ngen=toolbox.max_gen, \n", " verbose=verbose)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Running the algorithm" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "We are now ready to run our NSGA-II." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 20.5 s, sys: 234 ms, total: 20.7 s\n", "Wall time: 22 s\n" ] } ], "source": [ "%time res,_ = run_ea(toolbox)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "We can now get the Pareto fronts in the results (`res`)." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "fronts = tools.emo.sortLogNondominated(res, len(res))" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Resulting Pareto fronts" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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1c331rBr/8n/Tvk9/WjUul1RXJ0djo+ra23Xw1VEKe5WRnEc2bt26pd7eXnk8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\n5S9nbcN3OzcPbnHt7OxM2epeKoSNEuG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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 263, "width": 269 } }, "output_type": "display_data" } ], "source": [ "plot_colors = seaborn.color_palette(\"Set1\", n_colors=10)\n", "fig, ax = plt.subplots(1, figsize=(4,4))\n", "for i,inds in enumerate(fronts):\n", " par = [toolbox.evaluate(ind) for ind in inds]\n", " df = pd.DataFrame(par)\n", " df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n", " x=df.columns[0], y=df.columns[1], \n", " color=plot_colors[i])\n", "plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "* It is better to make an animated plot of the evolution as it takes place." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Animating the evolutionary process" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "We create a `stats` to store the individuals not only their objective function values." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "stats = tools.Statistics()\n", "stats.register(\"pop\", copy.deepcopy)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox.max_gen = 1000 # we need more generations!" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "Re-run the algorithm to get the data necessary for plotting." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 20.9 s, sys: 266 ms, total: 21.2 s\n", "Wall time: 21.6 s\n" ] } ], "source": [ "%time res, logbook = run_ea(toolbox, stats=stats)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "from matplotlib import animation\n", "from IPython.display import HTML" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def animate(frame_index, logbook):\n", " 'Updates all plots to match frame _i_ of the animation.'\n", " ax.clear() \n", " fronts = tools.emo.sortLogNondominated(logbook.select('pop')[frame_index], \n", " len(logbook.select('pop')[frame_index]))\n", " for i,inds in enumerate(fronts):\n", " par = [toolbox.evaluate(ind) for ind in inds]\n", " df = pd.DataFrame(par)\n", " df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n", " x=df.columns[0], y=df.columns[1], alpha=0.47,\n", " color=plot_colors[i % len(plot_colors)])\n", " \n", " ax.set_title('$t=$' + str(frame_index))\n", " ax.set_xlabel('$f_1(\\mathbf{x})$');ax.set_ylabel('$f_2(\\mathbf{x})$')\n", " return []" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "fig = plt.figure(figsize=(4,4))\n", "ax = fig.gca()\n", "anim = animation.FuncAnimation(fig, lambda i: animate(i, logbook), \n", " frames=len(logbook), interval=60, \n", " blit=True)\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "Here it is clearly visible how the algorithm \"jumps\" from one local-optimum to a better one as evolution takes place." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# MOP benchmark problem toolkits\n", "\n", "Each problem instance is meant to test the algorithms with regard with a given feature: local optima, convexity, discontinuity, bias, or a combination of them.\n", "\n", "* [*ZDT1-6*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): Two-objective problems with a fixed number of decision variables.\n", " * E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/zdt2000a.pdf))\n", "* [*DTLZ1-7*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): $m$-objective problems with $n$ variables.\n", " * K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/dtlz2002a.pdf))" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "* [*CEC'09*](http://dces.essex.ac.uk/staff/zhang/moeacompetition09.htm): Two- and three- objective problems that very complex Pareto sets.\n", " * Zhang, Q., Zhou, A., Zhao, S., & Suganthan, P. N. (2009). Multiobjective optimization test instances for the CEC 2009 special session and competition. In 2009 IEEE Congress on Evolutionary Computation (pp. 1–30). ([pdf](http://dces.essex.ac.uk/staff/zhang/MOEAcompetition/cec09testproblem0904.pdf.pdf))\n", "* [*WFG1-9*](http://www.wfg.csse.uwa.edu.au/publications.html#toolkit): $m$-objective problems with $n$ variables, very complex.\n", " * Huband, S., Hingston, P., Barone, L., & While, L. (2006). A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation, 10(5), 477–506. doi:10.1109/TEVC.2005.861417" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "How does our NSGA-II behaves when faced with different benchmark problems?" