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## Selection Methods

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### Fitness-Proportionate Selection (Roulette Wheel) ... Fitness-Proportionate Selection (Roulette Wheel) Used originally by Holland ... – PowerPoint PPT presentation

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Title: Selection Methods

1
Selection Methods
• Choosing the individuals in the population that
will create offspring for the next generation.
• Richard P. Simpson

2
Methods often used
• Fitness-Proportionate Selection (Roulette Wheel)
• Fitness-Proportionalte Selection (Stochastic
Universal Sampling)
• Sigma Scaling
• Elitism
• Boltzmann Selection
• Rank Selection
• Tournament Selection

3
Fitness-Proportionate Selection (Roulette Wheel)
• Used originally by Holland
• Here the expected number of times an individual
will bes selected to reproduce is that
individuals fitness divided by the average
fitness of the population
• Let T sum of the expected values of the
individuals in the population.
• Choose a random number between 0 and T
• Loop through the individuals in the pop. summing
the expected values until the sum is greater than
r.
• Select the individual that puts the sum over
this limit.

4
Fitness-Proportionate Selection (Roulette Wheel)
• This methods results in the expected number of
offspring for each individual
• Does not work well for small populations
• To correct this SUS(stochastic universal
sampling) has been proposed.
• Here one spins the wheel one using N equally
spaced points to select N parents.

5
SUS(stochastic universal sampling)
• Fitness-proportionate selections main problem
• Early in the search the fitness variance in the
population is high. The highly fit individuals
will multiply quickly and soon dominate the pop.
This is called premature convergence, ie
exploration is slows rapidly. Often finds non
optimal hills.
• Fitness-Proportionate Selection (Roulette Wheel)
• The rate of evolution depends on the variance of
fitnesses in the population.

6
Sigma Scaling
• Used to address the previous problem
• In these cases raw fitness values are mapped to
expected values so as to make the GA less
susceptible to premature convergence.
• Here an attempt is made to keep selection
pressure relatively constant over the course of
the run.
• Sigma scaling, an individuals expected value is
a function of its fitness, the population mean,
and the population standard deviation.

mean fitness
fitness
standard deviation at time t
7
Elitism
• Kenneth De Jong (1975)
• Can be used with many of the other selection
methods.
• Here a certain percent of the population is
carried forward to the next population.
• This implies that the best individual ever
discovered will appear in the final generations
population.
• Sometimes elitism significantly improves
performance, depends on the problem.

8
Boltzmann Selection
• Sometimes we would like to vary the selection
pressure over a run.
• We could start with low selection pressure and
increase it as we progress from generation to
generation.
• This implies that we are searching more during
the initial generations of the run and evolving
faster toward the end of the run.

9
Rank Selection
• This is another attempt to prevent premature
convergence.
• The individuals are sorted according to fitness.
• Ranking avoids giving the far largest share of
offspring to a small group of highly fit
individuals, and thus reduces the selection
pressure when the fitness variance is high.

before
after
10
Bakers ranking method
• Individuals are ranked according to fitness.
• the user chooses the expected value Max of the
individual with rank N, and Min, the expected
value of the individual with rank 1.
• Constrants Maxgt0 and Sum of ExpVal N
• 1lt Maxlt2 and Min 2 - Max

11
Truncation Selection
• In truncation selection individuals are sorted
according to their fitness. Only the best
individuals are selected for parents. These
selected parents produce uniform at random
offspring.
• The parameter for truncation selection is the
truncation threshold Trunc. Trunc indicates the
proportion of the population to be selected as
parents and takes values ranging from 50-10.
Individuals below the truncation threshold do not
produce offspring.

12
Tournament Selection
• Two individuals are chosen at random from the
population.. A random number r between 0 and 1
is chosen. If rltk (where k is a parameter say
.75) the more fit individual is selected
otherwise the least fit is selected. Do this
twice to retrieve to parents.
• Fitness-proportionate methods require two passes
thru the pop. for each generation. One to
determine the average and one to compute the
expected value of each individual.
• This is a very efficient method that works quite
well and suits itself to parallel solutions.

13
Fitness Uniform Selection(FUSS)
14
Population Search Space