1. Genetic Algorithms: An Overview 4 학습목표 GA 의 기본원리를 파악하고, Prisoner’s dilemma 와 sorting network 에의 응용 및 이론적 배경을 이해한 다

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?

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

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

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

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

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

Elements of GAs  Fitness function  GA operators  selection  crossover  mutation

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 … Generator Tester Candidate Solutions

GA and Traditional Search Methods  Search for stored data  Search for paths to goals  Search for solutions

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

Homework 1  Prisoner’s dilemma 문제의 해결을 위한 EC 방법을 인코딩, 오퍼레 이터, 결과에 대해 조사하시오.  Sorting network 문제의 해결을 위한 EC 방법을 인코딩, 오퍼레이터, 결과에 대해 조사하시오.

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 Player B CD C D

Iterated Prisoner’s Dilemma (2)  Representation of strategies History TableRecent Action ∙∙∙ Last ActionRecent Action ∙∙∙ Last Action Own HistoryOpponent’s History 010 ∙∙∙ 1 l = 2 : Example History N History

Iterated Prisoner’s Dilemma (3)  Test strategies StrategyCharacteristics Tit-For-TatInitially cooperate, and then follow opponent Trigger Initially cooperate. Once opponent defects, continuously defect AllDAlways defect CDCDCooperate and defect over and over CCDCooperate and cooperate and defect RandomRandom move Example Strategies Tit-for-Tat Trigger AllD CDCD CCD Random

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 Year DesignersBose, NelsonBatcher, KnuthShapiroGreen # comparators still the best known today

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

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

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