Advanced Mate Selection in Evolutionary Algorithms

Mate Selection Missouri University of Science and Technology Classic Mate Selection –Tournament –Roulette wheel –Panmictic Limitations –No genotypic restrictions on mating –More fit individuals mate more often –Fixed parameters during an EA run –Time consuming process of tuning mate selection parameters for each problem

Mate Selection Missouri University of Science and Technology Mate selection with restrictions –Niching –Assortative Mating –Outbreeding Mate selection learning mechanisms –Reinforcement learning –LOOMS and ELOOMS

Niching Missouri University of Science and Technology

Assortative Mating Missouri University of Science and Technology

Variable Dissortative Mating Genetic Algorithm (VDMGA) Negative assortative mating Hamming distance threshold restriction –Adaptive –Restriction tends to loosen over time –Assumes dissimilarity between genotypes improves performance Outperforms basic assortative mating techniques Missouri University of Science and Technology

Outbreeding

Reinforcement Learning in CGAs Cellular Genetic Algorithms (CGAs) –Individuals organized on a topological grid –More likely to mate with nearby neighbors Reinforcement learning based on offspring quality –Good offspring – moves individuals closer together on the grid –Bad offspring – moves individuals further apart on the grid Missouri University of Science and Technology

LOOMS and ELOOMS Learning Offspring Optimizing Mate Selection (LOOMS) –Every individual examined all other individuals in the population for best mate –Significant overhead Estimated LOOMS (ELOOMS) –Reduced overhead by looking for a good enough mate –Features looked for in mates converged to intermediate values Missouri University of Science and Technology

Estimated Learning Offspring Optimizing Mate Selection (ELOOMS)

Traditional Mate Selection MATES t – tournament selection t is user-specified

ELOOMS NO YES MATES YES NO YES

Mate Acceptance Chance (MAC) j How much do I like ? k b 1 b 2 b 3 … b L d 1 d 2 d 3 … d L

Desired Features j d 1 d 2 d 3 … d L # times past mates’ b i = 1 was used to produce fit offspring # times past mates’ b i was used to produce offspring b 1 b 2 b 3 … b L Build a model of desired potential mate Update the model for each encountered mate Similar to Estimation of Distribution Algorithms

ELOOMS vs. TGA L=500 With Mutation L=1000 With Mutation Easy Problem

ELOOMS vs. TGA Without Mutation With Mutation Deceptive Problem L=100

Why ELOOMS works on Deceptive Problem More likely to preserve optimal structure will equally like: – – – But will dislike individuals not of the form: –1111 xxxx

Why ELOOMS does not work as well on Easy Problem High fitness – short distance to optimal Mating with high fitness individuals – closer to optimal offspring Fitness – good measure of good mate ELOOMS – approximate measure of good mate

Learning Individual Mating Preferences (LIMP)

LIMP Individuals learn what features to look for in a mate – desired features Learning is based on the results of prior reproductions D-LIMP – each individual tracks their own desired features C-LIMP – desired features are tracked on a population level Missouri University of Science and Technology

LIMP – Mate Selection λ individuals look for a mate Each individual conducts a tournament to find a mate Comparison of desired features to potential mates’ genes Most suitable potential mate selected Missouri University of Science and Technology

Mate Selection – D-LIMP Missouri University of Science and Technology sksk.7 |.6 |.7 |.2 djdj j sksk =.30.65

.45 Mate Selection – C-LIMP Missouri University of Science and Technology sksk j sksk.8 |.9 |.2 |.7.3 |.4 |.8 |.8 d P0 d P1 sjsj =.60

Learning Desirable Mate Qualities Desired features update after recombination Track each parent’s gene contribution to offspring Outcome of the reproduction is examined –If the child is more fit than a parent, that parent considers its mate suitable –If the child is less fit than a parent, that parent considers its mate unsuitable Missouri University of Science and Technology

Learning D-LIMP Missouri University of Science and Technology |.9 |.3 |.8.7 |.6 |.7 |.2.7 |.6 |.3 |.8 jk m F( j )=20F( k )=15 F( m )=18.7 |.6 |.6 |.3 0 | 1 |.3 |.8.7 |.6 |.7 |.2.2 |.9 |.3 |.8

.8 |.9 |.2 |.7.3 |.4 |.8 |.8 d P0 d P1.8 |.9 |.1 |.7.3 |.4 |.8 |.9 d P0 d P1.1 |.4 |.8 |.9.8 | 1 |.1 |.7 d P0 d P1.8 |.9 |.2 |.7.3 |.4 |.8 |.8 d P0 d P1.8 |.9 |.1 |.7.3 |.4 |.8 |.9 d P0 d P1 Learning C-LIMP Missouri University of Science and Technology jk m F( j )=20F( k )=15 F( m )=18

Test Problems DTRAP –DTRAP1 –DTRAP2 NK Landscapes MAXSAT Performance Comparisons –Mean Best Fitness (MBF) –Number of Evaluations until Convergence Missouri University of Science and Technology

Tested Algorithms C-LIMP D-LIMP Variable Dissortative Mating Genetic Algorithm (VDMGA) Traditional Genetic Algoritm (TGA) Survival Selection Methods –Tournament –Restricted Tournament Replacement (RTR) Missouri University of Science and Technology

DTRAP1 Results Missouri University of Science and Technology TournamentRTR

DTRAP2 vs. DTRAP1 Results Missouri University of Science and Technology TournamentRTR

NK Landscape Results Missouri University of Science and Technology TournamentRTR

MAXSAT Results Missouri University of Science and Technology TournamentRTR

DTRAP1 Convergence Missouri University of Science and Technology TournamentRTR

NK Landscape Convergence Missouri University of Science and Technology TournamentRTR

MAXSAT Convergence Missouri University of Science and Technology TournamentRTR