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "problem_instances = {'ZDT1': benchmarks.zdt1, 'ZDT2': benchmarks.zdt2,\n", " 'ZDT3': benchmarks.zdt3, 'ZDT4': benchmarks.zdt4,\n", " 'DTLZ1': lambda ind: benchmarks.dtlz1(ind,2),\n", " 'DTLZ2': lambda ind: benchmarks.dtlz2(ind,2),\n", " 'DTLZ3': lambda ind: benchmarks.dtlz3(ind,2),\n", " 'DTLZ4': lambda ind: benchmarks.dtlz4(ind,2, 100),\n", " 'DTLZ5': lambda ind: benchmarks.dtlz5(ind,2),\n", " 'DTLZ6': lambda ind: benchmarks.dtlz6(ind,2),\n", " 'DTLZ7': lambda ind: benchmarks.dtlz7(ind,2)}" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 11, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "toolbox.max_gen = 1000\n", "\n", "stats = tools.Statistics(lambda ind: ind.fitness.values)\n", "stats.register(\"obj_vals\", np.copy)\n", "\n", "def run_problem(toolbox, problem):\n", " toolbox.register('evaluate', problem)\n", " return run_ea(toolbox, stats=stats)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 11 }, "slideshow": { "slide_type": "-" } }, "source": [ "Running NSGA-II solving all problems. Now it takes longer." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 3min 34s, sys: 1.95 s, total: 3min 36s\n", "Wall time: 3min 41s\n" ] } ], "source": [ "%time results = {problem: run_problem(toolbox, problem_instances[problem]) for problem in problem_instances}" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Creating this animation takes more programming effort." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "class MultiProblemAnimation:\n", " def init(self, fig, results):\n", " self.results = results\n", " self.axs = [fig.add_subplot(3,4,i+1) for i in range(len(results))]\n", " self.plots =[]\n", " for i, problem in enumerate(sorted(results)):\n", " (res, logbook) = self.results[problem]\n", " pop = pd.DataFrame(data=logbook.select('obj_vals')[0])\n", " plot = self.axs[i].plot(pop[0], pop[1], 'b.', alpha=0.47)[0]\n", " self.plots.append(plot)\n", " fig.tight_layout()\n", " \n", " def animate(self, t):\n", " 'Updates all plots to match frame _i_ of the animation.'\n", " for i, problem in enumerate(sorted(results)):\n", " #self.axs[i].clear()\n", " (res, logbook) = self.results[problem]\n", " pop = pd.DataFrame(data=logbook.select('obj_vals')[t])\n", " self.plots[i].set_data(pop[0], pop[1])\n", " self.axs[i].set_title(problem + '; $t=' + str(t)+'$') \n", " self.axs[i].set_xlim((0, max(1,pop.max()[0])))\n", " self.axs[i].set_ylim((0, max(1,pop.max()[1])))\n", " return self.axs" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "mpa = MultiProblemAnimation()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "fig = plt.figure(figsize=(14,6))\n", "anim = animation.FuncAnimation(fig, mpa.animate, init_func=mpa.init(fig,results), \n", " frames=toolbox.max_gen, interval=60, blit=True)\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(anim.to_html5_video())" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "* It is interesting how the algorithm deals with each problem: clearly some problems are harder than others.\n", "* In some cases it \"hits\" the Pareto front and then slowly explores it.\n", "\n", "**Read more about this in the class materials.**" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "# Experiment design and reporting results\n", "\n", "* Watching an animation of an EMO algorithm solve a problem is certainly fun. \n", "* It also allows us to understand many particularities of the problem being solved.\n", "* But, as [Carlos Coello](http://delta.cs.cinvestav.mx/~ccoello/) would say, we are *not* in an art appreciation class.\n", "* We should follow the key concepts provided by the [scientific method](http://en.wikipedia.org/wiki/Scientific_method).\n", "* I urge you to study the [experimental design](http://en.wikipedia.org/wiki/Design_of_experiments) topic in depth as it is an essential knowledge.\n", "\n", "**Evolutionary algorithms are stochastic algorithms, therefore their results must be assessed by repeating experiments until you reach an statistically valid conclusion.** " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## An illustrative simple/sample experiment\n", "\n", "Let's make a relatively simple but very important experiment:\n", "\n", "* **Question**: In our NSGA-II applied to a two-objective DTLZ3 problem: Is it more important to have a big population and let the algorithm run for a few iterations or is better to have a small population and let the algorithm run for larger number of iterations.\n", "* **Procedure**: We must perform an experiment testing different population sizes and maximum number of iterations while keeping the other parameters constant." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "### Notation\n", "\n", "As usual we need to establish some notation:\n", "\n", "* *Multi-objective problem* (or just *problem*): A multi-objective optimization problem, as defined above.\n", "* *MOEA*: An evolutionary computation method used to solve multi-objective problems.\n", "* *Experiment*: a combination of problem and MOEA and a set of values of their parameters.\n", "* *Experiment run*: The result of running an experiment.\n", "* We will use `toolbox` instances to define experiments. " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "We start by creating a `toolbox` that will contain the configuration that will be shared across all experiments." