Genetic Algorithm

An overview of Genetic AlgorithmBy David Beasley, David R. Bull and Ralph R. Martin

090070T – T.P.K. Dahanayakage090150N – K.M.T.V. Ganegedara

Introduction

Population Evolves Natural Selection Survival of the fittest

Applications? Computer, Bridges, Garment, etc.

Analogy

Think about successive generations

Analogy (ctd)

Evolve according to environment

Super-fit

Basic Concept

Set of solutions for a problem Each solution – fitness score

Reproduce a new set of solutions by “Cross-breeding” Most-fit: get selected Least-fit: not selected – die out

Result? Offsprings with characteristics from most-fit

What just happened?

Good characteristics of a generation was spread in a successive generation

Most promising areas of solution space are searched

Algorithm

BEGINGenerate populationCalculate fitness for each individualWHILE NOT CONVERGED DOBEGIN

FOR population_size/2 DOBEGIN

Select 2 parents for matingCombine and produce an offspringCalculate the fitness for the new individualInsert the offspring to the new generation

END

END

END

Lesson on Biology

Chromosome Organized collection of coiled DNA

DNA

Fitness function

Must represent the “fitness to the environment” or “ability” of a chromosome’s

Issues of fitness range Premature convergence Slow finishing

Reproduction

Selection of parents Random Favors the fittest

Crossover Single point crossover

Cut 2 chromosomes at a random point Swap over tails to create 2 new chromosomes

Reproduction (ctd)

Crossover is not the only case! 0.6 - 1.0 chance Otherwise replicate the parent

Mutation Alter the genes of crossover-ed with a

small probability

Example

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

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

0 1 0 1 0 0 1 0 0 1

0 1 0 1 1 0 1 0 0 1

Before mutation:

After mutation:

Convergence

Fitness of the BEST and AVERAGE moves to a global optimum

Gene is said to have converged 95% of the population has converged

Population is said to have converged All the genes have converged

Other techniques

“Schemata” and “Scheme”

Definition of Schema Pattern of gene String comprise {0,1,#}

Ex: Chromosome 0110 contains following “Schemata” #110, #1#0, 01##, etc.

A chromosome is said to contain a schema if it matches a particular schemata

Order of schema – Number of non-# symbols

Length of schema – Distance between outer most non-# symbols.

Ex: #1#0

Schema Theorem

Individuals in a population are given reproductive trials

Number of trials α Fitness of an individual Higher fitness value -> Good schemata

Good Schemata receives exponentially increasing number of trials in successive generations!

Building Block Hypothesis

Definition Schemata short in length and tend to

improve performance when incorporated to an individual

Properties of a successful coding scheme Related genes close together Little interaction between genes

Exploration and Exploitation

Exploration Exploring unknown areas

Exploitation Utilizing already-learnt to find better solutions

Tradeoff Ex: Random search and Hill climbing

GA combines both in an optimal way!

Practical Aspects of GA

Parent selection

Individuals are copied to a “mating pool” Highly fit – more copies Less fit – lesser copies

How to determine number of copies? Explicit fitness remapping Implicit fitness remapping

Explicit fitness remapping

Individual’s fitnessAverage fitness of population

Issue: Number of copies should be an integer

Solution: Fitness scaling Fitness windowing

Implicit fitness remapping

Tournament selection 2 random individuals Copy the one with higher fitness value

to the mating pool Continue until the pool is full

Generation gaps and steady-state replacement

Generation gap Proportion of individuals in a population replaced

in each generation

Steady-state replacement Only few individuals are replaced in a generation Considerations:

Parent selection – Random, Fitness Replacement – Random, Inverse fitness

Thank you

Q & A Session