Advanced Mate Selection in Evolutionary Algorithms

1. Advanced Mate Selection in Evolutionary Algorithms

2. 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

3. 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

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

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

6. 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

7. Outbreeding Missouri University of Science and Technology

8. 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

9. 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

10. Estimated Learning Offspring OptimizingMate Selection(ELOOMS)

11. Traditional Mate Selection 5 3 8 2 4 5 2 MATES • t – tournament selection • t is user-specified 5 4 5 8

12. ELOOMS YES YES MATES YES YES NO NO YES

13. Mate Acceptance Chance (MAC) d1 d2 d3 … dL How much do I like ? k j b1 b2 b3 … bL

14. Desired Features d1 d2 d3 … dL j b1 b2 b3 … bL # 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

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

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

17. Why ELOOMS works on Deceptive Problem • More likely to preserve optimal structure • 1111 0000 will equally like: • 1111 1000 • 1111 1100 • 1111 1110 • But will dislike individuals not of the form: • 1111 xxxx

18. 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

19. Learning Individual Mating Preferences (LIMP)

20. 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

21. 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

22. Mate Selection – D-LIMP .7 | .6 | .7 | .2 j 0110 dj 0001 sk 1000 0111 1010 sk .30 .65 = 1101 0101 Missouri University of Science and Technology

23. Mate Selection – C-LIMP .8 | .9 | .2 | .7 j dP0 0110 sj .3 | .4 | .8 | .8 dP1 0001 sk 1000 0111 1010 sk .45 .60 = 1101 0101 Missouri University of Science and Technology

24. 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

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

26. Learning C-LIMP 0101 1010 .8 | .9 | .1 | .7 .8 | .9 | .2 | .7 .8 | 1 | .1 | .7 .8 | .9 | .2 | .7 .8 | .9 | .1 | .7 dP0 dP0 dP0 dP0 dP0 j k F(j)=20 F(k)=15 .1 | .4 | .8 | .9 .3 | .4 | .8 | .9 .3 | .4 | .8 | .8 .3 | .4 | .8 | .9 .3 | .4 | .8 | .8 m dP1 dP1 dP1 dP1 dP1 0110 F(m)=18 Missouri University of Science and Technology

27. 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

28. 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

29. DTRAP1 Results Tournament RTR Missouri University of Science and Technology

30. DTRAP2 vs. DTRAP1 Results Tournament RTR Missouri University of Science and Technology

31. NK Landscape Results Tournament RTR Missouri University of Science and Technology

32. MAXSAT Results Tournament RTR Missouri University of Science and Technology

33. DTRAP1 Convergence Tournament RTR Missouri University of Science and Technology

34. NK Landscape Convergence Tournament RTR Missouri University of Science and Technology

35. MAXSAT Convergence Tournament RTR Missouri University of Science and Technology