age-based population dynamics in evolutionary algorithms

Age-Based Population Age-Based Population Dynamics in Dynamics in Evolutionary Evolutionary AlgorithmsAlgorithms

Lisa GuntlyLisa Guntly

Motivation

• Parameter specification complicates EAs

• Optimal parameter values can change during a run

• Age is an important factor in Biology

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-AutoEA1): linear decrease

SAGE1 RA (AGE)Rate of decrease from age

Survival Chance from Age (cont’d)

• Equation 2 (ABPS-AutoEA2): 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

SAGE 1 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

Performance Results - TSP size 20

Average over 30 runs

ABPS-AutoEA1 -

ABPS-AutoEA2 -

SAGE 1 RA (AGE)

SAGE 1 NAG2P

AGE2G

Performance Results - TSP size 40

Average over 30 runs

ABPS-AutoEA1 -

ABPS-AutoEA2 -

SAGE 1 RA (AGE)

SAGE 1 NAG2P

AGE2G

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

Initial Performance Analysis from Fitness Scaling Equation (cont’d)• Elitism improved performance slightly• Roulette wheel (fitness proportional) parent

selection improved performance on a larger TSPs but performed worse on smaller TSPs

• Independence from initial population size was maintained

• Adjustment of population size during the run was improved

Future Work

• Further exploration of fitness scaling methods

• Test on additional problems• Compare to other dynamic

population sizing schemes• Implement age-based offspring

sizing

Questions?Questions?