Evolutionary Algorithms: Introduction, Genetic Algorithms, Evolution Strategies, Evolutionary Programming

Part 3: Evolutionary Algorithms and Their Standard Instances On book : Evolutionary Computation – Basic Algorithms and Operators CHAPTERS 7. Introduction to evolutionary algorithms 8.Genetic algorithms 9. Evolution strategies 10. Evolutionary programming 11. Derivative methods in genetic programming Presented by Bado Lee

Introduction to evolutionary algorithms • What is Evolutionary algorithm? • 집단 유전학의 개체 진화 원리를 이용하는 solution space search 방법 • Evolutionary algorithm 이 소용없는 문제들 • Deterministic algorithm으로 쉽게 풀 수 있는 문제들 • Ex) shortest path 같은 문제들 • NP hard 이더라도 문제 공간이 아주 작은 문제들 (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

History of EA • 1950~60 독자적인 그룹이 생김 • GA (Genetic Algorithm) – John Holland 미국사람 • Crossover중요하게 생각 • Mutation 의 중요도는 상대적으로 별로 중요 하지 않음 • EP (Evolutionary Programming) • Fogel, Owens, Walsh - 미국사람 • Crossover 가 필요없다고 주장하는 사람들 • ES • Rechenberg – 독일사람 • Real valued vector 사용 • Parent 와 offspring의 population 이 일반적으로 같지 않음 (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Genetic Algorithm • First proposed and analyzed by John Holland (1975) • Representation - Bitstring representation • Method of selection – proportional selection • Primary method of producing variations – crossover • Most important characteristic is • CROSSOVER! (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Crossover and mutation • Chromosome – 염색체 (정보의 표현형) 또는 문제공간에서 하나의 solution으로 볼 수 있음 • John Holland 는 binary representation을 선호 • 다양한 솔루션을 생성 할 수 있다는 믿음 때문. 하지만 mutation을 늘리면 같은 효과를 얻을 수 있다. • 따라서 불필요한 constraint • Crossover - exploitation • 두 chromosome 을 부분결합하여 하나의 chromosome을 생성 • Mutation - exploration • Chromosome의 미소변형 (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Generation Gap : Replacement of k chromosomes among p population • Generation gap : k/p • If k->p :generational GA • 수렴이 느리고 computational cost 가 크다. • If k->1 : steady-state GA • 수렴이 빠른 대신에 Local optimal 한 solution에 도달할 가능성이 크다. 즉 premature convergence (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Problem Representation cont. • Inversion • Inverse a seq. of genes in the middle of GA running • Gene의 인접성을 고려하여 재배치함 • Messy GA • Allows variable-length chromosomes • Overspecification, underspecification overspecification 10*0 This means overspecification (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Problem Representation cont. • Locus based encoding • Graph bisection 의 문제 같은 경우에 용이한 표현형 • Order based edcoding • 인접성을 잘 표현할 수 있음 • Crossover에 취약 • Multi-dimensional encoding 등등 많은 표현형이 존재 가능하고 문제 specific하게 적용 되어야 함 절대적인 representation 존재 X (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Selection operator • Selection oprator • Crossover을 위한 selection 에서 어떤 Chromosome 을 선택할 지 결정 • Premature convergence를 피하기 위하여 다양한 method존재 • Roulette-wheel selection • Tournament selection • Rank-based selection • Sharing (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Evolutionary Strategy • Emphasis on • Problem-dependent representations!!! • Real valued search space • Traditionally on Euclidean search space • Archetype of ES If better than previous solution then ->>accept new solution (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Problem Representation • Real encoding • 실수값을 유전자에 할당 • 수의 크기 개념을 반영하기 유리 • Crossover 는 산술교차 사용 • 인자의 속성이 실수인 경우, 인자와 유전자가 1:1대응 • Phenotype genotype (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Rechenberg’s Magic number 0.2 • Until Success ratio more than 0.2 • Increase alpha – exploration • When it drops below 0.2 • Decrease alpha – exploitation • Schwefel’s proposal (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Contemporary evolution strategies • General algorithmic framework – by Schwefel • So simple ES can be expressed as (1+1)ES ->not in use Generates lambda offspring from mu parents and selects the mu best individuals form the lambda+mu individuals in total Always is (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Contemporary evolution strategies • Generates lambda offspring form mu parents but selects the mu best individuals only form lambda offspring Always is (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Evolutionary programming • Basic EC’s 4 main components • Initialization • Variation – only mutation • Evaluation (scoring) -fitness • Selection • Mostly size of the population remains constant • But this is no restriction • Different from GA because • EP is a top down versus bottom-up approach to optimization • Selection operates only on the phenotypic expressions of genotype (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Different from GA becausecont. • Underlying coding of the phenotype is only affected indirectly • Because • Realization that a sum of optimal parts rarely leads to an optimal overall solution • Do not believe in schemata theory • Solutions in an EP algorithms are judged solely on their fitness with respect to the given environment • No attempt is made to partition credit to individual components of the solutions • NO CROSSOVER – philosophically very important (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Initialization & Recombination • Initial population should be constructed under several constraints • SA. Number of Available terminals • Number of arguments required by functions • Recombined program should also satisfy constraints (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Why is GP interesting? • Conceptual shift of the problem being solved by the genetic algorithm • Parameter discovery ->> search for program directly • Changed way we think about solving problems • Capable of integrating a wide variety of existing capabilities • Parents : programs … children : also programs (C) 2010, SNU Biointelligence Lab, http://bi.snu.ac.kr/

Evolutionary Algorithms: Introduction, Genetic Algorithms, Evolution Strategies, Evolutionary Programming