Multimodal Function Optimization Using Local Ruggedness Information.
Jian Zhang, Xiaohui Yuan, Bill P. Buckles · 2004
In multimodal function optimization, niching tech-niques 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 as-sumptions. In this article, we propose a method to esti-mate 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 sam-ple the fitness landscape and compute its subspace fit-ness distance correlation (FDC) coefficients. An algo-rithm for estimating the granularity feature is described. The sharing distance and the population size are deter-mined 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.