Adaptive generalized crowding for genetic algorithms

Abstract

The genetic algorithm technique known as crowding preserves population diversity by pairing each offspring with a similar individual in the current population (pairing phase) and deciding which of the two will survive (replacement phase). The replacement phase of crowding is usually carried out through deterministic or probabilistic crowding, which have the limitations that they apply the same selective pressure regardless of the problem being solved and the stage of genetic algorithm search. The recently developed generalized crowding approach introduces a scaling factor in the replacement phase, thus generalizing and potentially overcoming the limitations of both deterministic and probabilistic crowding. A key problem not previously addressed, however, is how the scaling factor should be adapted during the search process in order to effectively obtain optimal or near-optimal solutions. The present work investigates this problem by developing and evaluating two methods for adapting, during search, the scaling factor. We call these two methods diversity-adaptive and self-adaptive generalized crowding respectively. Whereas the former method adapts the scaling factor according to the population's diversity, the latter method includes the scaling factor in the chromosome for self-adaptation. Our experiments with real function optimization, Bayesian network inference, and the Traveling Salesman Problem show that both diversity-adaptive and self-adaptive generalized crowding are consistent techniques that produce strong results, often outperforming traditional generalized crowding.

Runtime analysis of probabilistic crowding and restricted tournament selection for bimodal optimisation

“…Our results highlight the importance of scaling the fitness, as done in [1,14,15]. An open question is whether fitness scaling would enable probabilistic crowding to find both optima on Twomax, and if so, how much the fitness needs to be scaled.…”

“…A proof where fitness scaling has helped for a variant of the Simple GA on Onemax was given in [16]. We are confident that the proof arguments used here can also be used to analyse more advanced versions of crowding [7,15].…”

“…The idea is to use a low selection pressure to prevent the loss of niches of lower fitness [13]. Probabilistic crowding has been used for multimodal optimisation [1,13,14,15], in its plain form as well as in variants in which a scaling factor has been introduced into the replacement policy.…”

Niching in Evolutionary Multi-agent Systems

“…This concept have been extended in [15] into a generalized replacement rule. It consists of adding an additional parameter φ ∈ + ∪ {0} and the following probability (eq.…”

“…Values in the range 0 < φ < 1 allow a more gradual adjustment of the probability of having the less fit individual winning, independently of the actual fitness function. Interestingly, values of φ > 1 allowed to achieve good results for some fitness functions [15].…”