1. Linkage Learning in Evolutionary Algorithms

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

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) o Use a template to determine unidentified bits o Template of (0,0,0) gives (0,1,0) –Overspecified (2-bit problem) o First appearance from left to right provides the value for a location Cut-and-splice recombination –Cut: severs a string with p c probability o Probability corresponds to string length –Splice: joins two strings with p s probability Missouri University of Science and Technology

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

8. Linkage Identification by Nonlinearity Check (LINC) Non-linearity ∆F 1 + ∆F 2 = ∆F 12 ∆F 1 = change in fitness from perturbing locus 1 ∆F 2 = change in fitness from perturbing locus 2 ∆F 12 = change in fitness from perturbing locus 1 & 2 Due to noise in fitness, linkage identified with |∆F 12 – (∆F 1 + ∆F 2 )| > ε Missouri University of Science and Technology

9. Linkage Identification by Nonlinearity Check (LINC) Missouri University of Science and Technology 1 1 0 0 1 F=5 0 1 0 0 1 F=6 ∆F 1 =1 1 0 0 0 1 F=4 ∆F 2 =-1 0 0 0 0 1 F=5 ∆F 12 =0 |∆F 12 – (∆F 1 + ∆F 2 )| > ε |0 – (1 + -1)| > 1No Linkage 1 1 1 0 1 F=8 ∆F 2 =3 0 1 1 0 1 F=6 ∆F 12 =1 |1 – (1 + 3)| > 1Linkage Found

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 Missouri University of Science and Technology 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

12. Metabits Missouri University of Science and Technology 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 Recombination - If both metabits are 1, crossover prob =.1 - Otherwise, crossover prob =.01 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0

13. Linkage Evolving Genetic Operator Missouri University of Science and Technology 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’ ‘0 1’ ‘0 1 0’ 1’ ‘1’ ‘0

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

15. Probabilistic Expression Missouri University of Science and Technology 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

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