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "toolbox = base.Toolbox()" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "BOUND_LOW, BOUND_UP = 0.0, 1.0\n", "NDIM = 30\n", "# the explanation of this... a few lines bellow\n", "def eval_helper(ind):\n", " return benchmarks.dtlz3(ind, 2)\n", "\n", "toolbox.register(\"evaluate\", eval_helper)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def uniform(low, up, size=None):\n", " try:\n", " return [random.uniform(a, b) for a, b in zip(low, up)]\n", " except TypeError:\n", " return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n", "\n", "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n", "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n", "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n", "\n", "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n", "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n", "\n", "toolbox.register(\"select\", tools.selNSGA2)\n", "\n", "toolbox.mut_prob = 0.15" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "We add a `experiment_name` to `toolbox` that we will fill up later on. Here $n\\mathrm{pop}$ denotes the population size and $t_\\mathrm{max}$ the max. number of iterations." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "experiment_name = \"$n_\\mathrm{{pop}}={0};\\ t_\\mathrm{{max}}={1}$\"" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "total_evals = 500" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91 }, "slideshow": { "slide_type": "-" } }, "source": [ "We can now replicate this toolbox instance and then modify the mutation probabilities." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true, "internals": { "frag_helper": "fragment_end", "frag_number": 91 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "pop_sizes = (10,50,100)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": true }, "outputs": [], "source": [ "toolboxes=list([copy.deepcopy(toolbox) for _ in range(len(pop_sizes))])" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "Now `toolboxes` is a list of copies of the same toolbox. One for each experiment configuration (population size)." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 91, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "...but we still have to set the population sizes in the elements of `toolboxes`." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 91 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "for pop_size, toolbox in zip(pop_sizes, toolboxes):\n", " toolbox.pop_size = pop_size\n", " toolbox.max_gen = total_evals // pop_size\n", " toolbox.experiment_name = experiment_name.format(toolbox.pop_size, toolbox.max_gen)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ 10 50\n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ 50 10\n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ 100 5\n" ] } ], "source": [ "for toolbox in toolboxes:\n", " print(toolbox.experiment_name, toolbox.pop_size, toolbox.max_gen)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Experiment design\n", "\n", "As we are dealing with stochastic methods their results should be reported relying on an statistical analysis.\n", "\n", "* A given experiment (a `toolbox` instance in our case) should be repeated a *sufficient* amount of times. \n", "* In theory, the more runs the better, but how much in enough? In practice, we could say that about *30* runs is enough.\n", "* The non-dominated fronts produced by each experiment run should be compared to each other. \n", "* We have seen in class that a number of *performance indicators*, like the *hypervolume*, *additive* and *multiplicative epsilon indicators*, among others, have been proposed for that task.\n", "* We can use statistical visualizations like [box plots](http://en.wikipedia.org/wiki/Box_plot) or [violin plots](http://en.wikipedia.org/wiki/Violin_plot) to make a visual assessment of the indicator values produced in each run.\n", "* We must apply a set of [statistical hypothesis tests](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing) in order to reach an statistically valid judgment of the results of an algorithms. \n", "\n", "\n", "_Note_: I personally like the number [42](http://en.wikipedia.org/wiki/42_%28number%29) as it is the [answer to The Ultimate Question of Life, the Universe, and Everything](http://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life.2C_the_Universe.2C_and_Everything_.2842.29)." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "number_of_runs = 42" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "### Running experiments in parallel \n", "As we are now solving more demanding problems it would be nice to make our algorithms to run in parallel and profit from modern multi-core CPUs.\n", "\n", "* In DEAP it is very simple to parallelize an algorithm (if it has been properly programmed) by providing a parallel `map()` function via the `toolbox`.\n", "* Local parallelization can be achieved using Python's [`multiprocessing`](https://docs.python.org/2/library/multiprocessing.html) or [`concurrent.futures`](https://docs.python.org/3/library/concurrent.futures.html) modules.\n", "* Cluster parallelization can be achieved using IPython Parallel or [SCOOP](http://en.wikipedia.org/wiki/Python_SCOOP_%28software%29)." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Progress feedback\n", "\n", "* Another issue with these long experiments has to do being patient.\n", "* A little bit of feedback on the experiment execution would be cool.\n", "* We can use the integer progress bar from [IPython widgets](http://nbviewer.ipython.org/github/jvns/ipython/blob/master/examples/Interactive%20Widgets/Index.ipynb) and report every time an experiment run is finished." