FUNCTION GRANULARITY ESTIMATION FOR MULTIMODAL OPTIMIZATION

Abstract

In this article, we study the subspace function granularity and present a method to estimate the sharing distance and the optimal population size. To achieve multimodal function optimization, niching techniques diversify the population of Evolutionary Algorithms (EA) and encourage heterogeneous convergence to multiple optima. The key to a successful diversification is effective resource sharing. Without knowing the fitness landscape, resource sharing is usually determined by uninformative assumptions on the number of peaks. Using the Probably Approximately Correct (PAC) learning theory and the ∊-cover concept, a PAC neighborhood for a set of samples is derived. Within this neighborhood, we sample the fitness landscape and compute the subspace Fitness Distance Correlation (FDC) coefficients. Using the estimated granularity feature of the fitness landscape, the sharing distance and the population size are determined. Experiments demonstrate that by using the estimated population size and sharing distance an Evolutionary Algorithm successfully identifies multiple optima.