Multimodal Function Optimization Using Local Ruggedness Information

Jian Zhang, Xiaohui Yuan, and Bill P. Buckles

In multimodal function optimization, niching techniques create diversification within the population, thus encouraging heterogeneous convergence. The key to the effective diversification is to identify the similarity among individuals. Without knowledge of the fitness landscape, it is usually determined by uninformative assumptions. In this article, we propose a method to estimate the sharing distance for niching and the population size. Using the Probably Approximately Correct (PAC) learning theory and the -cover concept, we prove a PAC neighborhood of a local optimum exists for a given population size. The PAC neighbor distance is further derived. Within this neighborbood, we uniformly sample the fitness landscape and compute its subspace fitness distance correlation (FDC) coefficients. An algorithm for estimating the granularity feature is described. The sharing distance and the population size are determined when above procedure converges. Experiments demonstrate that by using the estimated population size and sharing distance an Evolutionary Algorithm (EA) can correctly identify multiple optima.

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