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "from ipywidgets import IntProgress\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "### A side-effect of using process-based parallelization\n", "\n", "Process-based parallelization based on `multiprocessing` requires that the parameters passed to `map()` be [pickleable](https://docs.python.org/3.4/library/pickle.html).\n", "\n", "* The direct consequence is that `lambda` functions can not be directly used. \n", "* This is will certainly ruin the party to all `lambda` fans out there! *-me included*.\n", "* Hence we need to write some wrapper functions instead.\n", "* But, that wrapper function can take care of filtering out dominated individuals in the results." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def run_algo_wrapper(toolbox):\n", " result, _ = run_ea(toolbox)\n", " local_pareto_set = tools.emo.sortLogNondominated(result, len(result), first_front_only=True)\n", " return local_pareto_set" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "# All set! Run the experiments..." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 331 ms, sys: 97.2 ms, total: 429 ms\n", "Wall time: 15.1 s\n" ] } ], "source": [ "%%time\n", "import concurrent.futures\n", "progress_bar = IntProgress(description=\"000/000\", max=len(toolboxes)*number_of_runs)\n", "display(progress_bar)\n", "\n", "results = {toolbox.experiment_name:[] for toolbox in toolboxes}\n", "with concurrent.futures.ProcessPoolExecutor() as executor:\n", " # Submit all the tasks...\n", " futures = {executor.submit(run_algo_wrapper, toolbox): toolbox\n", " for _ in range(number_of_runs)\n", " for toolbox in toolboxes}\n", " \n", " # ...and wait for them to finish.\n", " for future in concurrent.futures.as_completed(futures):\n", " tb = futures[future]\n", " results[tb.experiment_name].append(future.result())\n", " progress_bar.value +=1\n", " progress_bar.description = \"%03d/%03d:\" % (progress_bar.value, progress_bar.max)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114 }, "slideshow": { "slide_type": "-" } }, "source": [ "This is not a perfect implementation but... works!" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 114 }, "slideshow": { "slide_type": "-" } }, "source": [ "As running the experiments sometimes takes a long time it is a good practice to store the results." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import pickle" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 114 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "pickle.dump(results, open('nsga_ii_dtlz3-results.pickle', 'wb'))" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131 }, "slideshow": { "slide_type": "fragment" } }, "source": [ "In case you need it, this file is included in the github repository.\n", "\n", "To load the results we would just have to:" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "# loaded_results = pickle.load(open('nsga_ii_dtlz3-results.pickle', 'rb'))\n", "# results = loaded_results # <-- uncomment if needed" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "`results` is a dictionary, but a pandas `DataFrame` is a more handy container for the results." ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "res = pd.DataFrame(results)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Headers may come out unsorted. Let's fix that first. " ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end" }, "slide_helper": "subslide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/html": [ "
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4[[0.9999071795487058, 0.597551943491093, 0.738...[[0.99990936520471, 0.09148086217380487, 0.188...[[0.9987082847513086, 0.6251687696069047, 0.17...
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" ], "text/plain": [ " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \\\n", "0 [[0.9977275932042845, 0.9965136379259723, 0.51... \n", "1 [[0.9994523656808363, 0.15096009667708038, 0.7... \n", "2 [[0.9933887753816163, 0.11289114848347837, 0.4... \n", "3 [[0.9995015319036422, 0.5255243150173985, 0.53... \n", "4 [[0.9999071795487058, 0.597551943491093, 0.738... \n", "\n", " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "0 [[0.9984083629151556, 0.09353025978685643, 0.7... \n", "1 [[0.9999296140942003, 0.6362939526923219, 0.00... \n", "2 [[0.9997638765656464, 0.2829054976583878, 0.89... \n", "3 [[0.998903716395094, 0.6948982307664169, 0.190... \n", "4 [[0.99990936520471, 0.09148086217380487, 0.188... \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \n", "0 [[0.9998822922333848, 0.3606206000614993, 0.86... \n", "1 [[0.9990418574002103, 0.8049558879536657, 0.48... \n", "2 [[0.9999169320345067, 0.10912800384098932, 0.7... \n", "3 [[0.9939804258490037, 0.5537945580214072, 0.49... \n", "4 [[0.9987082847513086, 0.6251687696069047, 0.17... " ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.head()" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_type": "subslide" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "res = res.reindex_axis([toolbox.experiment_name for toolbox in toolboxes], axis=1)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/html": [ "
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$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$
0[[0.9984083629151556, 0.09353025978685643, 0.7...[[0.9998822922333848, 0.3606206000614993, 0.86...[[0.9977275932042845, 0.9965136379259723, 0.51...
