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