Chapter 8: Introduction to Evolutionary Computation Chapter 8: Introduction to Evolutionary Computation Computational Intelligence: Second Edition Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
Computational Intelligence: Second Edition
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Contents
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Some Theories about Evolution
Evolution is an optimization process:the aim is to improve the ability of an organism to survive indynamically changing and competitive environments
Two main theories on biological evolution:
Lamarckian (1744-1829) viewDarwinian (1809-1882) view
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Lamarckian Evolution
Heredity, i.e. the inheritance of acquired traits
Individuals adapt during their lifetimes, and transmit theirtraits to their offspring
Offspring continue to adapt
Method of adaptation rests on the concept of use and disuse
Over time individuals lose characteristics they do not requireand develop those which are useful by “exercising” them
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Darwinian Evolution
Theory of natural selection and survival of the fittestIn a world with limited resources and stable populations, eachindividual competes with others for survival
Those individuals with the “best” characteristics (traits) aremore likely to survive and to reproduce, and thosecharacteristics will be passed on to their offspring
These desirable characteristics are inherited by the followinggenerations, and (over time) become dominant among thepopulation
During production of a child organism, random events causerandom changes to the child organism’s characteristics
What about Alfred Wallace?
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Evolutionary Computation
Evolutionary computation (EC) refers to computer-based problemsolving systems that use computational models of evolutionaryprocesses, such as
natural selection,
survival of the fittest, and
reproduction,
as the fundamental components of such computational systems
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Main Components of an Evolutionary Algorithm
Evolution via natural selection of a randomly chosenpopulation of individuals can be thought of as a searchthrough the space of possible chromosome values
In this sense, an evolutionary algorithm (EA) is a stochasticsearch for an optimal solution to a given problem
Main components of an EA:an encoding of solutions to the problem as a chromosome;a function to evaluate the fitness, or survival strength ofindividuals;initialization of the initial population;selection operators; andreproduction operators.
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Generic Evolutionary Algorithm: Algorithm 8.1
Let t = 0 be the generation counter;Create and initialize an nx -dimensional population, C(0), to consistof ns individuals;while stopping condition(s) not true do
Evaluate the fitness, f (xi (t)), of each individual, xi (t);Perform reproduction to create offspring;Select the new population, C(t + 1);Advance to the new generation, i.e. t = t + 1;
end
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Evolutionary Computation Paradigms
Genetic algorithms model genetic evolution.Genetic programming, based on genetic algorithms, butindividuals are programs.Evolutionary programming, derived from the simulation ofadaptive behavior in evolution (i.e. phenotypic evolution).Evolution strategies, geared toward modeling the strategicparameters that control variation in evolution, i.e. theevolution of evolution.Differential evolution, similar to genetic algorithms, differingin the reproduction mechanism used.Cultural evolution, which models the evolution of cultureCo-evolution, in competition or cooperation
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
The Chromosome
Characteristics of individuals are represented by long strings ofinformation contained in the chromosomes of the organism
Chromosomes are structures of compact intertwined moleculesof DNA, found in the nucleus of organic cells
Each chromosome contains a large number of genes, where agene is the unit of heredity
An alternative form of a gene is referred to as an allele
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
The “Artificial” Chromosome
In the context of EC, the following notation is used:
Chromosome (genome) Candidate solutionGene A single variable to be optimizedAllelle Assignment of a value to a variable
Two classes of evolutionary information:
A genotype describes the genetic composition of an individual,as inherited from its parents
A phenotype is the expressed behavioral traits of an individualin a specific environment
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Binary Representation
Binary-valued variables: xi ∈ {0, 1}nx , i.e. each xij ∈ {0, 1}Nominal-valued variables: each nominal value can be encodedas an nd -dimensional bit vector where 2nd is the total numberof discrete nominal values for that variable
Continuous-valued variables: map the continuous search spaceto a binary-valued search space:
Each continuous-valued variable is mapped to annd -dimensional bit vector
φ : R → (0, 1)nd
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Binary Representation (cont)
Transform each individual
x = (x1, . . . , xj , . . . , xnx )
with xj ∈ R to the binary-valued individual,
b = (b1, . . . ,bj , . . . ,bnx )
wherebj = (b(j−1)nd+1, . . . , bjnd
)
with bl ∈ {0, 1} and the total number of bits, nb = nxnd
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Binary Representation (cont)
