Advanced Mate Selection in Evolutionary Algorithms Mate Selection

Advanced Mate Selection in Evolutionary Algorithms

Mate Selection • 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 Missouri University of Science and Technology

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

Niching 0110 1001 0111 1000 1110 0001 1111 1110 1111 1000 Missouri University of Science and Technology 0001

Assortative Mating 1110 1001 0110 1111 0111 1000 1111 1000 0001 Missouri University of Science and Technology 1001

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 Missouri University of Science and Technology

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 5 3 8 2 4 5 2 MATES • t – tournament selection • t is user-specified 5 4 5 8

ELOOMS NO YES YES YES MATES

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

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

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

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

Why ELOOMS works on Deceptive Problem • More likely to preserve optimal structure • 1111 0000 will equally like: – 1111 1000 – 1111 1110 • 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 j . 7 |. 6 |. 7 |. 2 0110 0001 dj sk 1000 0111 1010 sk . 65 =. 30 1101 0101 Missouri University of Science and Technology

Mate Selection – C-LIMP j 0110 0001 sj d. P 0 . 8 |. 9 |. 2 |. 7 d. P 1 . 3 |. 4 |. 8 sk 1000 0111 1010 sk . 45 =. 60 1101 0101 Missouri University of Science and Technology

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 j 0101 . 7 |. 6 |. 7. 6 |. 2. 3 F(j)=20 1010 m 0110 k . 2 0 |. 9 1 |. 3 |. 8 F(k)=15 . 7 |. 6 |. 3 |. 8 F(m)=18 Missouri University of Science and Technology

Learning C-LIMP j 0101 F(j)=20 1010 m 0110 F(k)=15 k d. P 0 . 8 |. 9 1 |. 2. 1 |. 7 d. P 1 . 1 |. 4 |. 8. 3. 9 F(m)=18 Missouri University of Science and Technology

Test Problems • DTRAP – DTRAP 1 – DTRAP 2 • 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

DTRAP 1 Results Tournament RTR Missouri University of Science and Technology

DTRAP 2 vs. DTRAP 1 Results Tournament RTR D-LIMP C-LIMP VDMGA TGA 0 50 100 DTRAP 2 DTRAP 1 Missouri University of Science and Technology

NK Landscape Results Tournament RTR Missouri University of Science and Technology

MAXSAT Results Tournament RTR Missouri University of Science and Technology

DTRAP 1 Convergence Tournament RTR Missouri University of Science and Technology

NK Landscape Convergence Tournament RTR Missouri University of Science and Technology

MAXSAT Convergence Tournament RTR Missouri University of Science and Technology