Introduction to Genetic Algorithms Yonatan Shichel

introduction tointroduction to

Genetic AlgorithmsGenetic AlgorithmsYonatan ShichelYonatan Shichel

Genetic AlgorithmsGenetic Algorithms

Bio-InspiredBio-Inspired artificial intelligence

class of probabilistic optimization

algorithms

Well-suited for nonlinear/hard problems

with a large search space

Developed by John Holland

Influenced by Darwin’s Origin of species

What are Genetic Algorithms?What are Genetic Algorithms?

EvolutionEvolution

VarietyVariety of species individuals

within the population

CompetitionCompetition for limited resources

OverproductionOverproduction of offspring

generation

Survival of the fittestSurvival of the fittestOrigin of Species, 1859

Darwin’s principlesDarwin’s principles

EvolutionEvolution

Initial population• Variety of shapes, colors, behaviors

• Each individual fits differently to the

environment

HHow does it work?ow does it work?

EvolutionEvolution

Initial population

Reproduction• Offspring combines both parents properties

• Siblings may differ

in properties

• Mutations may occur


EvolutionEvolution

Initial population

Reproduction

Limited environmental resources• Only a portion of the

individuals survive

• Survival chances –

according to fitness

measure...

• ... usually.


EvolutionEvolution

ObservationsObservations

Changes in the population content• “good” properties are kept, “bad” are distinct

• evolutionary pressure


The computational modelThe computational modelproduce an initial population of individuals

while (termination condition not met) do

evaluate the fitness of all individuals

select fitter individuals for reproduction

recombine between individuals

mutate individuals


The computational modelThe computational modelproduce an initial populationinitial population of individuals

while (termination conditiontermination condition not met) do

evaluateevaluate the fitness of all individuals

selectselect fitter individuals for reproduction

recombinerecombine between individuals

mutatemutate individuals


The computational modelThe computational model

GGnn

55

44

12

31

95

32

87

12

0

65

53

2

91

73

+

GGn+n+

11

=

crossover

mutation

fitness

GA in actionGA in action

The Knapsack problem (NP)The Knapsack problem (NP)

There are N items:

• Each item i has a weight wi

• Each item i has a value vi

The knapsack has a limited capacity of

W units.

The problem description:• Maximize

• While

i

iv

Wwi

i


The Knapsack problem (NP)The Knapsack problem (NP)

For example:

Knapsack capacity = 100

A B C D E F G H I J14 26 19 45 5 25 34 18 30 12

20 24 18 70 14 23 50 17 41 21


Before we begin…Before we begin…

1. Define the genome encodinggenome encoding

2. Define the fitness functionfitness function


Genome EncodingGenome Encoding

Bit array:

0 = don’t take the item

1 = take the item

(items taken: A, B, E)

1 1 0 0 1 0 0 0 0 0

A B - - E - - - - -


Genome EncodingGenome Encoding

Bit array:

0 = don’t take the item

1 = take the item

(items taken: A, B, C, D, E, F, G, I)

1 1 1 1 1 1 1 0 1 0

A B C D E F G - I -


Fitness FunctionFitness Function

otherwisewW

WwvFitness

itemsi

itemsi

itemsi

:

:

A B C D E F G H I J

14 26 19 45 5 25 34 18 30 12

20 24 18 70 14 23 50 17 41 21

58

10045

EBA

EBA

vvvFitness

www


Fitness FunctionFitness Function

otherwisewW

WwvFitness

itemsi

itemsi

itemsi

:

:

A B C D E F G H I J

14 26 19 45 5 25 34 18 30 12

20 24 18 70 14 23 50 17 41 21

98

100198

IGFEDCBA

IGFEDCBA

wwwwwwwwWFitness

wwwwwwww


Fitness EvaluationFitness Evaluation

produce an initial population of individuals


evaluateevaluate the fitness of all individuals



mutate individuals


Fitness EvaluationFitness Evaluation

For each individual, calculate the fitness value:


SelectionSelectionproduce an initial population of individuals



selectselect fitter individuals for reproduction


mutate individuals


SelectionSelection

Fitness-proportionate (roulette wheel)

Rank Selection (scaling)

Tournament Selection

…


CrossoverCrossover





recombinerecombine between individuals

mutate individuals


CrossoverCrossover

Using a crossover probability PC per individual:

Single point crossover

Two/multi points crossover

Uniform / weighted crossover

…


MutationMutation






mutatemutate individuals


MutationMutation

Using a crossover probability PM per bit:

Bit flip mutation

Bit switch mutation

…


Crossover & Mutation examplesCrossover & Mutation examples


Initial PopulationInitial Populationproduce an initial populationinitial population of individuals





mutate individuals


Initial PopulationInitial Population

Create a fixed size population using:

Random generated individuals

Individuals resulted from previous

evolutionary runs


Initial PopulationInitial Population

Example of random population:


Termination ConditionTermination Condition


while (termination conditiontermination condition not met) do




mutate individuals


Termination ConditionTermination Condition

When an optimal solution is found

When the results converge to constant value

After a predetermined number of generations


Sample Evolutionary RunSample Evolutionary Run

Population size: 100 individuals

Crossover: Single pt., PC=0.9

Mutation: Bit flip, PM=0.01

Selection: tournament, groups of 2

Termination condition: after 100

generations


Sample Evolutionary RunSample Evolutionary Run


ConclusionsConclusions

GA is nondeterministic – two runs may

end with different results

There’s no indication whether best

individual is optimal

Fitness tends to converge during time


GA variationsGA variations

Coevolution• Cooperative

• Competitive

Parallel GA

Hybrid GA

Documents

Introduction to Genetic Algorithms Yonatan Shichel