Decoding each bj back to a floating-point representation:
Φj(b) = xmin,j +xmax ,j − xmin,j
2nd − 1
(nd−1∑l=1
bj(nd−l)2l
)
That is, use the mapping,
Φj : {0, 1}nd → [xmin,j , xmax ,j ]
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Binary Representation (cont)
Problems with using a binary representation:
Conversion form a floating-point value to a bitstring of nd bitshas the maximum attainable accuracy
xmax,j−xmin,j
2nd−1 for eachvector component, j = 1, . . . , nx
Binary coding introduces Hamming cliffs:
Hamming cliff is formed when twonumerically adjacent values have bitrepresentations that are far apart
710 = 01112 vs 810 = 10002
Large change in solution is needed forsmall change in fitness
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Gray Coding
In Gray coding, the Hamming distance between therepresentation of successive numerical values is oneFor 3-bit representations:
Binary Gray
0 000 0001 001 0012 010 0113 011 0104 100 1105 101 1116 110 1017 111 100
Converting binary strings to Gray bitstrings:
g1 = b1
gl = bl−1bl + bl−1bl
where bl is bit l of the binary number
b1b2 · · · bnb
b1 is the most significant bitComputational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Gray Coding (cont)
A Gray code representation, bj can be converted to afloating-point representation using
Φj(b) = xmin,j+xmax ,j − xmin,j
2nd − 1
nd−1∑l=1
nd−l∑q=1
b(j−1)nd+q
mod 2
2l
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Other Representations
Other representations:
Real-valued representations, where xij ∈ RInteger-valued representations, where xij ∈ ZDiscrete-valued representations, where xij ∈ dom(xj)
Tree-based representations as used in Genetic Programming
Mixed representations
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Initialization
A population of candidate solutions is maintained
Values are randomly assigned to each gene from the domainof the corresponding variable
Uniform random initialization is used to ensure that the initialpopulation is a uniform representation of the entire searchspace
What are the consequences of the size of the initialpopulation?
Computational complexity per generationNumber of generations to convergeQuality of solutions obtained – Exploration ability
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Survival of the Fittest
Based on the Darwinian model, individuals with the bestcharacteristics have the best chance to survive and toreproduce
A fitness function is used to determine the ability of anindividual of an EA to survive
The fitness function, f , maps a chromosome representationinto a scalar value:
f : Γnx → R
where Γ represents the data type of the elements of annx -dimensional chromosome
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Objective Function
The fitness function represents the objective function, Ψ,which represents the optimization problemSometimes the chromosome representation does notcorrespond to the representation expected by the objectivefunction, in which case
f : SCΦ→ SX
Ψ→ R Υ→ R+
SC represents the search space of the objective functionΦ represents the chromosome decoding functionΨ represents the objective function
Υ represents a scaling functionFor example:
f : {0, 1}nbΦ→ Rnx
Ψ→ R Υ→ R+
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Objective Function Types
Types of objective functions, resulting in different problem types:
Unconstrained objective functions, but still subject toboundary constraints
Constrained objective functions
Multi-objective functions, where more than one objective hasto be optimized
Dynamic or noisy objective functions
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Selection Operators
Relates directly to the concept of survival of the fittest
The main objective of selection operators is to emphasizebetter solutionsSelection steps in an EA:
Selection of the new populationSelection of parents during reproduction
Selective pressure:Takeover timeRelates to the time it requires to produce a uniform populationDefined as the speed at which the best solution will occupy theentire population by repeated application of the selectionoperator aloneHigh selective pressure reduces population diversity
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Random Selection
Each individual has a probability of 1ns
to be selected
ns is the size of the population
No fitness information is used
Random selection has the lowest selective pressure
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Proportional Selection
Biases selection towards the most-fit individuals
A probability distribution proportional to the fitness is created,and individuals are selected by sampling the distribution,
ϕs(xi (t)) =fΥ(xi (t))∑nsl=1 fΥ(xl(t))
ns is the total number of individuals in the populationϕs(xi ) is the probability that xi will be selectedfΥ(xi ) is the scaled fitness of xi , to produce a positivefloating-point value
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Proportional Selection: Sampling Methods
Roulette wheel selection: Assuming maximization andnormalized fitness values (Algorithm 8.2):
Let i = 1, where i denotes the chromosome index;Calculate ϕs(xi );sum = ϕs(xi );Choose r ∼ U(0, 1);while sum < r do
i = i + 1, i.e. advance to the next chromosome;sum = sum + ϕs(xi );
endReturn xi as the selected individual;
High selective pressure
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Proportional Selection: Stochastic Universal Sampling
Uses a single random value to sample all of the solutions bychoosing them at evenly spaced intervals
