EE749Introduction to Artificial Intelligence

Genetic Algorithms

The Simple GA

Principles of Genetic AlgorithmsGenetic algorithms (GA’s) are iterative, adaptive, general-purpose search strategies

They are driven by the following principlesevolution operates on chromosomes

chromosomes are strings of genes

chromosomes define the characteristics of an individual

less fit individuals tend not to survive (natural selection)

offspring inherit properties from their parents by the process of reproduction

individuals that are more successful reproduce more

IndividualsEach possible candidate solution is an individual

A set of possible solutions is maintained

a population of individuals

Each individual consists of a string of symbols from a fixed set of symbols (an alphabet)

in the simple GA, the symbols are ‘0’ and ‘1’

each variable is represented by a binary string

each variable is the equivalent of a biological gene

the total string of genes is a chromosome

Fitness FunctionsEach chromosome is evaluated and assigned a value known as its fitness value

the chromosome is split into its constituent genes

each gene is decoded to give the corresponding variable’s value

the variables are used to evaluate the fitness function

The fitness value is used to determinethe individual’s rate of reproduction

the higher the fitness, the more change of being selected

Each iteration is called a generation

GA OverviewAt each generation, each individual is evaluated by a fitness function and assigned a fitness value

the fitness value somehow measures how good the individuals is as a solution to the problem

New individuals are produced by selecting individuals from the current population on the basis of their fitness values

Some individuals within the population may be altered by the application of genetic operators

This is repeated until a decision is made to stop

GA OutlineLet P represent a population and P(t) represent the state of population P at time t

ThenInitialise P(t = 0); /* P(0) is the starting population */Evaluate P(t = 0); /* evaluate each individual */WHILE ( NOT termination condition ) DO

Generate P(t + 1) from P(t);/* by a process of

reproduction */t = t + 1;Evaluate P(t);

END (* while*)

Selection StrategyDetermine how many new offspring to produce

there are many variations, but in the simple GA we produce a new population of the same size as the old

Determine which individuals are to be used

again, there are variations, but the simplest is termed ‘roulette’ selection

each individual is assigned a probability based on their fitness as a straight proportion of overall fitness

individuals are randomly picked, according to their fitness proportion, to survive into the next generation

‘Roulette’ ExampleFor example: f(x) = x2, x = [0, 31]

No. String x x2 ps

1 01101 13 169 0.144

2 11000 24 576 0.492

3 01000 8 64 0.055

4 10011 19 361 0.309

1170

Range

0.000 0.143

0.144 0.635

0.636 0.690

0.691 0.999

The following random numbers are generated:0.521, 0.968, 0.112, 0.753

so individuals 2, 4, 1, 4 survive to the next generation

Genetic Operators

Reproduction produces a new generation selected according to fitness, but it does not introduce any new variation into the population

genetic operators are applied to generate variation

The two operators used in the simple GA arecrossover

mutation

Each operator is applied to each newly selected individual with a certain probability

it’s very hard to guess what these probabilities should be

CrossoverTwo individuals are chosen randomly

a crossover point is selected at random

the strings are swapped to the right of crossover point

For example

OLD1 = 01010111

OLD2 = 11110101

and position five is chosen, giving

NEW1 = 01010101

NEW2 = 11110111

Mutation

One individual is chosen randomly

one or more mutation points are selected at random

the symbols in the string are changed (somehow)

in simple GA with binary ‘0’s and ‘1’s, the bit is ‘flipped’

For example

OLD = 10010101

is selected for mutation at points 2, 4 and 8

NEW = 11000100

Operator ProbabilitiesThe probability of applying each operator is application dependent and is usually discovered empirically (i.e. by trying several alternatives)

As a heuristic (‘rule of thumb’)crossover

often applied so that 50 to 75% of the individuals in the population undergo crossover

i.e. 0.50 to 0.75 probability of being applied

mutationoften applied to each bit with prob. 1 / (total number of bits)

e.g. 10 individuals of 10 bits = 100 bits; pmutate = 0.01 per bit