Linkage Learning in Evolutionary Algorithms

1. Linkage Learning in Evolutionary Algorithms

2. Recombination • Recombination explores the search space • Classic Recombination • N-point crossover • Uniform • Limitation • Disrupting good partial solutions via crossover is problematic Missouri University of Science and Technology

3. Linkage Learning • Linkage learning focuses on keeping linked genes together • Main classifications of linkage learning • Perturbation-based • Linkage Adaption • Probabilistic Model Building / Estimation of Distribution algorithms Missouri University of Science and Technology

4. Perturbation-based Methods • Metrics for determining linkage • Non-linear • Non-monotonic • Epitasis • Process • Two gene locations examined • Calculate fitness after perturbing each location separately and both together • Calculate metric • Add to a linkage set if metric indicates link Missouri University of Science and Technology

5. Perturbation-based Methods • Messy Genetic Algorithm • Linkages identified during evolution • Genes encoded as gene, allele pairs • Partial solutions are combined • Linkage identification and nonlinearity check procedure • Identification separated from the evolutionary process • Linkage information used to avoid linkage breaks in recombination Missouri University of Science and Technology

6. Messy Genetic Algorithm • Messy string: ((2 1), (1 0), (2 0)) • Underspecified (3-bit problem) • Use a template to determine unidentified bits • Template of (0,0,0) gives (0,1,0) • Overspecified (2-bit problem) • First appearance from left to right provides the value for a location • Cut-and-splice recombination • Cut: severs a string with pc probability • Probability corresponds to string length • Splice: joins two strings with ps probability Missouri University of Science and Technology

7. Messy Genetic Algorithm • 2 phase evolutionary process • Primordial • Deals with small string segments – Building Blocks • Building Blocks are reproduced to generate good quality pieces • Juxtapositional • Cut, splice and other genetic operators are involved to combine the good Building Blocks • Full solutions are formed Missouri University of Science and Technology

8. Linkage Identification by Nonlinearity Check (LINC) • Non-linearity ∆F1 + ∆F2 = ∆F12 ∆F1 = change in fitness from perturbing locus 1 ∆F2 = change in fitness from perturbing locus 2 ∆F12 = change in fitness from perturbing locus 1 & 2 Due to noise in fitness, linkage identified with |∆F12 – (∆F1 + ∆F2)| > ε Missouri University of Science and Technology

9. Linkage Identification by Nonlinearity Check (LINC) 1 1 0 0 1 F=5 0 1 0 0 1 F=6 ∆F1 = 1 1 0 0 0 1 1110 1 F=8 ∆F2 =3 F=4 ∆F2 = -1 0110 1 0 0 0 0 1 F=5 ∆F12 = 0 F=6 ∆F12 = 1 |∆F12 – (∆F1 + ∆F2)| > ε |0 – (1 + -1)| > 1 No Linkage |1– (1+3)| > 1Linkage Found Missouri University of Science and Technology

10. Linkage Adaption • Borrows from gene representation and modification in biology • Movable genes • Non-coding segments • Early techniques • Punctuation marks • Metabits • Linkage Evolving Genetic Operator Missouri University of Science and Technology

11. Punctuation Marks 1 ’ 1 0 0 1 0 ’ 1 1 1 0 0 1 ’ 1 1 0 ’ 1 0 1 ’ 0 0 Recombination 1 ’ 1 ’0 0 1 0 ’ 0 1 ’ 1 0 Missouri University of Science and Technology

12. Metabits 11 11 00 00 01 00 11 01 01 00 1001 0101 10 01 10 01 00 00 • Recombination • If both metabits are 1, crossover prob = .1 • Otherwise, crossover prob = .01 11 11 00 00 01 00 10 01 00 00 Missouri University of Science and Technology

13. Linkage Evolving Genetic Operator 1 1’ ‘0 0 1 ‘0’ ‘1 1’ ‘1’ ‘0 0‘1’ ‘1 1’ ‘0 1 0’ 1 0 0 • Recombination • Punctuation marks next to each other indicate linked genes • Crossover can’t occur between linkages 1 1’ ‘01’ ‘0 1 0’ 1’ ‘1’ ‘0 Missouri University of Science and Technology

14. Linkage Adaption • Linkage Learning Genetic Algorithm • Recent technique • Specialized chromosome representation • Movable genes • Non-coding segments • Probabilistic expression • Promoters • Linkage represented by the distance between genes Missouri University of Science and Technology

15. Probabilistic Expression Point of Interpretation A: (5,1) (4,0) (4,1) (3,0) (3,1)(5,0) = **001 B: (4,0) (4,1) (3,0) (3,1) (5,0)(5,1) = **000 Missouri University of Science and Technology

16. Probabilistic Model Building • Statistical models of the current generation generate new solutions • Early linkage learning • pairwise statistical measurements • Advanced linkage learning • Dependency trees • Bayesian networks • Marginal product models Missouri University of Science and Technology

17. Linkage Tree Genetic Algorithm • Statistical linkage learning process • Standard EA structure • Process • Linkage tree built every generation using hierarchal clustering • Linkage tree traversed to create crossover masks for offspring creation • Two parents compete with offspring pair • Two best continue down linkage tree Missouri University of Science and Technology