Genetic Algorithms

Underlying Concept

Charles Darwin outlined the principle of natural selection.

Natural Selection is the process by which evolution occurs.

The fittest members of a species will survive and propagate more than those less fit.

Development of GAs

In 1975 John Holland developed the idea of Genetic Algorithms

These are algorithms that mimic the principles of natural selection to solve problems.

Often used for Optimization problems, and for biological simulations.

The Basic Idea

Possible solutions to a problem are labelled “Chromosomes”

An initial population of these chromosomes is created and mated via crossover and mutation algorithms to create 'offspring'

This process is repeated until the optimal solution is found.

Step-By-Step GAs Step 1: Choose an initial population of

chromosomes Step 2: Create an offspring population from the

parent population Step 3:the offspring undergo a crossover Step 4: mutations occur in the offspring population

(this is based on a probability algorithm) Step 5: evaluate the fitness of each offspring Step 6: replace parents with offspring, and repeat 2-

5 until the optimal solution is reached

Psuedocode!Choose an initial population of chromosomeswhile (termination condition not satisfied) do

repeatif(crossover condition satisfied) then{

select parent chromosomes;choose crossover parameters;perform crossover;}

if(mutation condition satisfied) then{select chromosome for mutation;choose mutation point;perform mutation;

}Evaluate fitness of offspring;

until sufficient offspring created;select new population;

end whileCourtesy of Reves, Colin R. Genetic Algorithms – Principles and Perspectives : a Guide to GA Theory.

Step 1 – The Initial Population

These will be randomly generated strings in the problem set

The number of members in the initial population is determined on a case by case basis, but it is usually reliable in most cases to use lg(string length) initial chromosomes.

Step 2 & 3 – Create Offspring and Crossover

Two parents are chosen from the set, and an offspring is created.

The parent's chromosomes are then combined into the offspring through a process called “crossover”, in which certain genes from each parent are mixed together.

Crossover Schemes Linear Crossovers:

single-point crossoverA 'crossover point' is randomly chosenAll of the genes (alleles) after the crossover point from

one parent are copied into their corresponding location on the other.

(a,b,c,d,e,f,g) and (1,2,3,4,5,6,7)Crossover point is 3 (a,b,3,4,5,6,7) and (1,2,c,d,e,f,g) are createdThese are the offspring of the 2 parents

There are many other crossover techniques, most involving the same concept, but multiple crossover points

N-Point Crossover AlgorithmChoose a random integer n;choose n cross points;generate random permutation ð of (1...,n+1) for segment order;designate one parent for copying;k <-- 1;

repeatcopy all compatible alleles of segment ðk from designated parent;swap parent designations;k++;

until k = n+1;if child incomplete then insert legal alleles at required position, using random tie

breaking if necessary.

Step 4 - Mutations?

An important event for the evolution of any species is mutation. A new trait is developed, and if it is beneficial, often it will be propagated.

The same must be true for GAs Mutation is not always required in all matings. So a probability of

mutation equation should be set up (this will vary depending on the problem).

Each time a new child is created a random number is generated and checked by this mutation equation to see if a mutation should occur.

Step 5: Evaluate the Fitness In order to decide which traits are beneficial

and should be passed on, a fitness algorithm must be performed on the children.

These fitness algorithms are completely problem specific

There are 2 basic types of algorithm Probability dependent Rank Dependent

Probability Dependent Selection

Each one of the offspring is analysed using some problem specific algorithm to determine the probability that it will lead to a successful solution

Roulette wheel type: Each offspring is assigned a segment of the

roulette wheel based on its probability. A random number is then generated, and

whichever section of the wheel it fall into is the offspring that is chosen for reproduction

Rank Dependent Selection

Each offspring is analysed by a ranking algorithm and its fitness is returned as some number.

The greater the number the greater the fitness All of these ranks are ordered, and the best fit

offspring are chosen for reproduction.

Other Selection Methods

Scaling Generational Hierarchical

Step 6

The chosen offspring are then made the parents for the next iteration of the process

The algorithm repeats until some specified condition (Problem Specific) is met.

Analysis of GAs

Strengths GAs are ‘parallel’

Can examine multiple solutions at once

Limitations Deceptive fitness functions Can be time consuming Only deal with one trait at a time