Download Evolutionary Computation Seminar Ch. 16 ~ 19

Evolutionary Computation Seminar
Ch. 16 ~ 19
Evolutionary Computation. Vol. 2. Advanced Algorithms and Operators
Summarized and Presented by
Heo, Min-Oh
Contents

Diffusion (Cellular) models
PART 4
ADVANCED TECHNIQUES IN
EVOLUTIONARY 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
automaton
 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
individual, 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 ranking.
 Importance of an analysis of the variance of
selection 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
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)

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)
:
f(): Average fitness values for schema
fo (): observed fitness values for schema
n (): number of copies for schema

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.
Sizing for accurate schema
sampling (2/3)

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)

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 목
적함수를 최대화 하는 문제에 쓰임
 n 차원의 목적변수를 코딩하지 않고 실수로 다룸
 개체는 문제의 해에 해당하는 n 개의 실수벡터 (목
적변수, x) 와 이에 대응하는 전략변수 (σ, α) 로 구성
 m개의 해를 가진 population P
 i번째 해 표현 예:
 Mutation
 개체의
형질에 정규분포의 랜덤 값을 더하는 것으로 정의
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

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
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

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
 Examples)
 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.