EC Awards Lecture EC Awards Lecture ~~ Spring Spring 20082008
Advances in Parameterless Advances in Parameterless Evolutionary AlgorithmsEvolutionary Algorithms
Lisa GuntlyLisa GuntlyAndré NwambaAndré Nwamba
Research Advisor: Dr. Daniel TauritzResearch Advisor: Dr. Daniel Tauritz
Natural Computation LaboratoryNatural Computation Laboratory
Evolutionary Algorithms (EAs)
Evolutionary Algorithm (EA)
Solution
User Parameters Problem
Evolutionary Algorithms
Create Initial Population
Evaluate Fitness
Termination
Select Parents
Create Offspring
Evaluate FitnessSelect Survivors
No
Yes
Solution
Motivation
• Parameter specification complicates EAs– Expert knowledge required– Time-consuming– Sub-optimal - optimal parameter values
can change during a run
The Effects of Parameter Values
300
400
500
600
700
800
900
1000
6000
1100
0
1600
0
2100
0
2600
0
3100
0
3600
0
4100
0
4600
0
5100
0
5600
0
6100
0
6600
0
7100
0
7600
0
8100
0
8600
0
9100
0
9600
0
Fitness Evaluations
Fit
nes
s
OPT
TGA
Parameter Optimal Traditional
Population Size 500 50
Offspring Size 50 50
Crossover 2-point 1-point
Mutation Rate .1% .1%
Parent Selection Random 2-1 Tournament
Survivor Selection Truncation Truncation
Parameterless EAs: Our Approach
• Completely Parameterless EAs• Biological metaphors may be useful• Typical parameters:
– Population size– Parent selection operators– Offspring size– Survival selection– Mutation operators– Crossover operators
Futility-Based Offspring Futility-Based Offspring Sizing (FuBOS)Sizing (FuBOS)
André NwambaAndré Nwamba
FuBOS: Futility-Based Offspring Sizing
• Minimize wasted computation effort
Approach
• Look at change in average fitness of the offspring
• Average fitness of all n offspring• Average fitness of n-1 previously
created offspring• Threshold value
1
1
1
11
1
n n
ii
ii
offn
offn
Experimental Setup
• Compared FuBOS-EA and manually tuned EA (OOS-EA)
• FuBOS-EA uses ε=.001• Test problems: DTRAP, SAT, and
ONEMAX• Used population sizes of 100, 500, 1000• All tests used same parameters • Performance compared using One-Way
ANOVA with significance level of .05
Results
Mean Best Fitness for DTRAP (averaged over 60 runs) of size 250
800
810
820
830
840
850
860
100 500 1000
Population Size
Fit
nes
s
OOS-EA
FuBOS-EA
Results
Mean Best Fitness for SAT (averaged over 60 runs) with 1000 variables and 4250 clauses
4130
4140
4150
4160
4170
4180
4190
4200
4210
4220
100 500 1000
Population Size
Fit
nes
s
OOS-EA
FuBOS-EA
Results
Fitness Evaluations needed to find optimal solution for ONEMAX (averaged over 60 runs)
40000
50000
60000
70000
80000
90000
100000
110000
100 500 1000
Population Size
Fit
nes
s E
valu
atio
ns
OOS-EA
FuBOS-EA
Results
λgen and Fitness over time for FuBOS-EA on the DTRAP problem of
size 250 with population size of 500
0
100
200
300
400
500
600
700
800
900
0 20000 40000 60000 80000 100000
Fitness Evals
Fit
nes
s/O
ffsp
rin
g H
ad
Best Fitness
Offspring
Results
Mean Best Fitness for DTRAP (averaged over 60 extended runs) of size 250
800
810
820
830
840
850
860
870
880
890
900
100 500 1000
Population Size
Fit
nes
s
OOS-EA
FuBOS-EA
Conclusions
• Competitive performance• Extra parameter
FuBOS Future Work
• The “epsilon problem”• Genetic Diversity• Parent Selection• Combine with dynamic population
sizing
Age-Based Population Age-Based Population Sizing (ABPS)Sizing (ABPS)
Lisa GuntlyLisa Guntly
The Importance of Age
• Age significantly impacts survival in natural populations
Methods
• Survival chance (Si) of an individual is based on age and fitness
• Main Equation
SiFiFBSAGE
Fitness of i
Best Fitness
Survival Chance from Age
• Age is tracked by individual, and is incremented every generation
• Two equations explored for SAGE
• Equation 1 (ABPS-EA1): linear decrease
SAGE1 RA (AGE)Rate of decrease from age
Survival Chance from Age (cont’d)
• Equation 2 (ABPS-EA2): more dynamic
SAGE1 NAG2P
AGE2G
Number of individuals in the same age group
Population size Number of generations the EA will run
Survival Chance from Age (cont’d)
• Effects of
– More individuals of the same age will decrease their survival chance
– Age will decrease survival chance relative to the maximum age (G)
NAG Si
SAGE1 NAG2P
AGE2G
Experimental Setup
• Testing done on TSP (size 20/40/80)• Offspring size is constant• Compared to a manually tuned EA • Examine effects of
– Initial population size– Offspring size
• Tracked population statistics– Size– Average age– Global best fitness (GBF)
Performance Results - TSP size 20
Average over 30 runs
ABPS-EA1 -
ABPS-EA2 -
SAGE 1 RA (AGE)
SAGE 1 NAG2P
AGE2G
Global best fitness
Performance Results - TSP size 40
Average over 30 runs
ABPS-EA1 -
ABPS-EA2 -
SAGE 1 RA (AGE)
SAGE 1 NAG2P
AGE2G
Global best fitness
Initial Population Size Effect
3 different runs
Tracking Population Size and Average Age
Same single run
Equation with Fitness Scaling
• Attempt to fix the lack of selection pressure from fitness
• New Main Equation
SiFi
FB FWFWSAGESi
FiFBSAGE
Fitness of i
Best FitnessWorst Fitness
Fitness Scaling
Initial Performance Analysis from Fitness Scaling Equation
Average over 30 runs
SAGE 1 NAG2P
AGE2G
using
Global best fitness
Initial Performance Analysis from Fitness Scaling Equation (cont’d)• Independence from initial population
size was maintained• Dynamic adjustment of population size
during the run was improved• Additional selection pressure from
elitism improved performance slightly
ABPS Conclusions
• Independence from initial population value was achieved
• Autonomous adjustment of population size during a single EA run was successful
• Fitness scaling is needed for ABPS to work on more difficult problems
ABPS Future Work
• Further exploration of fitness scaling methods
• Test on other difficult problems• Compare to other dynamic population
sizing schemes
• Implement age-based offspring sizing
ImpactImpact
Impact
• Increases industry usability• Higher performance EAs• Progress towards completely
parameterless EA
Questions?Questions?
FuBOS Experimental Setup
Parameter Value
Initialization Each bit is initialized to either a 0 or 1 with a uniform probability
Parent Selection Random
Survivor Selection Truncation
Recombination Uniform Crossover for SAT and ONEMAX and 2-point crossover for DTRAP
Mutation Rate 1/l (l being the length of the bitstring)
Termination Condition 100000 fitness evaluations for SAT and DTRAP, Optimal solution found for ONEMAX
Experimental Setup
• DTRAP
• SAT
• ONEMAX
4 4( )
3
xf x
x otherwise
1 2 3 4 2 3 5( ) ( ) ...x x x x x x x
