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					Genetic Algorithms

    Dan Locker
      An Do
         Underlying Concept

 In his book The Origin of Species 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 chromosomes
 while (termination condition not satisfied) do
     repeat
           if(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;                           Courtesy of Reves, Colin R. Genetic Algorithms
end while                                               – 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 crossover
         A 'crossover point' is randomly chosen
         All 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 created

         These 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 Algorithm
Choose 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;
      repeat
           copy 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

				
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posted:2/24/2012
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