Age-Based Population Dynamics in Evolutionary Algorithms Lisa 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 ( S i ) of an individual is based on age and fitness Main Equation S i  F i F B S AGE Fitness of i Best Fitness

Survival Chance from Age Age is tracked by individual, and is incremented every generation Two equations explored for S AGE Equation 1 (ABPS-AutoEA1): linear decrease S AGE  1  R A ( ) Rate of decrease from age

Survival Chance from Age (cont’d) Equation 2 (ABPS-AutoEA2): more dynamic S AGE  1  N AG 2P  AGE 2G 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) N AG SiSi S AGE  1  N AG 2P  AGE 2G

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 -

Performance Results - TSP size 40 Average over 30 runs ABPS-AutoEA1 - ABPS-AutoEA2 -

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 S i   F i F B  F W F W S AGE S i  F i F B S Fitness of i Best Fitness Worst Fitness Fitness Scaling

Initial Performance Analysis from Fitness Scaling Equation Average over 30 runs 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?