GA for mam

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Genetic

Algorithm

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Genetic Algorithms

Bio-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 Darwins Origin of species

What are Genetic Algorithms?

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Evolution

Variety of species individuals within

the population

Competition for limited resources

Overproduction of offspring

generation

Survival of the fittestOrigin of Species, 1859

Darwins principles

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Evolution

Initial population

Variety of shapes, colors, behaviors

Each individual fits differently to the environment

How does it work?

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Evolution

Initial population

Reproduction

Offspring combines both parents properties

Siblings may differ

in properties

Mutations may occur

How does it work?

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Evolution

Initial population

Reproduction

Limited environmental resources

Only a portion of the

individuals survive

Survival chances

according to fitnessmeasure...

... usually.

How does it work?

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Evolution

Changes in the population content

good properties are kept, bad are distinct

evolutionary pressure

Observations

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Genetic Algorithms

produce an initial population of individuals

while (termination condition not met) do

evaluate the fitness of all individualsselect fitter individuals for reproduction

recombine between individuals

mutate individuals

The computational model

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Genetic Algorithms





mutate individuals


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Genetic Algorithms


Gn

55

44

12

31

95

32

87

120

65

53

2

91

73

+

Gn+1

=

crossover

mutation

fitness

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GA in action

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

The Knapsack problem (NP)

i

iv

Ww

i

i

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GA in action

For example:

Knapsack capacity = 100

The Knapsack problem (NP)

JIHGFEDCBA

1230183425545192614

21411750231470182420

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GA in action

A. Define the genome encoding

B. Define the fitness function

Before we begin

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GA in action

Bit array:

0 = dont take the item1 = take the item

(items taken: A, B, E)

Genome Encoding

0000010011

-----E--BA

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GA in action

Bit array:

0 = dont take the item

1 = take the item

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

Genome Encoding

0101111111

-I-GFEDCBA

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GA in action

Fitness Function

otherwisewW

Wwv

Fitness

items

i

items

i

items

i

:

:

JIHGFEDCBA

1230183425545192614

21411750231470182420

58

10045

EBA

EBA

vvvFitness

www

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GA in action

Fitness Function

otherwisewW

Wwv

Fitness

items

i

items

i

items

i

:

:

JIHGFEDCBA

1230183425545192614

21411750231470182420

98

100198

IGFEDCBA

IGFEDCBA

wwwwwwwwWFitness

wwwwwwww

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Genetic Algorithms



evaluate the fitness of all individuals

select fitter individuals for reproduction


mutate individuals

Fitness Evaluation

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Genetic Algorithms

For each individual, calculate the fitness value:

Fitness Evaluation

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Genetic Algorithms





mutate individuals

Selection

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Genetic Algorithms

Fitness-proportionate (roulette wheel)

Rank Selection (scaling)

Tournament Selection

Selection

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Genetic Algorithms






mutate individuals

Crossover

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Genetic Algorithms

Using a crossover probability PCper individual:

Single point crossover

Two/multi points crossover Uniform / weighted crossover

Crossover

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Genetic Algorithms






mutate individuals

Mutation

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Genetic Algorithms

Using a crossover probability PMper bit:

Bit flip mutation

Bit switch mutation

Mutation

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Genetic Algorithms

Crossover & Mutation examples

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Genetic Algorithms





mutate individuals

Initial Population

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Genetic Algorithms

Create a fixed size population using:

Random generated individuals

Individuals resulted from previous

evolutionary runs

Initial Population

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GA in action

Example of random population:

Initial Population

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Genetic Algorithms

When an optimal solution is found

When the results converge to constant value

After a predetermined number of generations

Termination Condition

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Genetic Algorithms

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 Run

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Genetic Algorithms

Sample Evolutionary Run

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Genetic Algorithms

GA is nondeterministictwo runs may end

with different results

Theres no indication whether bestindividual is optimal

Fitness tends to converge during time

Conclusions

Documents

GA for mam