Improving Genetic Algorithms Performance via Deterministic Population Shrinkage Juan Luis Jimenez Laredo 1 Carlos Fernandes 1 Juan Julian Merelo 1 Christian Gagn´ e 2 1 GeNeura Team Department of Computer Architecture and Technology University of Granada, Spain 2 Computer Vision and Systems Laboratory (CVSL) D´ epartement de g´ enie ´ electrique et de g´ enie informatique Universit´ e Laval, Quebec City (Qu´ ebec), Canada GECCO 2009, Montr´ eal (Qu´ ebec), Canada Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 1 / 17
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Improving Genetic Algorithms Performance viaDeterministic Population Shrinkage
Juan Luis Jimenez Laredo1 Carlos Fernandes1
Juan Julian Merelo1 Christian Gagne2
1GeNeura TeamDepartment of Computer Architecture and Technology
University of Granada, Spain
2Computer Vision and Systems Laboratory (CVSL)Departement de genie electrique et de genie informatique
Universite Laval, Quebec City (Quebec), Canada
GECCO 2009, Montreal (Quebec), Canada
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 1 / 17
Scope
Hypothesis: Different convergence stages of a genetic algorithm mayrequire different population sizes
Model: A Simple Variable Population Sizing (SVPS) scheme whereonly population shrinkage is considered
Aim: Get empirical evidences of performance improvement withSVPS over a fixed-size scheme
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 2 / 17
Scope
Hypothesis: Different convergence stages of a genetic algorithm mayrequire different population sizes
Model: A Simple Variable Population Sizing (SVPS) scheme whereonly population shrinkage is considered
Aim: Get empirical evidences of performance improvement withSVPS over a fixed-size scheme
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 2 / 17
Scope
Hypothesis: Different convergence stages of a genetic algorithm mayrequire different population sizes
Model: A Simple Variable Population Sizing (SVPS) scheme whereonly population shrinkage is considered
Aim: Get empirical evidences of performance improvement withSVPS over a fixed-size scheme
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 2 / 17
Outline
Background on population sizing
Methodology
I Generalized l-trap functionI Bisection method for estimating correct population sizeI Simple Variable Population Sizing
Experimental results
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 3 / 17
Outline
Background on population sizing
MethodologyI Generalized l-trap function
I Bisection method for estimating correct population sizeI Simple Variable Population Sizing
Experimental results
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 3 / 17
Outline
Background on population sizing
MethodologyI Generalized l-trap functionI Bisection method for estimating correct population size
I Simple Variable Population Sizing
Experimental results
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 3 / 17
Outline
Background on population sizing
MethodologyI Generalized l-trap functionI Bisection method for estimating correct population sizeI Simple Variable Population Sizing
Experimental results
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 3 / 17
Outline
Background on population sizing
MethodologyI Generalized l-trap functionI Bisection method for estimating correct population sizeI Simple Variable Population Sizing
Experimental results
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 3 / 17
Sizing theory:I Focus is on the correct sizing of population for the fixed-sized schemeI But theory for fixed-size scheme can be helpful for variable-size schemes
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 4 / 17
Generalized l-trap Function
l-trap function (Ackley, 1987):I l : problem size (number of
possible values in range)I a: value of local optimumI b: value of global optimumI z : slope-change location
Currently, experiments witha = l − 1, b = l and z = l − 1
I 2-trap: not deceptiveI 3-trap: partially deceptiveI 4-trap: deceptive
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 5 / 17
Generalized l-trap Function
l-trap function (Ackley, 1987):I l : problem size (number of
possible values in range)I a: value of local optimumI b: value of global optimumI z : slope-change location
Currently, experiments witha = l − 1, b = l and z = l − 1
I 2-trap: not deceptiveI 3-trap: partially deceptiveI 4-trap: deceptive
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 5 / 17
Scaling the Problem Difficulty
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 6 / 17
Scaling the Problem Difficulty
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 6 / 17
Working Hypothesis
Minimizing number of solutions evaluated while guaranteeing asuccess rate
Working hypothesis: larger population required at the beginning
I Start with a diverse sampling of the search spaceI As convergence occurs, smaller population required
Use a deterministic schedule of the population size
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 7 / 17
Working Hypothesis
Minimizing number of solutions evaluated while guaranteeing asuccess rate
Working hypothesis: larger population required at the beginningI Start with a diverse sampling of the search spaceI As convergence occurs, smaller population required
Use a deterministic schedule of the population size
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 7 / 17
Working Hypothesis
Minimizing number of solutions evaluated while guaranteeing asuccess rate
Working hypothesis: larger population required at the beginningI Start with a diverse sampling of the search spaceI As convergence occurs, smaller population required
Use a deterministic schedule of the population size
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 7 / 17
Working Hypothesis
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 8 / 17
Simple Variable Population Sizing (SVPS)
Reduce population by a variable ratio at each generation:
ng = n0
(1− (1− ρ)
(g
gmax
)τ)I n0: initial population sizeI ng : population size at generation gI g : current generation numberI gmax : last generation numberI τ : resizing speed parameterI ρ: resizing severity parameter
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 9 / 17
Simple Variable Population Sizing (SVPS)
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 10 / 17
Estimating the Correct Population Size (SR of 0.98)
1) Rough estimation (ni+1 = 2ni ):
n1 = 4, SR=0.2 n2 = 8, SR=0.95 n3 = 16, SR=0.995
2) Bisection (ni+1 =nmax
i +nmini
2 ), stop whennmax
i −nmini
nmini
< 116 :
n4 = 12, SR=0.99 n5 = 10, SR=0.982
3) Refinement (ni+1 = b0.99nic):n6 = 9, SR=0.9803
Correct population size is 9 for a success rate of 0.98
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 11 / 17
Estimating the Correct Population Size (SR of 0.98)
1) Rough estimation (ni+1 = 2ni ):n1 = 4, SR=0.2
n2 = 8, SR=0.95 n3 = 16, SR=0.995
2) Bisection (ni+1 =nmax
i +nmini
2 ), stop whennmax
i −nmini
nmini
< 116 :
n4 = 12, SR=0.99 n5 = 10, SR=0.982
3) Refinement (ni+1 = b0.99nic):n6 = 9, SR=0.9803
Correct population size is 9 for a success rate of 0.98
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 11 / 17
Estimating the Correct Population Size (SR of 0.98)