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Population Sizing as an Emergent Behavior. Jason Cook. Motivation. Ease of use Limit necessary manual tuning Potentially improve performance. Problem Statement. Remove the population size parameter Introduce no new parameters Maintain useful level of accuracy. Solution Method. - PowerPoint PPT Presentation
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Population Sizing as Population Sizing as an Emergent an Emergent Behavior Behavior Jason CookJason Cook
MotivationMotivation
Ease of useEase of use Limit necessary manual tuningLimit necessary manual tuning Potentially improve performancePotentially improve performance
Problem StatementProblem Statement
Remove the population size parameterRemove the population size parameter Introduce no new parametersIntroduce no new parameters Maintain useful level of accuracyMaintain useful level of accuracy
Solution MethodSolution Method
Set up the population size as an Set up the population size as an emergent behavioremergent behavior
Replace survivor selection with a survival Replace survivor selection with a survival chancechance
SRSRii = ( = (FFii – – FFminmin)) / ( / (FFmaxmax – – FFminmin))
Experimental SetupExperimental Setup
Compare with a traditional EACompare with a traditional EA Two main test problems: Griewank Function Two main test problems: Griewank Function
and D-TRAP Problemand D-TRAP Problem Survival Method:Survival Method:
Survival Chance Survival Chance or or
N-TournamentN-Tournament Other operators and parameter held constant Other operators and parameter held constant
for both EAsfor both EAs
Griewank FunctionGriewank Function
NN dimensional minimization problem dimensional minimization problem Many local optimaMany local optima Optimal solution: Optimal solution: xxii = 0 = 0
D-TRAPD-TRAP
250 4-bit pieces250 4-bit pieces Each piece is worth:Each piece is worth:
3 – 3 – uu if if uu ≤ 3 ≤ 3 44 otherwiseotherwise
Optimal solution: Optimal solution: xxii = 0 = 0
ResultsResults
Progression of Fitness values of the Griewank Function
0
10
20
30
40
50
60
70
80
90
100
50 1100 2150 3200 4250 5300 6350 7400 8450 9500
Fitness Evaluations
MB
F (
% o
f m
axim
um
fit
nes
s)
EA-OPT Auto-PS-EA
Results (Continued):Results (Continued):
Changes in Population Size in the Griewank Function
0
100
200
300
400
500
600
50 1100 2150 3200 4250 5300 6350 7400 8450 9500
Fitness Evaluations
Po
pu
lati
on
Siz
e
Results (Continued):Results (Continued):
Progression of Fitness Values for the D-TRAP problem
0
10
20
30
40
50
60
70
80
90
100
510 1560 2610 3660 4710 5760 6810 7860 8910 9960
Fitness Evaluations
MB
F (
% o
f m
ax
imu
m p
os
sib
le f
itn
es
s)
Fixed Population Size
Dynamic Population Size
Results (Continued):Results (Continued):
Changes in Population Size during the D-TRAP problem
0
50
100
150
200
250
510 1560 2610 3660 4710 5760 6810 7860 8910 9960
Fitness Evaluations
Po
pu
lati
on
Siz
e
AnalysisAnalysis
Performs as well or better than a Performs as well or better than a traditional EAtraditional EA
Still affected by the initial population sizeStill affected by the initial population size
Future WorkFuture Work
More test problemsMore test problems Use a more competitive EA to test Use a more competitive EA to test
againstagainst
Questions?Questions?
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