Genetic Algorithms. Underlying Concept Charles Darwin outlined the principle of natural selection. ...
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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