Mesa Chromosomes 16gg8 ESD.77 Chromosome(string) l「 alleles gene 01011110100 01 Each chromosome represents a solution often using strings of Os and 1s. each bit typically corresponds to a gene. This is called binary encoding The values for a given gene are the alleles A chromosome in isolation is meaningless need decoding of the chromosome into phenotypic values o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
12 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Chromosomes Chromosomes Chromosome (string) gene 0 1 0 1 1 1 1 0 1 0 0 1 ….. 0 1 alleles Each chromosome represents a solution, often using strings of 0’s and 1’s. Each bit typically corresponds to a gene. This is called binary encoding. The values for a given gene are the alleles. A chromosome in isolation is meaningless - need decoding of the chromosome into phenotypic values
M esd GA over several generations 1688 ESD.77 Initialize Population( initialization) Select individual for mating(selection) SO0①×①S Mate individuals and produce children (crossover) Mutate children(mutation) Insert children into population (insertion) n Are stopping criteria satisfied? Finish Ref: Goldberg o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
13 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics GA over several generations GA over several generations Initialize Population (initialization ) Select individual for mating (selection ) Mate individuals and produce children (crossover ) Mutate children (mutation ) Insert children into population (insertion ) Are stopping criteria satisfied ? Finish y n next generation Ref: Goldberg
M The ga game” 16gg8 ESD.77 Ca 15 minutes Population size: N=40 Mean fitness: F=6.075 Generation 1 (Fitness F=total number of 1's in chromosome) 2 2 GA Game Initial Population 10 789012 8963330 3004247 52o-0 864 0 406075 123456789101112 Fitness value 0<=F<=12 Goal: Maximize number of 1"s o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
14 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics “The GA Game” The GA Game” Ca. 15 minutes 111 212 313 4 5 20 5 8 40 6 9 54 7 6 42 8 3 24 9 3 27 10 3 30 11 0 0 12 0 0 40 6.075 GA Game Initial Population 0 2 4 6 8 10 1 2 3 4 5 6 7 8 9 10 11 12 Fitness Value Number of Individuals Generation 1: Population size: N=40 Mean Fitness: F=6.075 (Fitness F = total number of 1’s in chromosome) 0 <= F <= 12 Goal: Maximize Number of “1”s
Mlesd Creating a GA on Computer 16gg8 ESD.77 (1)define the representation(encoding-decoding (2 define fitness"function F incorporate feasibility(constraints)and objectives (3 define the genetic operators initialization selection crossover mutation insertion (4) execute initial algorithm run monitor average population fitness identify best individual (5 tune algorithm adjust selection, insertion strategy, mutation rate o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
15 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Creating a GA on Computer Creating a GA on Computer (1) define the representation (encoding-decoding) (2) define “fitness” function F - incorporate feasibility (constraints) and objectives (3) define the genetic operators - initialization, selection, crossover, mutation, insertion (4) execute initial algorithm run - monitor average population fitness - identify best individual (5) tune algorithm - adjust selection, insertion strategy, mutation rate
M Encoding-Decoding 16gg8 ESD.77 genotype phenotype coded domain decision domain expression Biology UGCAACCGU (DNA"blocks) sequencing blue eye decodin Design 10010011110 (chromosome) encoding Genetic Code: (U, C, G, A are the four bases of the nucleotide building blocks of messenger-RNA): Uracil-Cytosin Radius r=2.57[m Adenin-Guanin -a triplet leads to a particular aminoacid(for protein synthesis )e.g. UGG-tryptophane o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
16 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Encoding Encoding - Decoding Decoding genotype phenotype Biology Design “blue eye” UGCAACCGU (“DNA” blocks) 10010011110 expression (chromosome) decoding encoding Radius R=2.57 [m] H sequencing coded domain decision domain Genetic Code: (U,C,G,A are the four bases of the nucleotide building blocks of messenger-RNA): Uracil-CytosinAdenin-Guanin - A triplet leads to a particular aminoacid (for protein synthesis) e.g. UGG-tryptophane