Evolutionary Computation: An Introduction to Genetic Algorithms, Study notes of Computer Science

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Evolutionary Computation

Lecture 1 January, 2007^ Ivan Garibay [email protected]

1/15/

University of Central Florida,

School of EECS

Lecture 1

• What is Evolutionary Computation?
  • Evolution, Genetics, DNA – Historical Perspective
    • Genetic Algorithm Components
      • Individuals, Populations – Fitness – Selection – Genetic Operators
        • Example

1/15/

University of Central Florida,

School of EECS

Evolution

•^

Charles Darwin (1859): “On the origin of speciesby means of natural selection”

-^

Reproduction does not produce a perfect copy,always minor variations (mutations)

-^

Some variations are advantageous some are not

-^

Individuals with advantageous variations aremore likely to survive and reproduce (naturalselection, or the survival of the fittest)

-^

The variations and inheritable

-^

Species are continuously adapting to theirenvironment

1/15/

University of Central Florida,

School of EECS

Genetics

-^

Science of heredity

-^

Gregor Mendel (1865): units ofinheritance: Genes (“traits”)

-^

Organisms form by cells

-^

Each cell has informationnecessary to construct a neworganism = genome

-^

Genome = set of chromosomes

-^

Chromosome = set of genes

-^

Genes are DNA segmentsassociated with a characteristic(i.e. eye color)

-^

Allele is a particular gene value(blue, black, etc)

1/15/

University of Central Florida,

School of EECS

Historical perspective

Evolutionary Computation

Genetic Algorithms •Holland, 1975•Population based•Crossover and mutation•Study adaptation•Schema Theorem

Evolutionary Strategies •Rechenberg, 1965•Population of two•Only mutation•Real value parameteroptimization

Evolutionary Programming •Fogel, Owens, and Walsh, 1966 •Only mutation•Evolving Finite StateMachines

1/15/

University of Central Florida,

School of EECS

GA terminology: from biology

Chromosome (string)

gene

Population

individual

Generation

i^

Generation

i +

CrossoverMutation Genetic Operators

Fitness based

Selection

1/15/

University of Central Florida,

School of EECS

Genetic Algorithm Components

• Population of individuals • Fitness Function • Selection Function • Genetic Operators

1/15/

University of Central Florida,

School of EECS

Individuals

•^

Each individual represent a candidate solution

-^

String of ‘1’s and ‘0’ (binary representation)

-^

Could take any other form (tree, integers, etc)

-^

Needs to be decoded to have meaning:Genotype to Phenotype

0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1

allele

gene

1/15/

University of Central Florida,

School of EECS

Binary Representation

• Example: encoding 4 parameters • Param1 value = 1000 = 8 • Param2 value = 1011 = 11 • Etc.,

1/15/

University of Central Florida,

School of EECS

Fitness function

•^

Problem specific component

-^

Function takes as input an individual(chromosome)

-^

Function return a numerical value thatdetermines how good the individual is

-^

Natural Selection: fitness function = environment

-^

Genetic Algorithm: fitness function is userdefined

-^

Typically higher is better

1/15/

University of Central Florida,

School of EECS

Fitness proportional Selection •^

Holland, 1975.

-^

Expected number of times an individual isselected to reproduce is proportional to itsfitness relative to the total population fitness.^ – where

f(i)

is the fitness of individual

i

and

f

is

the sum of fitness of all individuals in a pop.

•^

Actual number of offspring may be far fromexpected number

P

(i) = f(i) / fs

sum

1/15/

University of Central Florida,

School of EECS

Rank Selection

• Similar to Proportional • Proportional to their rank instead • Rank selection is weaker than proportional

in diverse populations

• Rank is stronger than proportional in

converged populations

P

(i) = r(i) / rs

sum

1/15/

University of Central Florida,

School of EECS

Genetic Operators

• Crossover
  • Biologically inspired – Combine genes from two individuals to form

an off-spring (sexual reproduction)

• Mutation
  • Biologically inspired – DNA is copied with errors = mutations – Most of the time mutation = problem – Some times = advantage

1/15/

University of Central Florida,

School of EECS

Parent 1:Parent 2:

Offspring 1Offspring 2

Crossover point

One-point Crossover

• Simplest form of crossover• Advantage: Fairly large change in

individuals with very little disruption ofinformation