gecco-09-ga-improvement-with-svps
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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
Population Sizing
Sizing scheme:I Fixed size: canonical approachI Deterministic methods: function-based adjustment (e.g. Saw-tooth)I Adaptive methods: on-line adjustment (e.g. GAVaPS)
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
Population Sizing
Sizing scheme:I Fixed size: canonical approachI Deterministic methods: function-based adjustment (e.g. Saw-tooth)I Adaptive methods: on-line adjustment (e.g. GAVaPS)
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)
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)
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)
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)
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
Population Sizes for a Success Rate of 0.98
m: number of concatenated trap functions
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 12 / 17
Experimental Setting
Selectorecombinative binary Genetic Algorithm:I Population sizes set according to bisection method for a success rate of
0.98I Two parents tournament selectionI One-point crossover (probability of 1.0)I No mutation
Trap problems tested:
I Problem sizes, l = {2, 3, 4}I Number of sub-functions, m = {2, 4, 8, 16, 32, 64}
SVPS setting:
I Speed, τ = 0.125, . . .×1.5 , 32I Severity, ρ = 0.25, . . .+0.05 , 1
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 13 / 17
Experimental Setting
Selectorecombinative binary Genetic Algorithm:I Population sizes set according to bisection method for a success rate of
0.98I Two parents tournament selectionI One-point crossover (probability of 1.0)I No mutation
Trap problems tested:I Problem sizes, l = {2, 3, 4}I Number of sub-functions, m = {2, 4, 8, 16, 32, 64}
SVPS setting:
I Speed, τ = 0.125, . . .×1.5 , 32I Severity, ρ = 0.25, . . .+0.05 , 1
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 13 / 17
Experimental Setting
Selectorecombinative binary Genetic Algorithm:I Population sizes set according to bisection method for a success rate of
0.98I Two parents tournament selectionI One-point crossover (probability of 1.0)I No mutation
Trap problems tested:I Problem sizes, l = {2, 3, 4}I Number of sub-functions, m = {2, 4, 8, 16, 32, 64}
SVPS setting:I Speed, τ = 0.125, . . .×1.5 , 32I Severity, ρ = 0.25, . . .+0.05 , 1
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 13 / 17
Speed (τ) and Severity (ρ)
Size of circles show improvement over fixed-size population
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 14 / 17
Saved Computational Effort
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 15 / 17
Conclusion
SVPS requires a smaller number of evaluations than a fixedpopulation sizing scheme
The improvement is much more noticeable for large population sizesas the problem instances scale
There is not a single but a set of possible strategies for SVPS(different τ -ρ combinations)
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 16 / 17
Conclusion
SVPS requires a smaller number of evaluations than a fixedpopulation sizing scheme
The improvement is much more noticeable for large population sizesas the problem instances scale
There is not a single but a set of possible strategies for SVPS(different τ -ρ combinations)
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 16 / 17
Conclusion
SVPS requires a smaller number of evaluations than a fixedpopulation sizing scheme
The improvement is much more noticeable for large population sizesas the problem instances scale
There is not a single but a set of possible strategies for SVPS(different τ -ρ combinations)
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 16 / 17
Questions
Thanks for your attention!
Laredo et al. (Granada / Laval) Improving GAs via Population Shrinkage GECCO 2009 17 / 17