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3[[0.998903716395094, 0.6948982307664169, 0.190...[[0.9939804258490037, 0.5537945580214072, 0.49...[[0.9995015319036422, 0.5255243150173985, 0.53...
4[[0.99990936520471, 0.09148086217380487, 0.188...[[0.9987082847513086, 0.6251687696069047, 0.17...[[0.9999071795487058, 0.597551943491093, 0.738...
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" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "0 [[0.9984083629151556, 0.09353025978685643, 0.7... \n", "1 [[0.9999296140942003, 0.6362939526923219, 0.00... \n", "2 [[0.9997638765656464, 0.2829054976583878, 0.89... \n", "3 [[0.998903716395094, 0.6948982307664169, 0.190... \n", "4 [[0.99990936520471, 0.09148086217380487, 0.188... \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "0 [[0.9998822922333848, 0.3606206000614993, 0.86... \n", "1 [[0.9990418574002103, 0.8049558879536657, 0.48... \n", "2 [[0.9999169320345067, 0.10912800384098932, 0.7... \n", "3 [[0.9939804258490037, 0.5537945580214072, 0.49... \n", "4 [[0.9987082847513086, 0.6251687696069047, 0.17... \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "0 [[0.9977275932042845, 0.9965136379259723, 0.51... \n", "1 [[0.9994523656808363, 0.15096009667708038, 0.7... \n", "2 [[0.9933887753816163, 0.11289114848347837, 0.4... \n", "3 [[0.9995015319036422, 0.5255243150173985, 0.53... \n", "4 [[0.9999071795487058, 0.597551943491093, 0.738... " ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.head()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## A first glace at the results" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131 }, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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NfN82ImELr+LilBzsbIm7nsOrL+1tdPNERLacui8u09bWhm3bD41LJBJEo9El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\n/b8956rW69lSL7FzvEIjTrlpe52DRxp04oxiwce1EwKlmBor0e1nKytZnU8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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 208, "width": 655 } }, "output_type": "display_data" } ], "source": [ "a = res.applymap(lambda pop: [toolbox.evaluate(ind) for ind in pop])\n", "plt.figure(figsize=(11,3))\n", "for i, col in enumerate(a.columns):\n", " plt.subplot(1, len(a.columns), i+1)\n", " for pop in a[col]:\n", " x = pd.DataFrame(data=pop)\n", " plt.scatter(x[0], x[1], marker='.', alpha=0.5)\n", " plt.title(col) " ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "The local Pareto-optimal fronts are clearly visible!" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Calculating performance indicators\n", "\n", "* As already mentioned, we need to evaluate the quality of the solutions produced in every execution of the algorithm. \n", "* We will use the hypervolumne indicator for that.\n", "* Larger hypervolume values are better.\n", "* We already filtered each population a leave only the non-dominated individuals." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 131, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Calculating the *reference point*: a point that is **“worst”** than any other individual in every objective." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 131 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def calculate_reference(results, epsilon=0.1):\n", " alldata = np.concatenate(np.concatenate(results.values))\n", " obj_vals = [toolbox.evaluate(ind) for ind in alldata]\n", " return np.max(obj_vals, axis=0) + epsilon" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 145 }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "reference = calculate_reference(res)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 145, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "array([ 3475.29022518, 3547.26733352])" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reference" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 145, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "We can now compute the hypervolume of the Pareto-optimal fronts yielded by each algorithm run." ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 145 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import deap.benchmarks.tools as bt" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 145 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "hypervols = res.applymap(lambda pop: bt.hypervolume(pop, reference))" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 150, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
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$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$
01.154701e+079.976071e+069.555584e+06
11.122888e+071.022963e+079.082437e+06
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41.134042e+071.029052e+078.665202e+06
\n", "
" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "0 1.154701e+07 \n", "1 1.122888e+07 \n", "2 1.173466e+07 \n", "3 1.143605e+07 \n", "4 1.134042e+07 \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "0 9.976071e+06 \n", "1 1.022963e+07 \n", "2 9.776245e+06 \n", "3 9.906633e+06 \n", "4 1.029052e+07 \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "0 9.555584e+06 \n", "1 9.082437e+06 \n", "2 9.107024e+06 \n", "3 9.150103e+06 \n", "4 8.665202e+06 " ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hypervols.head()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 150, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## How can we interpret the indicators?" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152 }, "slideshow": { "slide_type": "fragment" } }, "source": [ "### Option A: Tabular form" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/html": [ "
