Harnessing Evolution: Evolution Strategies Christian Jacob Dept. - PowerPoint PPT Presentation

Harnessing Evolution: Evolution Strategies Christian Jacob Dept. of Computer Science Dept. of Biochemistry & Molecular Biology University of Calgary Christian Jacob, University of Calgary www.swarm - design.org

Intelligent Designs Christian Jacob, University of Calgary www.swarm - design.org

In Search for Better “ Designs ” global maximum local maxima local maxima Christian Jacob, University of Calgary www.swarm - design.org

Evolution in Action … Christian Jacob, University of Calgary www.swarm - design.org

Evolutionary Search • Knowledge Reservoir Set of possible solutions • Gleaning a reservoir of knowledge � om interactions � ith the environment. • Selection Fitness - dependent number of o ff spring • The sieve of selection cu � s out incorrect / unuseful “ knowledge ” . • V ariation V ariations of individual solutions • The learning system invents new variants of its old ideas that are tested against environmental demands. Christian Jacob, University of Calgary www.swarm - design.org

Evolution Strategies 1. Motivation: Cumulative Selection 2. Evolution Strategies a. Enlightening Experiments b. Evolutionary Search Spaces c. Evolution Schemes 3. ES Chromosomes and Mutations a. Object and Strategy Parameters b. Mutations of Object Parameters c. Adaptation of Strategy Parameters Recombinations d. 4. Evolution Strategies Visualized in Action E. Appendix: Meta - Evolution Strategies F. Appendix: EC Test Functions Christian Jacob, University of Calgary www.swarm - design.org

Cumulative Selection EVOLUTION OF STRUCTURE, STEP BY STEP (O) (a) ,LPYJK,ZPBGXWKTEKSQ,KLVCFZSJFGVZQWG ETTLXTKOL RF STRZGPURE CSYEPYBY SQEP (b) EVOLUDION OF STRUKTURE STEP BZ,STEB (c) Christian Jacob, University of Calgary www.swarm - design.org

Cumulative Selection • A simpli fi ed version of the evolutionary principle of adaptation is used to search for a prede fi ned string – starting from an initially random sequence of characters and – using iterated mutation and cumulative selection. • Random strings are compared to an objective sentence. Christian Jacob, University of Calgary www.swarm - design.org

Cumulative Selection Algorithm 1. Initialization : Generate an initial set S = { s 1 , …, s n } of n individuals. 2. Initial evaluation : Evaluate all individuals and calculate their fi tnesses. 3. Selection : Choose the best individual s best ∈ S . 4. Mutation : From the best individual, generate a set of n - 1 mutants: M = { s i ’ := mut ( s best ) | i = 1 , …, n - 1 } . 5. Evaluation : Evaluate all mutants and calculate their fi tnesses. 6. Termination check : a. If at least one of the individuals has achieved the maximum fi tness, stop. b. Otherwise, generate a new selection set: S = { s best } ∪ M. 7. Continue with step 3. Christian Jacob, University of Calgary www.swarm - design.org

Strings Encoded by Numbers Input: Output: Each letter is encoded by its ASCII code. Input: τ Output: τ inv Input: Output: From Evolvica Notebooks: http://www.cpsc.ucalgary.ca/ ~ jacob/IEC Christian Jacob, University of Calgary www.swarm - design.org

Mutation on Strings • W e de fi ne string mutation on a string s = s 1 … s N as follows: mut ( s, r, p ) = s 1 ’ … s N ’ where s i ’ = s i if χ real ( 0,1 ) > p. s i ’ = m ( s i , r ) otherwise. m ( x , r ) = τ inv ( τ ( x ) + χ int (- r, r ) ) . • χ int ( y, z ) or χ real ( y, z ) returns a uniformly distributed, integer or real random number from the interval [ y, z ] . • The character x is translated into its number encoding τ ( x ) . Christian Jacob, University of Calgary www.swarm - design.org

String Mutations s: EVOLUTION OF STRUCTURE, STEP BY STEP EVOLUTION OF STRUCTURE, STEP BY STEP s: mut(s, 1, 0.1) mut (s,1,0.2): EVNLVTION OF SURUCTURE, STEP BY STEP DVOLUTIONZOF STRUDSUQE, SSEP,CY SSEP : EVOLUTION OF STRUCTURE, STEP BY STEP s: EVOLUTION OF STRUCTURE, STEP BY STEP s: mut(s, 1, 0.2) mut (s,2,0.2): EVOLUTIOM OF STRVCTURE. STEP BZ STEP FVOLUTIONYOF STTUCTURE, QTEP BY STEP : EVOLUTION OF STRUCTURE, STEP BY STEP s: EVOLUTION OF STRUCTURE, STEP BY STEP s: mut(s, 1, 0.5) mut (s,5,0.2): EWNLVUHON,OE SSSUCUVRD.ZSUEP,CY,STEQ EVOLUTNON OFCOTRYFTUME, STEPBB STFP : Mutation on strings Mutation on strings with mutation radius 1 with mutation rate 0.2 and di ff erent mutation rates and varying mutation radii From Evolvica Notebooks: http://www.cpsc.ucalgary.ca/ ~ jacob/IEC Christian Jacob, University of Calgary www.swarm - design.org

