Evolutionary Computation Seminar

Ch. 16 ~ 19Evolutionary Computation. Vol. 2. Advanced Algorithms and Operators

Summarized and Presented by

Heo, Min-Oh

Contents

Diffusion (Cellular) models

PART 4 ADVANCED TECHNIQUES IN EVOLU-TIONARY COMPUTATION

Population sizing Mutation parameters Recombination parameters

Diffusion (Cellular) models

Placing one individual per processor Pseudocode for a single process

Diffusion (Cellular) models

Any EA of this form is equivalent to a cellular au-tomaton

Issues (considering cost of communication in a parallel environment)¨ Selection¨ Recombination¨ Choosing parents¨ Deme attribute: size, shape of the neighborhood

One issue: Deme attribute

Something unique

Choosing parents¨ Muehlenbein (1989) chose the four neighbors, the indi-

vidual, and the global best individual was chosen twice. (7 parents) p-sexual voting

¨ Random walk 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 rank-ing. Importance of an analysis of the variance of se-lection schemes.

PART 4 ADVANCED TECHNIQUES IN EVOLUTIONARY COMPUTATION

Population sizing

Basic Idea ¨ The computational leverage (i.e. schema processing

ability) of implicit parallelism is maximized¨ The accuracy of schema average fitness values indi-

cated 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 un-derestimate the number of building blocks as

¨ number of building blocks monotonically expands Population size: 1 Population size: ∞

Sizing for optimal schema processing(2/2)

¨ Measure of computational leverage: the average real-time rate of schemata processing

¨ 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

: expected # of unique schemata in the initial, random population

Sizing for accurate schema sampling (1/3) Optimal population size for schema processing rate may not be the optimal

size for ultimate GA effectiveness. Sampling error in small populations

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 (H1) > f (H2) ,

there is a probability that fo(H1) < fo(H2) occur error

¨ By central limit thm, fo –values follows normal distribution with mean f (H) and variance σ2/n(H)

¨ Error probability (fo(H1) < fo(H2) is α):

setting n(H1) and n(H2) such that the error probability is lowered below the desired level. raising n(H) ‘sharpens’ the associated normal dist.

f(): Average fitness values for schema

fo (): observed fitness values for schema

n (): number of copies for schema

Sizing for accurate schema sampling (2/3) Some rules of thumb introduced with Some diffi-

culties¨ The values and ranges of f ( H ) are not known before-

hand for any schemata¨ the values of σ2 are neither known nor estimated

Sizing for accurate schema sampling (3/3) 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

Mutation parameter for self-adaptation (ES)¨ Evolving set of mutation parameter

Mutation parameter for direct schedules (GA)¨ Dealing with Pm

Evolution Strategy

¨ n 차원 공간에서 정의된 목적변수에 대해 정의된 목적함수를 최대화 하는 문제에 쓰임

¨ n 차원의 목적변수를 코딩하지 않고 실수로 다룸¨ 개체는 문제의 해에 해당하는 n 개의 실수벡터

( 목적변수 , x) 와 이에 대응하는 전략변수 (σ, α) 로 구성

¨ m 개의 해를 가진 population P¨ i 번째 해 표현 예 : ¨ Mutation

개체의 형질에 정규분포의 랜덤 값을 더하는 것으로 정의

Mutation parameter for self-adaptation

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

K: normalized convergence velocity

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

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

time-varying mutation rate (Hesser and Maenner)

optimal schedules of the mutation rate ¨ finding a schedule that maximizes the convergence ve-

locity or minimizes the absorption time of the algo-rithm

¨ For (1+1) –genetic algorithm, is almost optimal ¨ As the number of offspring individuals increases, the

optimal mutation rate as well as the associated conver-gence velocity increase

Nondeterministic schedules for controlling the 'amount‘of mutation

t/T=0.6, b=5t/T=0.2, b=5

Recombination parameters

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 por-

tions 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 diver-sity) due to hitchhiking

Phenotypic-level recombination (problem spe-cific)

¨ Some difficult cases Hamming cliffs: large changes in the binary encoding are re-

quired to make small changes to the real values

¨ Real-valued representation EA, ES Interval schemata

¨ Representation for permutation or ordering problems

Control of recombination pa-rameters

¨ 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 incor-

rect 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 recombina-tion The rules had three possible outputs dealing with

population size, recombination rate, and mutation rate

Examples)¨ switching mechanism to decide between two recombi-

nation 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.