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$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$
count4.200000e+014.200000e+014.200000e+01
mean1.140611e+071.000509e+078.969749e+06
std3.290728e+052.324033e+052.982720e+05
min1.040199e+079.481858e+068.436061e+06
25%1.119742e+079.868847e+068.815870e+06
50%1.144434e+071.000275e+078.900598e+06
75%1.165122e+071.014667e+079.131239e+06
max1.195610e+071.047124e+079.626931e+06
\n", "
" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "count 4.200000e+01 \n", "mean 1.140611e+07 \n", "std 3.290728e+05 \n", "min 1.040199e+07 \n", "25% 1.119742e+07 \n", "50% 1.144434e+07 \n", "75% 1.165122e+07 \n", "max 1.195610e+07 \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "count 4.200000e+01 \n", "mean 1.000509e+07 \n", "std 2.324033e+05 \n", "min 9.481858e+06 \n", "25% 9.868847e+06 \n", "50% 1.000275e+07 \n", "75% 1.014667e+07 \n", "max 1.047124e+07 \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "count 4.200000e+01 \n", "mean 8.969749e+06 \n", "std 2.982720e+05 \n", "min 8.436061e+06 \n", "25% 8.815870e+06 \n", "50% 8.900598e+06 \n", "75% 9.131239e+06 \n", "max 9.626931e+06 " ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hypervols.describe()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "### Option B: Visualization" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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4cOAA8vPzUV5e3umYQC8Vbo3S4Nao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\nRrZgMKgTh3dq//YNq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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 276, "width": 780 } }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(11,4))\n", "plt.subplot(121, title='Violin plots of NSGA-II with $P_{\\mathrm{mut}}$')\n", "seaborn.violinplot(data=hypervols, palette='Set2')\n", "plt.ylabel('Hypervolume'); plt.xlabel('Configuration')\n", "plt.subplot(122, title='Box plots of NSGA-II with $P_{\\mathrm{mut}}$')\n", "seaborn.boxplot(data=hypervols, palette='Set2')\n", "plt.ylabel('Hypervolume'); plt.xlabel('Configuration');\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Option C: Statistical hypothesis test" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "* Choosing the correct statistical test is essential to properly report the results.\n", "* [Nonparametric statistics](http://en.wikipedia.org/wiki/Nonparametric_statistics) can lend a helping hand.\n", "* [Parametric statistics](http://en.wikipedia.org/wiki/Parametric_statistics) could be a better choice in some cases. \n", "* Parametric statistics require that *all* data follow a known distribution (frequently a normal one).\n", "* Some tests -like the [normality test](http://en.wikipedia.org/wiki/Normality_test)- can be apply to verify that data meet the parametric stats requirements.\n", "* In my experience that is very unlikely that all your EMO result meet those characteristics." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "We start by writing a function that helps us tabulate the results of the application of an statistical hypothesis test." ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 152 }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "import itertools\n", "import scipy.stats as stats" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def compute_stat_matrix(data, stat_func, alpha=0.05):\n", " '''A function that applies `stat_func` to all combinations of columns in `data`.\n", " Returns a squared matrix with the p-values'''\n", " p_values = pd.DataFrame(columns=data.columns, index=data.columns)\n", " for a,b in itertools.combinations(data.columns,2):\n", " s,p = stat_func(data[a], data[b]) \n", " p_values[a].ix[b] = p\n", " p_values[b].ix[a] = p\n", " return p_values" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 152, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "The [Kruskal-Wallis H-test](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.kruskal.html) tests the null hypothesis that the population median of all of the groups are equal.\n", "\n", "* It is a non-parametric version of [ANOVA](http://en.wikipedia.org/wiki/Analysis_of_variance). \n", "* The test works on 2 or more independent samples, which may have different sizes. \n", "* Note that rejecting the null hypothesis does not indicate which of the groups differs. \n", "* Post-hoc comparisons between groups are required to determine which groups are different." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 163 }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "KruskalResult(statistic=110.49079579338292, pvalue=1.0167836238281895e-24)" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.kruskal(*[hypervols[col] for col in hypervols.columns])" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "We now can assert that the results are not the same but which ones are different or similar to the others the others?" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "In case that the null hypothesis of the Kruskal-Wallis is rejected the Conover–Inman procedure (Conover, 1999, pp. 288-290) can be applied in a pairwise manner in order to determine if the results of one algorithm were significantly better than those of the other.\n", "\n", "* Conover, W. J. (1999). *Practical Nonparametric Statistics*. John Wiley & Sons, New York, 3rd edition.