# Evolutionary Computation Seminar Ch 16 19 Evolutionary Computation

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Evolutionary Computation Seminar Ch. 16 ~ 19 Evolutionary Computation. Vol. 2. Advanced Algorithms and Operators Summarized and Presented by Heo, Min-Oh

Contents l Diffusion (Cellular) models PART 4 ADVANCED TECHNIQUES IN EVOLUTIONARY COMPUTATION Population sizing l Mutation parameters l Recombination parameters l

Diffusion (Cellular) models Placing one individual per processor l Pseudocode for a single process l

Diffusion (Cellular) models Any EA of this form is equivalent to a cellular automaton l Issues (considering cost of communication in a parallel environment) l ¨ Selection ¨ Recombination ¨ Choosing parents ¨ Deme attribute: size, shape of the neighborhood

One issue: Deme attribute

Something unique l Choosing parents ¨ Muehlenbein (1989) chose the four neighbors, the individual, and the global best individual was chosen twice. (7 parents) p-sexual voting ¨ Random walk l Theoretical research in diffusion models ¨ In experiments comparing proportional, ranking and binary tournament selection (De Jong and Sarma (1995)) tournament selection perform worse than linear ranking. Importance of an analysis of the variance of selection schemes.

PART 4 ADVANCED TECHNIQUES IN EVOLUTIONARY COMPUTATION

Population sizing l Basic Idea ¨ The computational leverage (i. e. schema processing ability) of implicit parallelism is maximized ¨ The accuracy of schema average fitness values indicated by a finite sample of the schemata in a population

Sizing for optimal schema processing(1/2) ¨ probability that a single string matches a particular schema H: ¨ probability of one or more matches in a population of size n: ¨ total expected number of schemata in the population ¨ Given the previous count of schemata, one can slightly underestimate the number of building blocks as ¨ number of building blocks monotonically expands size: 1 < Population size: ∞ < Population

Sizing for optimal schema processing(2/2) ¨ Measure of computational leverage: the average real-time rate of schemata processing : expected # of unique schemata in the initial, random population ¨ Estimating convergence time < Assume: If one considers convergence to all but one of the population members to the same string, the convergence time is < time t, varies with the degree of parallelization < ¨ Message from this analysis < should use the smallest population possible inspired micro-GA

Sizing for accurate schema sampling (1/3) l Optimal population size for schema processing rate may not be the optimal size for ultimate GA effectiveness. Sampling error in small populations l variance of average fitness values of these schemata exists due to the various combinations of bits that can be placed in the ‘don’t care’ positions. : Collateral noise ¨ If one assumes f (H 1) > f (H 2) , there is a probability that fo(H 1) < fo(H 2) occur error ¨ By central limit thm, fo –values follows normal distribution with mean f (H) and variance σ2/n(H) ¨ Error probability (fo(H 1) < fo(H 2) is α) : f(): Average fitness values for schema fo (): observed fitness values for schema n (): number of copies for schema l setting n(H 1) and n(H 2) such that the error probability is lowered below the desired level. raising n(H) ‘sharpens’ the associated normal dist.

Sizing for accurate schema sampling (2/3) l Some rules of thumb introduced with Some difficulties ¨ The values and ranges of f ( H ) are not known beforehand for any schemata ¨ the values of σ2 are neither known nor estimated

Sizing for accurate schema sampling (3/3) l method of dynamically adjusting population size ¨ Adaptively resizes the population based on the absolute expected selection loss ¨ If the fitness values are nearly equal, the overlap in the distributions will be great a large population. ¨ If the fitness values are nearly equal, their importance to the overall search may be minimal, precluding the need for a large population on their account

Mutation Parameter l Mutation parameter for self-adaptation (ES) ¨ Evolving set of mutation parameter l Mutation parameter for direct schedules (GA) ¨ Dealing with Pm

Mutation parameter for self-adaptation K: normalized convergence velocity < Two Learning rate and new (1995) version < The mutation of Rotation angles • Recommended value for β=0. 0853 (5º) ¨ Changing mutation step size (Rechenberg, 1994) • Recommended value for α = 1. 3

Mutation parameters for direct schedules l Mutation is a background operator for GA

l Varying mutation rate over the generations (Fogarty, 1989) < Result: Both significantly improves the on-line performance of GAs if evolution is started with a population of all zero bits

l time-varying mutation rate (Hesser and Maenner) l optimal schedules of the mutation rate ¨ finding a schedule that maximizes the convergence velocity or minimizes the absorption time of the algorithm ¨ For (1+1) –genetic algorithm, is almost optimal ¨ As the number of offspring individuals increases, the optimal mutation rate as well as the associated convergence velocity increase

Nondeterministic schedules for controlling the 'amount‘of mutation t/T=0. 2, b=5 t/T=0. 6, b=5

Recombination parameters l Genotypic-level recombination (bit level) ¨ Ex) 1 -pt crossover, n-pt crossover, uniform crossover ¨ 2 Characters (De jong & Spears, 1992) < Productivity power: p to generate different offspring from parents < exploration power: moving power to go farther away from current point ¨ 2 biases (Eshelman et al, 1989) < Positional bias (schema bias): dependency upon the location of the alleles in the chromosome < Distributional bias (recombinative bias): the amount of material that is expected to be exchanged is distributed around some values as opposed to being uniformly distributed. < cf) length bias: dependency upon the length of a schema

Genotypic-level recombination - Heuristics < Reducing allele loss rates to save both offspring < Reduced surrogate combination: concentrating on those portions of a chromosome in which the alleles of two parents are not the same < When the population size is small or when the population is almost homogeneous disruption is most useful < high-recombinative-bias and low-schema-bias recombination to combat premature convergence (i. e. loss of genetic diversity) due to hitchhiking

Phenotypic-level recombination (problem specific) ¨ Some difficult cases < Hamming cliffs: large changes in the binary encoding are required to make small changes to the real values ¨ Real-valued representation < EA, ES < Interval schemata ¨ Representation for permutation or ordering problems

Control of recombination parameters ¨ Static techniques < assume that one particular recombination operator should be applied at some static rate for all problems ¨ Predictive techniques < designed to predict the performance of recombination operators < Computing the past performance of an operator as an estimate of the future performance of an operator ¨ Adaptive techniques < Recognize when bias is correct or incorrect, and recover from incorrect biases when possible < Tag-based: attach extra information to a chromosome, which is both evolved by the EA and used to control recombination < Rule-based: adapt recombination using control mechanisms and data structures that are external to the EA

Rule-based adaptive recombination The rules had three possible outputs dealing with population size, recombination rate, and mutation rate l Examples) l ¨ switching mechanism to decide between two recombination operators that often perform well ¨ Using finite-state automata to identify groups of bits that should be kept together during recombination ¨ operator tree to fire recombination more often ¨ fuzzy rules for GAs.