1. Genetic Algorithms: An Overview

1. 1. Genetic Algorithms: An Overview 학습목표 GA의 기본원리를 파악하고, Prisoner’s dilemma와sorting network에의 응용 및 이론적 배경을 이해한다

2. Outline • Brief history of EC • Appeal of evolution • Biological terminology • Search space and fitness landscape • Elements of GA • Simple GA • GA and traditional search methods • Some applications of Gas • Two brief examples • How do Gas work?

3. GA: An Overview • EAs can be regarded as population-based, stochastic generate-and-test algorithms • Two issues • How to generate offspring? • How to test (select) them? • EAs represent a whole family of algorithms, with different representation, search operators, etc • EC covers at least four major areas • EC is closely related to AI, CS, Operations Research, Machine Learning, Engineering, etc

4. Brief History • Rechenberg (1965, 1973): evolution strategies • Schwefel (1975, 1977) • Fogel, Owens & Walsh (1966): evolutionary programming • John Holland: GA • chromosomes • natural selection • genes & allele (0 or 1) • crossover/recombination with haploid • schema

5. Appeal of Evolution • Searching through a huge number of possibilities for solutions • computational protein engineering, financial market • A computer program to be adaptive • bottom-up paradigm: emergence of intelligence • Designing innovative solutions to complex problems • immune systems • Rules of evolution is simple • species evolve by means of random variation, followed by natural selection where the fittest tend to survive and reproduce

6. Biological Terminology • chromosomes(strings of DNA): blueprint for the organism • a gene encodes a trait (eye color, …) • alleles: possible settings for a trait (blue, brown, …) • genome: multiple chromosomes in a cell • genotype: particular set of genes • phenotype: its physical & mental characteristics • diploid vs haploid

7. Search Spaces & Fitness Landscapes • search space • some collection of candidate solutions to a problem and some notion of distance between candidate solutions • fitness landscape • a representation of the space of all possible genotypes along with their fitnesses • hill, peak, valley

8. Elements of GAs • Fitness function • GA operators • selection • crossover • mutation

9. Simple GA: Generate-and-Test • Loop • Generate a candidate solution • Test the candidate solution • Until a satisfactory solution is found or no more candidate solutions can be found Candidate Solutions Generator Tester …

10. GA and Traditional Search Methods • Search for stored data • Search for paths to goals • Search for solutions

11. Some Applications of GAs • Optimization • Automatic programming • Machine learning • Economics • Immune systems • Ecology • Population genetics • Evolution and learning • Social systems

12. Homework 1 • Prisoner’s dilemma 문제의 해결을 위한 EC 방법을인코딩, 오퍼레이터, 결과에 대해 조사하고, EC방법의 가능성에 대해서 기술하시오. • Sorting network 문제의 해결을 위한 EC방법에 대해서도 위와 같이 조사하시오.

13. Iterated Prisoner’s Dilemma (1) • Non-zero sum, non-cooperative games • The 2 player version • The purpose here is not to find the optimal solution for some simplified conditions, but to study how to find it • Fitness evaluation • Entirely determined by the total payoff obtained through playing against each other • The initial population was generated at random Player A C D 3 5 C 3 0 Player B 0 1 D 1 5

14. 0 1 0 ∙∙∙ 1 Iterated Prisoner’s Dilemma (2) • Representation of strategies Own History Opponent’s History History Table Recent Action ∙∙∙ Last Action Recent Action ∙∙∙ Last Action 2NHistory l = 2 : Example History 11 01

15. Iterated Prisoner’s Dilemma (3) • Test strategies • Example Strategies Tit-for-Tat CDCD 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 Trigger CCD 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 AllD Random 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1

16. Sorting Networks (1) • A sorting algorithm in essence, but can be represented graphically for the ease of understanding • Used widely in switching circuits, routing algorithms, and other areas in interconnection networks • Two issues • Number of comparators • Number of layers • Best known networks with 16 inputs still the best known today

17. Sorting Networks (2) • Comparators • Graphical representation of a sorting network small sorted output unsorted input large input element unsorted input sorted output a layer

18. How do GAs Work? (1) • Traditional assumption • GA works by discovering, emphasizing, and recombining good “building blocks” of solutions in a highly parallel fashion • Schemas = building blocks • A set of bit strings that can be described by a template made up of ones, zeros, and asterisks (don’t cares) • Instance of H: strings fit the template H • Order: defined bits (non-asterisks) in a H • Defining length: distance between its outermost defined bits • How does GA process schemas? • A bit string of length l = an instance of 2^l different schemas • No. of schema instances in a population of n strings • 2^l ~ n*2^l

19. How do GAs Work? (2) • Schema Theorem • P. 29: equation (1.2)  lower bound in destructive effects of crossover and mutation • Desription: Growth of a schema from one generation to the next • Implication: Short, low-order schemas whose average fitness remains above the mean will receive exponentially increasing numbers of samples over time • Reason: no. of samples of those schemas that are not disrupted and remain above average in fitness increases by a factor of U/F at each generation