String Evolution: DEMOS Mut. Radius: 1 Mut. Rate: 0.1 Mut. Radius: 1 Mut. Rate: 0.5 Mut. Radius: 5 Mut. Rate: 0.1 Mut. Radius: 5 Mut. Rate: 0.5 Christian Jacob, University of Calgary www.swarm - design.org

String Evolution: DEMOS Mut. Radius: 1 Mut. Rate: 0.1 Mut. Radius: 5 Mut. Rate: 0.1 Mut. Radius: 1 Mut. Rate: 0.5 Mut. Radius: 5 Mut. Rate: 0.5 Christian Jacob, University of Calgary www.swarm - design.org

String Evolution Mut. Radius: 2, Mut. Rate: 0.1 Christian Jacob, University of Calgary www.swarm - design.org

String Evolution Hamming Distance Plots Mutation radius: 2 Mutation radius: 4 Mutation radius: 2 Mutation rate: 0.1 Mutation rate: 0.1 Mutation rate: 0.2 Christian Jacob, University of Calgary www.swarm - design.org

Evolution Strategies 1. Motivation: Cumulative Selection 2. Evolution Strategies • Enlightening Experiments • Evolutionary Search Spaces • Evolution Schemes 3. ES Chromosomes and Mutations • Object and Strategy Parameters • Mutations of Object Parameters • Adaptation of Strategy Parameters • Recombinations Evolution Strategies Visualized in Action 4. E. Appendix: Meta - Evolution Strategies F. Appendix: EC Test Functions Christian Jacob, University of Calgary www.swarm - design.org

Evolution Strategies ( ES ) Ingo Rechenberg Hans - Paul Schwefel ( 1973 ) Evolution for Engineering Design Christian Jacob, University of Calgary www.swarm - design.org

Evolution of Joint Plates Christian Jacob, University of Calgary www.swarm - design.org

Evolution of Joint Plates: Results Drag Drag Mutations Mutations Christian Jacob, University of Calgary www.swarm - design.org

Evolution of Bent Pipes Christian Jacob, University of Calgary www.swarm - design.org

Evolution of Bent Pipes: Results Drag Mutations Christian Jacob, University of Calgary www.swarm - design.org

Evolution of a Jet Nozzle Christian Jacob, University of Calgary www.swarm - design.org

Evolution of a Jet Nozzle: Results Experiment performed in 1968. [I. Rechenberg: Evolutionsstrategie ‘94 Frommann-Holzboog, 1994.] Christian Jacob, University of Calgary www.swarm - design.org

Evolution Strategies 1. Motivation: Cumulative Selection 2. Evolution Strategies • Enlightening Experiments • Evolutionary Search Spaces • Evolution Schemes ES Chromosomes and Mutations 3. • Object and Strategy Parameters • Mutations of Object Parameters • Adaptation of Strategy Parameters • Recombinations 4. Evolution Strategies Visualized in Action E. Appendix: Meta - Evolution Strategies Appendix: EC Test Functions F. Christian Jacob, University of Calgary www.swarm - design.org

Evolutionary Algorithm Building Blocks Individuals : . . . . . . . . . . . . . . . µ Genotype of Phenotype of P opulation of an individual an individual, µ individuals realization Genetic Operators : t x x x 2x . . . x . . . . . . . . . . . . x . . . . . . . . . x x x µ x x x Duplication Mutation Isolation for Recombination t time units Selection and Evaluation : w Q . . . . . . . . . . . . . . . . . . . . . µ µ Q Evaluation Selection Random selection Christian Jacob, University of Calgary www.swarm - design.org

( 1+1 )- ES and ( 1,1 )- ES 2x 2x . . . . . . . . . . . . Q Q . . . . . . . . . . . . . . . . . . Q Q . . . . . . (a) (b) (1+1) ES (1,1) ES Christian Jacob, University of Calgary www.swarm - design.org

( 1+ λ )- ES and ( 1, λ )- ES 2x 2x 2x . . . . . . . . . . . . ... Q Q Q 2x 2x 2x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... Mutation ... 1+ λ Q 1 2 λ . . Q Q Q . . . . . . . . . . . . . . . . . . (a) . Selection Evaluation ... (1+ λ ) ES λ Q 1 2 λ . . . (b) (1 , λ ) ES Christian Jacob, University of Calgary www.swarm - design.org

( µ + λ )- ES and ( µ , λ )- ES 2x 2x 2x 2x 2x 2x w w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... µ µ Q Q Q Q Q Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... µ+ λ λ Q Q 1 2 λ 1 2 λ . . . . . . . . . . . . . . . . . . µ (a) µ (b) Christian Jacob, University of Calgary www.swarm - design.org

( µ / 2 , λ )- ES 2x 2x 2x 2x 2x 2x w . . . . . . . . . . . . . . . . . . . . . . . . . . . ... µ Recombination w w w . . . Mutation . . . . . . ... Q Q Q . . . . . . . . . . . . Selection Evaluation . . . . . . ... λ Q 1 2 λ . . . . . . . . . µ Christian Jacob, University of Calgary www.swarm - design.org