A New Selection Operator Dedicated to Speciation

Most niching methods create and maintain subpopulations of individuals characterized by some similarities. This paper defines the clearing procedure as a niching method that supplies the available resources of a niche only to the best individuals of each subpopulation: the winners. The clearing is naturally adapted to elitist strategies. Elitist clearing preserves good individuals from the destructive effects of genetic drift and reproduction operators, while maintaining a high level of diversity. These properties can dramatically improve the performance of genetic algorithms used for multimodal optimization. The basic clearing procedure selects the winners for reproduction. A standard selection operator then generates a competition between the winners from every subpopulation. This paper shows, through experiments, that this kind of over-selection is harmful. The concept of clearing based selection operator that ensures an equal number of offspring to every winner, regardless of its fitness is introduced. The experiments involve both easy and difficult multimodal function optimizations. They show that a clearing based selection operator can reduce the premature convergence rate, compared to a clearing procedure associated with an SUS selection. 1 GENETIC ALGORITHMS AND MULTIMODAL OPTIMIZATION A simple genetic algorithm (Goldberg, 1989) (SGA) is suitable for searching for the optimum of unimodal functions in a bounded search space. However, both experiments and analysis show that the SGA cannot find the multiple global maxima of a multimodal function (Goldberg, 1989)(Mahfoud, 1995). This limitation can be overcome by a mechanism that creates and maintains several subpopulations within the search space, in such a way that each highest maximum of the multimodal function can attract one of them. These mechanisms are referred to as “niching methods” (Mahfoud, 1995). Most niching methods gather together the individuals which present some similarities into subpopulations. Regulating mechanisms are necessary to stabilize these subpopulations generation by generation. These mechanisms can be implemented within the operators that are applied at each generation of the genetic algorithm: ◊ the selection operator selects the individuals for the reproduction process; ◊ the reproduction operator modifies the selected individuals to generate new individuals. This operator can be composed of several elementary operators such as the crossover and the mutation; ◊ the substitution operator determines which individuals must disappear from the current population to make room for the new ones. The sharing method (Goldberg, Richardson, 1987) is a niching mechanism which interferes with the selection operator. It is based on the sharing of limited renewal resources, between individuals characterized by some similarities, according to the principle stated by J.H. Holland in 1975 (Holland, 1992). The basic method is known for its reliability, however, it suffers from some drawbacks such as the requirement of large population sizes, and its algorithmic complexity which is O(n2), where n is the size of the population. It is also necessary to know the value of parameter σshare which strongly depends on the distances between the searched maxima. This latter parameter is often difficult to estimate. These drawbacks have been removed in part by the works of Goldberg et al. (1992) and Yin and Germay (1993). The restricted mating techniques take place within the reproduction operator. They allow the individuals to mate preferably if they belong to a same subpopulation. The membership of an individual is determined through the value of a label concatenated to its genotype. The label, also named tag bits, can mutate, allowing the individuals to change of subpopulation: this is a migration mechanism. This kind of method does not increase the algorithmic complexity, from which derives its advantage. Furthermore it can be naturally implemented on parallel machines (Cantú-Paz, 1995). W. Spears combines this concept with the sharing method to improve its reliability (Spears, 1995). The behavior of this technique facing difficult problems is a topical question. The crowding (De Jong, 1975) takes place within the substitution operator. According to this method, a new individual replaces the most similar individual from a sample of the population. The deterministic crowding (Mahfoud, 1995) improves the method, leading towards a better reliability. This technique does not affect the complexity of the genetic algorithm. Mahfoud showed that this method was able to solve hard problems, but it requires a great number of evaluations of the fitness function, compared to some other techniques. The clearing procedure previously presented in (Petrowski, 1996) also derives from the niching principle stated by J.H. Holland like the sharing method. But, instead of evenly sharing the available resources among the individuals of a subpopulation, the clearing procedure supplies these resources only to the best individuals of each subpopulation. It is applied at the selection operator level. Its reliability is similar to that of the basic sharing method with a lower complexity and much smaller population sizes. This paper first presents the basic clearing procedure and subsequently an elitist variant. Next, some improvements are proposed to reduce the complexity and to control the subpopulations into an easier and more efficient way. The utility of a selection operator associated with a clearing procedure is then discussed and the concept of “clearing based selection operator” is introduced. Section 3 describes some tests on both easy and difficult functions. Finally, these results are compared with those obtained from sharing and deterministic crowding. 2 CLEARING THE SEARCH SPACE