Selection Operators in Visual Studio .NET

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Selection Operators
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Selection operators are applied in EP to select those individuals that will survive to the next generation In the original EP, and most variations of it, the new population is selected from all the parents and their o spring That is, parents and o spring compete to survive Di ering from other EAs, competition is based on a relative tness measure and not an absolute tness measure An absolute tness measure refers to the actual tness function that quanti es how optimal a candidate solution is On the other hand, the relative tness measure expresses how well an individual performs compared to a group of randomly selected competitors (selected from the parents and o spring) As suggested by Fogel [275], this is possibly the rst hint towards coevolutionary optimization For more detail on coevolution and relative tness measures, refer to 15 This section only points out those methods that have been applied to EP For the purposes of this section, notation is changed to correspond with that of EP literature In this light, is used to indicate the number of parent individuals (ie population size, ns ), and is used to indicate the number of o spring The rst step in the selection process is to calculate a score, or relative tness, for each parent, xi (t), and o spring, xi (t) De ne P(t) = C(t) C (t) to be the competition pool, and let ui (t) P(t), i = 1, , + denote an individual in the competition pool Then, for each ui (t) P(t) a group of nP competitors is randomly selected from the remainder of individuals (ie from P(t)\{ui (t)}) A score is calculated for each ui (t) as follows
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si (t) =
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sil (t)
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194 where (assuming minimization) sil (t) =
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1 if f (ui (t)) < f (ul (t)) 0 otherwise
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Wong and Yuryevich [916], and Ma and Lai [542] proposed an alternative scoring strategy where f (ul (t)) 1 if r1 < f (ul (t))+f (ui (t)) sil (t) = (1126) 0 otherwise where the nP opponents are selected as l = 2 r2 + 1 , with r1 , r2 U (0, 1) In this case, if f (ui (t)) << f (ul (t)), in which case the tness of ui is signi cantly better than that of ul , then ui will have a high probability of being assigned a winning score of 1 This approach is less strict than the requirement that f (ui (t)) < f (ul (t)), somewhat reducing the e ects of selection pressure Based on the score assigned to each individual, ui (t), any of a number of selection methods can be used (as summarized in Section 85): Elitism: the best individuals from P(t) are selected to form the new population, C(t + 1) Tournament selection: The best individuals are stochastically selected using tournament selection Proportional selection: selected: Each individual is assigned a probability of being ps (ui (t)) = si (t) 2 l=1 sl (t) (1127)
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Roulette-wheel selection can then be used to select the individuals for the next generation Nonlinear ranking selection [933]: Individuals are sorted in ascending order of score and then ranked Then, ps u(2 i) (t) = i
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Instead of using a stochastic selection, ranking can be used to nd the elite individuals to form the new population Di erent methods have also been proposed to decide which of the parent or its o spring will survive to the next generation Wei et al [894] proposed that each parent produces more than one o spring, where the number of o spring produced is determined by the tness of the individual The more t the parent is, the more o spring are generated The best o spring generated from a parent is selected (based on absolute tness measure), and competes with the parent for survival Competition between the parent and o spring is based on simulated annealing [894] The o spring, xi (t), survives to the next generation if f (xi (t)) < f (xi (t)) or if e( (f (xi (t)) f (xi (t)))/ (t)) > U (0, 1) (1129)
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