An Introduction to Genetic Algorithms Lecture 2 November, 2010 Ivan Garibay [email protected].

An Introduction to Genetic Algorithms

Lecture 2

November, 2010

Ivan Garibay

[email protected]

04/20/23 University of Central Florida, Department of EECS

2

Motivation: learn from nature

• Nature evolve strikingly complex organisms in response to complex environmental adaptation problems with apparent ease

• Localize and extract principles from nature

• Apply them to design algorithms

Introduction


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Evolution• Charles Darwin (1859): “On the origin of species

by 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 are

more likely to survive and reproduce (natural selection, or the survival of the fittest)

• The variations are inheritable• Species are continuously adapting to their

environment

Basic Evolutionary Process

• Population

• Birth and Dead

• Fitness

• Variational Inheritance


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Genetics• Science of heredity • Gregor Mendel (1865): units of

inheritance: Genes (“traits”)• Organisms form by cells• Each cell has information

necessary to construct a new organism = genome

• Genome = set of chromosomes• Chromosome = set of genes• Genes are DNA segments

associated with a characteristic (i.e. eye color)

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


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DNA: Information

• DNA molecule is an information structure:– Store information digitally

(chain of nucleotides)– Nucleotide = deoxyribose

sugar + phosphate + Nitrogenous base

– 4 Nitrogenous bases: Adenine, Thymine, Cytosine, Guanine

• DNA is an amazingly efficient, highly specialized structure for information storage, replication, expression and evolution


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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 parameter optimization

Evolutionary Programming

•Fogel, Owens, and Walsh, 1966•Only mutation•Evolving Finite State Machines


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GA terminology: from biologyChromosome (string)

genePopulation

individual

Generation i Generation i+1

CrossoverMutation

Genetic Operators

Fitness basedSelection


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Simple Genetic Algorithm

procedure GAbegin

initialize population;while termination condition not satisfied dobegin

evaluate current population members;select parents from current population;apply genetic operators to selected parents;set offspring equal to current population;

endend


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Genetic Algorithm Components

• Population of individuals (population)

• Selection Function (birth and dead)

• Fitness Function (fitness)

• Genetic Operators (variational inheritance)


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Individuals

• Each individual represent a candidate solution• String of ‘1’s and ‘0’ (binary representation GAs)• In general, any information structure can be

subject to evolution (integers, reals, trees, 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


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Problem Representation• Problem specific• Different representations are

different problems for a GA• Map a string (structure) into

a instance of a solution• Representation is very

important– Define the space to be

explored– Define the space structure:

variations are meaningful

Rethinking Evolutionary Computation

Genome (DNA) Organisms

Computational Instance of Evolutionary ProblemStructure Solution

Bit String Ordering of cities for TSP

Logo instructions Antena

Genotype toPhenotype


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Binary Representation

• Example: encoding 4 parameters

• Param1 value = 1000 = 8

• Param2 value = 1011 = 11

• Etc.,


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Fitness function

• Problem specific component• Function takes as input an individual

(chromosome)• Function return a numerical value that

determines how good the individual is• Natural Selection: fitness function = environment• Genetic Algorithm: fitness function is user

defined • Typically higher is better


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Selection

• Survival of the fittest• Select the best individuals • Based on fitness function• Drives exploitation: exploit good genes

found so far • Multiple Types

– Proportional– Rank– Tournament (most used)


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Fitness proportional Selection• Holland, 1975.• Expected number of times an individual is selected to reproduce is proportional to

its fitness 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 from expected number Ps(i) = f(i) / fsum


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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

Ps(i) = r(i) / rsum


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Tournament Selection

• Computationally efficient.– Previous methods require 2 passes:

• Compute sum• Calculate expected number of offspring.

– Rank selection also requires a sort.

1. Select two individuals2. Generate a random number, r, 0 ≤ r ≤ 13. If r < k, select the better of the 2 individuals

else, select the worse of the 2 individuals

where k is a parameter.


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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


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1101110001100110

1100011001111100

Parent 1:

Parent 2:

Offspring 1

Offspring 2

Crossover point

One-point Crossover

• Simplest form of crossover

• Advantage: Fairly large change in individuals with very little disruption of information


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Other Crossover Ops

• Two point: select two points and exchange middles

• Uniform: with probability px exchange or not each bit


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11011100 11011000

Mutation

• Single parent operator

• Mutation rate (M) is per bit– Mutation rate per individual = M * L (individual

length)– As a start: M = 1/L per bit

• Issues– Low mutation rate: minimal exploration– High mutation rate: too disruptive


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Initialization

• Initial Populations are randomly generated

• Binary case are all randomly generated binary strings


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GA Convergence


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Termination Criteria

• Found solution

• Number of generations

• Stagnation – no more fitness improvement

An Introduction to Genetic Algorithms Lecture 2 November, 2010 Ivan Garibay [email protected].

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