\n", "\n", "_Note_: If you want to get an extended summary of this method check out my [PhD thesis](http://lmarti.com/pubs). " ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "def conover_inman_procedure(data, alpha=0.05):\n", " num_runs = len(data)\n", " num_algos = len(data.columns)\n", " N = num_runs*num_algos\n", "\n", " _,p_value = stats.kruskal(*[data[col] for col in data.columns])\n", " \n", " ranked = stats.rankdata(np.concatenate([data[col] for col in data.columns]))\n", " \n", " ranksums = []\n", " for i in range(num_algos):\n", " ranksums.append(np.sum(ranked[num_runs*i:num_runs*(i+1)]))\n", "\n", " S_sq = (np.sum(ranked**2) - N*((N+1)**2)/4)/(N-1)\n", "\n", " right_side = stats.t.cdf(1-(alpha/2), N-num_algos) * \\\n", " math.sqrt((S_sq*((N-1-p_value)/(N-1)))*2/num_runs)\n", " \n", " res = pd.DataFrame(columns=data.columns, index=data.columns)\n", "\n", " for i,j in itertools.combinations(np.arange(num_algos),2):\n", " res[res.columns[i]].ix[j] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n", " res[res.columns[j]].ix[i] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n", " return res" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ NaN \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ True \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ True \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ True \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ NaN \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ True \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ True \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ True \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ NaN " ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conover_inman_procedure(hypervols)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "We now know in what cases the difference is sufficient as to say that one result is better than the other." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Another alternative is the [Friedman test](http://en.wikipedia.org/wiki/Friedman_test).\n", "\n", "* Its null hypothesis that repeated measurements of the same individuals have the same distribution. \n", "* It is often used to test for consistency among measurements obtained in different ways. \n", " * For example, if two measurement techniques are used on the same set of individuals, the Friedman test can be used to determine if the two measurement techniques are consistent." ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "FriedmanchisquareResult(statistic=82.047619047619037, pvalue=1.5261102074586963e-18)" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "measurements = [list(hypervols[col]) for col in hypervols.columns]\n", "stats.friedmanchisquare(*measurements)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 163, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "[Mann–Whitney U test](http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test) (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test (WRS), or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that two populations are the same against an alternative hypothesis, especially that a particular population tends to have larger values than the other.\n", "\n", "It has greater efficiency than the $t$-test on non-normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the $t$-test on normal distributions." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ NaN \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ 1.67658e-15 \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ 1.56072e-15 \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ 1.67658e-15 \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ NaN \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ 2.96475e-15 \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ 1.56072e-15 \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ 2.96475e-15 \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ NaN " ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "raw_p_values=compute_stat_matrix(hypervols, stats.mannwhitneyu)\n", "raw_p_values" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "The [familywise error rate](http://en.wikipedia.org/wiki/Familywise_error_rate) (FWER) is the probability of making one or more false discoveries, or [type I errors](http://en.wikipedia.org/wiki/Type_I_and_type_II_errors), among all the hypotheses when performing multiple hypotheses tests.\n", "\n", "_Example_: When performing a test, there is a $\\alpha$ chance of making a type I error. If we make $m$ tests, then the probability of making one type I error is $m\\alpha$. Therefore, if an $\\alpha=0.05$ is used and 5 pairwise comparisons are made, we will have a $5\\times0.05 = 0.25$ chance of making a type I error.\n", "\n", "* FWER procedures (such as the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction)) exert a more stringent control over false discovery compared to False discovery rate controlling procedures. \n", "* FWER controlling seek to reduce the probability of even one false discovery, as opposed to the expected proportion of false discoveries. \n", "* Thus, FDR procedures have greater power at the cost of increased rates of type I errors, i.e., rejecting the null hypothesis of no effect when it should be accepted." ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "One of these corrections is the [Šidák correction](http://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction) as it is less conservative than the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction):\n", "$$\\alpha_{SID} = 1-(1-\\alpha)^\\frac{1}{m},$$\n", "where $m$ is the number of tests.\n", "\n", "* In our case $m$ is the number of combinations of algorithm configurations taken two at a time,\n", "$$\n", "m = {\\mathtt{number\\_of\\_experiments} \\choose 2}.