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Home » 2011 » August » 22 » Genetic Algorithms 2
11:22 PM
Genetic Algorithms 2

Genetic Algorithms

Page: 1 3
6. Parent/Survivor Selection:
  1. Strategies
    • Survivor selection
      1. Always keep the best one
      2. Elitist: deletion of the K worst
      3. Probability selection : inverse to their fitness
      4. Etc.
    • Too strong fitness selection bias can lead to sub-optimal solution 
    • Too little fitness bias selection results in unfocused and meandering search
    • Parent selection
      1. Chance to be selected as parent proportional to fitness
        • Roulette wheel
      2. To avoid problems with fitness function
        • Tournament
      3. Not a very important parameter
      4. Uniform randomly selection
      5. Probability selection : proportional to their fitness
      6. Tournament selection (Multiple Objectives)
        • Build a small comparison set Randomly select a pair with the higher rank one beats the lower one Non-dominated one beat the dominated one Niche count: the number of points in the population within                      certain distance, higher the niche count, lower the rank.
      7. Etc.
  2. Others
    • Global Optimal
    • Parameter Tuning
    • Parallelism
    • Random number generators
7. Example Of Coding For TSP:
  1. Binary
    • Cities are binary coded; chromosome is string of bits
      1. Most chromosomes code for illegal tour
      2. Several chromosomes code for the same tour
  2. Path
    • Cities are numbered; chromosome is string of integers
      1. Most chromosomes code for illegal tour
      2. Several chromosomes code for the same tour
  3. Ordinal
    • Cities are numbered, but code is complex
    • All possible chromosomes are legal and only one chromosome for each tour
  4. Several others
8. Roulette wheel:
  1. Sum the fitness of all chromosomes, call it T
  2. Generate a random number N between 1 and T
  3. Return chromosome whose fitness added to the running total is equal to or larger than N
  4. Chance to be selected is exactly proportional to fitness
Chromosome    : 1   2   3    4   5   6
Fitness       : 8   2   17   7   4   11
Running total : 8  10   27  34 38   49
N (1 £ N £ 49):              23
Selected      :         3

9. Tournament:
  1. Binary tournament
    • Two individuals are randomly chosen; the fitter of the two is selected as a parent
  2. Probabilistic binary tournament
    • Two individuals are randomly chosen; with a chance p, 0.5<p<1, the fitter of the two is selected as a parent
  3. Larger tournaments
    1. n individuals are randomly chosen; the fittest one is selected as a parent
  4. By changing n and/or p, the GA can be adjusted dynamically
10. Problems With Fitness Range:
  1. Premature Convergence
    • DFitness too large
    • Relatively superfit individuals dominate population
    • Population converges to a local maximum
    • Too much exploitation; too few exploration
  2. Slow Finishing
    • DFitness too small
    • No selection pressure
    • After many generations, average fitness has converged, but no global maximum is found; not sufficient difference between best and average fitness
    • Too few exploitation; too much exploration
11. Solutions For These Problems:
  1. Use tournament selection
    • Implicit fitness remapping
  2. Adjust fitness function for roulette wheel
    • Explicit fitness remapping
      1. Fitness scaling
      2. Fitness windowing
      3. Fitness ranking
12. Fitness Function:
  1. Purpose
    • Parent selection
    • Measure for convergence
    • For Steady state: Selection of individuals to die
    • Should reflect the value of the chromosome in some "real” way
    • Next to coding the most critical part of a GA
  2. Fitness scaling
    • Fitness values are scaled by subtraction and division so that worst value is close to 0 and the best value is close to a certain value, typically 2
      1. Chance for the most fit individual is 2 times the average
      2. Chance for the least fit individual is close to 0
    • Problems when the original maximum is very extreme (super-fit) or when the original minimum is very extreme (super-unfit)
      1. Can be solved by defining a minimum and/or a maximum value for the fitness
  3. Example of Fitness Scaling
  4. Fitness windowing
    • Same as window scaling, except the amount subtracted is the minimum observed in the n previous generations, with n e.g. 10
    • Same problems as with scaling
  5. Fitness Ranking
    • Individuals are numbered in order of increasing fitness
    • The rank in this order is the adjusted fitness
    • Starting number and increment can be chosen in several ways and influence the results
    • No problems with super-fit or super-unfit
    • Often superior to scaling and windowing
  6. Fitness Evaluation
    • A key component in GA
    • Time/quality trade off
    • Multi-criterion fitness
  7. Multi-Criterion Fitness
    • Dominance and Indifference
      1. For an optimization problem with more than one objective function (fi, i=1,2,…n)
      2. given any two solution X1 and X2, then
        • X1 dominates X2 ( X1      X2), if  fi(X1) >= fi(X2), for all i = 1,…,n 
        • X1 is indifferent with X2 ( X1  ~  X2), if X1 does not dominate X2, and X2 does not dominate X1
    • Pareto Optimal Set
      1. If there exists no solution in the search space which dominates any member in the set P, then the solutions belonging the the set P constitute a global Pareto-optimal set.
      2. Pareto optimal front
    • Dominance Check
    • Weighted sum
      1. F(x) = w1f1(x1) + w2f2(x2) +…+wnfn(xn
      2. Problems?
        1. Convex and convex Pareto optimal frontSensitive to the shape of the Pareto-optimal front
        2. Selection of weights?
          • Need some pre-knowledge
          • Not reliable for problem involving uncertainties
    • Optimizing single objective
      1. Maximize:   fk(X) Subject to: fj(X) <= Ki    ,i <> k ,    X in F where F is the solution space.
    • Preference based weighted sum 
      1. (ISMAUT Imprecisely Specific Multiple Attribute Utility Theory) 
      2. F(x) = w1f1(x1) + w2f2(x2) +…+wnfn(xn)
      3. Preference
        1. Given two know individuals X and Y, if we prefer X than Y, then F(X) > F(Y), that is w1(f1(x1)-f1(y1)) +…+wn(fn(xn)-fn(yn)) > 0
  8. All the preferences constitute a linear space Wn={w1,w2,…,wn
    • w1(f1(x1)-f1(y1)) +…+wn(fn(xn)-fn(yn)) > 0 
    • w1(f1(z1)-f1(p1)) +…+wn(fn(zn)-fn(pn)) > 0, etc
  9. For any two new individuals Y’ and Y’’, how to determine which one is more preferable?
Construct the dominant relationship among some indifferent ones according to the preferences.

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Category: Algorithms | Views: 926 | Added by: Ansari | Rating: 0.0/0
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