Subspace FDC for sharing distance estimation

Niching techniques diversify the population of evolutionary algorithms, encouraging heterogeneous convergence to multiple optima. The key to an effective diversification is identifying the similarity among individuals. With no prior knowledge of the fitness landscapes, it is usually determined by uninformative assumptions on the number of peaks. We propose a method to estimate the sharing distance and the corresponding population size. Using the probably approximately correct (PAC) learning theory and the e-cover concept, we derive the PAC neighbor distance of a local optimum. Within this neighborhood, uniform samples are drawn and we compute the subspace fitness distance correlation (FDC) coefficients. An algorithm is developed to estimate the granularity feature of the fitness landscapes. The sharing distance is determined from the granularity feature and furthermore, the population size is decided. Experiments demonstrate that by using the estimated population size and sharing distance an evolutionary algorithm (EA) correctly identifies multiple optima.