\n", "$$\n", "* There are other corrections that can be used." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "0.016952427508441503" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.misc import comb\n", "alpha=0.05\n", "alpha_sid = 1 - (1-alpha)**(1/comb(len(hypervols.columns), 2))\n", "alpha_sid" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Let's apply the corrected alpha to `raw_p_values`. If we have a cell with a `True` value that means that those two results are the same." ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false, "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " $n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ False \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ True \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ True \n", "\n", " $n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ \\\n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ True \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ False \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ True \n", "\n", " $n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ \n", "$n_\\mathrm{pop}=10;\\ t_\\mathrm{max}=50$ True \n", "$n_\\mathrm{pop}=50;\\ t_\\mathrm{max}=10$ True \n", "$n_\\mathrm{pop}=100;\\ t_\\mathrm{max}=5$ False " ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "raw_p_values.applymap(lambda value: value <= alpha_sid)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "## Further -and highly recommended- reading\n", "\n", "* Cohen, P. R. (1995). _Empirical Methods for Artificial Intelligence_ (Vol. 139). Cambridge: MIT press. [link](http://mitpress.mit.edu/books/empirical-methods-artificial-intelligence)\n", "* Bartz-Beielstein, Thomas (2006). _Experimental Research in Evolutionary Computation: The New Experimentalism_. Springer [link](http://link.springer.com/book/10.1007%2F3-540-32027-X)\n", "* García, S., & Herrera, F. (2008). _An Extension on “Statistical Comparisons of Classifiers over Multiple Data Sets” for all Pairwise Comparisons_. Journal of Machine Learning Research, 9, 2677–2694. [pdf](http://www.jmlr.org/papers/v9/garcia08a.html)" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "# Final remarks\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "frag_helper": "fragment_end", "frag_number": 172, "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "In this class/notebook we have seen some key elements:\n", "\n", "1. The Pareto dominance relation in action.\n", "2. The NSGA-II algorithm.\n", "3. Some of the existing MOP benchmarks. \n", "4. How to perform experiments and draw statistically valid conclusions from them.\n", "\n", "Bear in mind that:\n", "\n", "* When working in EMO topics problems like those of the CEC'09 or WFG toolkits are usually involved.\n", "* The issue of devising a proper experiment design and interpreting the results is a fundamental one.\n", "* The experimental setup presented here can be used with little modifications to single-objective optimization and even to other machine learning or stochastic algorithms." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
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\n", " This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n", "
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" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/json": { "Software versions": [ { "module": "Python", "version": "3.6.0 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]" }, { "module": "IPython", "version": "5.2.2" }, { "module": "OS", "version": "Darwin 16.4.0 x86_64 i386 64bit" }, { "module": "scipy", "version": "0.18.1" }, { "module": "numpy", "version": "1.11.3" }, { "module": "matplotlib", "version": "2.0.0" }, { "module": "seaborn", "version": "0.7.1" }, { "module": "deap", "version": "1.1" } ] }, "text/html": [ "
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Sat Mar 04 02:05:51 2017 BRT
" ], "text/latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 3.6.0 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)] \\\\ \\hline\n", "IPython & 5.2.2 \\\\ \\hline\n", "OS & Darwin 16.4.0 x86\\_64 i386 64bit \\\\ \\hline\n", "scipy & 0.18.1 \\\\ \\hline\n", "numpy & 1.11.3 \\\\ \\hline\n", "matplotlib & 2.0.0 \\\\ \\hline\n", "seaborn & 0.7.1 \\\\ \\hline\n", "deap & 1.1 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Sat Mar 04 02:05:51 2017 BRT} \\\\ \\hline\n", "\\end{tabular}\n" ], "text/plain": [ "Software versions\n", "Python 3.6.0 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]\n", "IPython 5.2.2\n", "OS Darwin 16.4.0 x86_64 i386 64bit\n", "scipy 0.18.1\n", "numpy 1.11.3\n", "matplotlib 2.0.0\n", "seaborn 0.7.1\n", "deap 1.1\n", "Sat Mar 04 02:05:51 2017 BRT" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# To install run: pip install version_information\n", "%load_ext version_information\n", "%version_information scipy, numpy, matplotlib, seaborn, deap" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# this code is here for cosmetic reasons\n", "from IPython.core.display import HTML\n", "from urllib.request import urlopen\n", "HTML(urlopen('https://raw.githubusercontent.com/lmarti/jupyter_custom/master/custom.include').read().decode('utf-8'))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ " " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" }, "notify_time": "30", "widgets": { "state": { "fd0fbdf2f74c4fcfbc639df8f8988531": { "views": [ { "cell_index": 117 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 0 }