Like roulette wheel sampling, construct a wheel with sectionsfor each of the ns chromosomes
Instead of one hand that is spun once for each sample, amulti-hand is spunt just once
The hand has ns arms, equally spaced
The number of times chromosome i is sampled is the numberof arms that fall into the chromosomes section of the wheel
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Tournament Selection
Selects a group of nts individuals randomly from thepopulation, where nts < ns
Select the best individual from this tournament
For crossover with two parents, tournament selection is donetwice
Tournament selection limits the chance of the best individualto dominate
Large nts versus small nts
Selective pressure depends on the value of nts
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Rank-Based Selection
Uses the rank ordering of fitness values to determine theprobability of selection
Selection is independent of absolute fitness
Non-deterministic linear sampling:
Selects an individual, xi , such that i ∼ U(0,U(0, ns − 1))The individuals are sorted in decreasing order of fitness valueRank 0 is the best individualRank ns − 1 is the worst individual
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Rank-Based Selection (cont)
Linear ranking:
Assumes that the best individual creates λ̂ offspring, and theworst individual λ̃1 ≤ λ̂ ≤ 2 and λ̃ = 2− λ̂The selection probability of each individual is calculated as
ϕs(xi (t)) =λ̃ + (fr (xi (t))/(ns − 1))(λ̂− λ̃)
ns
where fr (xi (t)) is the rank of xi (t)
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Rank-Based Selection (cont)
Nonlinear ranking:
ϕs(xi (t)) =1− e−fr (xi (t))
β
ϕs(xi ) = ν(1− ν)np−1−fr (xi )
fr (xi ) is the rank of xi
β is a normalization constantν indicates the probability of selecting the next individual
Rank-based selection operators may use any sampling methodto select individuals
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Boltzmann Selection
Based on the thermodynamical principles of simulatedannealing
Selection probability:
ϕ(xi (t)) =1
1 + ef (xi (t))/T (t)
T (t) is the temperature parameter
An initial large value ensures that all individuals have an equalprobability of being selected
As T (t) becomes smaller, selection focuses more on the goodindividuals
Can use any sampling method
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Boltzmann Selection (cont)
Boltzmann selection can be used to select between twoindividuals
For example, if
U(0, 1) >1
1 + e(f (xi (t))−f (x′i (t)))/T (t)
then x′i (t) is selected; otherwise, xi (t) is selected
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
(µ +, λ)-Selection
Deterministic rank-based selection methods used inevolutionary strategies
µ indicates the number of parents
λ is the number of offspring produced from each parent
(µ, λ)-selection selects the best µ offspring for the nextpopulation
(µ + λ)-selection selects the best µ individuals from both theparents and the offspring
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Elitism
Ensures that the best individuals of the current populationsurvive to the next generation
The best individuals are copied to the new population withoutbeing mutated
The more individuals that survive to the next generation, theless the diversity of the new population
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Hall of Fame
Similar to the list of best players of an arcade game
For each generation, the best individual is selected to beinserted into the hall of fame
Contain an archive of the best individuals found from the firstgeneration
The hall of fame can be used as a parent pool for thecrossover operator
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
Types of Operators
Reproduction: process of producing offspring from selectedparents by applying crossover and/or mutation operatorsCrossover is the process of creating one or more newindividuals through the combination of genetic materialrandomly selected from two or more parentsMutation:
The process of randomly changing the values of genes in achromosomeThe main objective is to introduce new genetic material intothe population, thereby increasing genetic diversityMutation probability and step sizes should be smallProportional to the fitness of the individual?Start with large mutation probability, decreased over time?
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
When to Stop
Limit the number of generations, or fitness evaluations
Stop when population has converged:
Terminate when no improvement is observed over a number ofconsecutive generationsTerminate when there is no change in the populationTerminate when an acceptable solution has been foundTerminate when the objective function slope is approximatelyzero
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation
Chapter 8: Introduction to Evolutionary Computation
IntroductionGeneric Evolutionary AlgorithmRepresentationInitial PopulationFitness FunctionSelectionReproduction OperatorsStopping ConditionsEvolutionary Computation versus Classical Optimization
EC vs CO
The search process:
CO uses deterministic rules to move from one point in thesearch space to the next pointEC uses probabilistic transition rulesEC applies a parallel search of the search space, while CO usesa sequential search
Search surface information:
CO uses derivative information, usually first-order orsecond-order, of the search space to guide the path to theoptimumEC uses no derivative information, but fitness information
Computational Intelligence: Second Edition Chapter 8: Introduction to Evolutionary Computation