FireflyAlgorithm Class Reference

#include <ql/experimental/math/fireflyalgorithm.hpp>

Inheritance diagram for FireflyAlgorithm:

Classes
class	Intensity
	Base intensity class. More...
class	RandomWalk
	Base Random Walk class. More...

Public Member Functions
	FireflyAlgorithm (Size M, ext::shared_ptr< Intensity > intensity, ext::shared_ptr< RandomWalk > randomWalk, Size Mde=0, Real mutationFactor=1.0, Real crossoverFactor=0.5, unsigned long seed=SeedGenerator::instance().get())
void	startState (Problem &P, const EndCriteria &endCriteria)
EndCriteria::Type	minimize (Problem &P, const EndCriteria &endCriteria) override
	minimize the optimization problem P

Protected Attributes
std::vector< Array >	x_
std::vector< Array >	xI_
std::vector< Array >	xRW_
std::vector< std::pair< Real, Size > >	values_
Array	lX_
Array	uX_
Real	mutation_
Real	crossover_
Size	M_
Size	N_
Size	Mde_
Size	Mfa_
ext::shared_ptr< Intensity >	intensity_
ext::shared_ptr< RandomWalk >	randomWalk_
std::mt19937	generator_
std::uniform_int_distribution< QuantLib::Size >	distribution_
MersenneTwisterUniformRng	rng_

Detailed Description

The main process is as follows: M individuals are used to explore the N-dimensional parameter space: \( X_{i}^k = (X_{i, 1}^k, X_{i, 2}^k, \ldots, X_{i, N}^k) \) is the kth-iteration for the ith-individual. X is updated via the rule

\[X_{i, j}^{k+1} = X_{i, j}^k + I(X^k)_{i,j} + RandomWalk_{i,j}^k \]

The intensity function I(X) should be monotonic The optimization stops either because the number of iterations has been reached or because the stationary function value limit has been reached.

The current implementation extends the normal Firefly Algorithm with a differential evolution (DE) optimizer according to: Afnizanfaizal Abdullah, et al. "A New Hybrid Firefly Algorithm for Complex and Nonlinear Problem". Volume 151 of the series Advances in Intelligent and Soft Computing pp 673-680, 2012. http://link.springer.com/chapter/10.1007%2F978-3-642-28765-7_81

In effect this implementation provides a fully fledged DE global optimizer as well. The Firefly Algorithm was easy to combine with DE because it already contained a step where the current solutions are sorted. The population is then divided into two subpopulations based on their order. The subpopulation with the best results are updated via the firefly algorithm. The worse subpopulation is updated via the DE operator:

\[Y^{k+1} = X_{best}^k + F(X_{r1}^k - X_{r2}^k) \]

and

\[X_{i,j}^{k+1} = Y_{i,j}^{k+1}\ \text{if} R_{i,j} <= C \]

\[X_{i,j}^{k+1} = X_{i,j}^{k+1}\ \text{otherwise} \]

where C is the crossover constant, and R is a random uniformly distributed number.

Examples

GlobalOptimizer.cpp.

Member Function Documentation

minimize()

EndCriteria::Type minimize ( Problem & P, const EndCriteria & endCriteria )

overridevirtual

minimize the optimization problem P

Implements OptimizationMethod.