Multimodal Optimization by Decomposition of the Search Space in Regions

A multimodal function is a function with more than one optimum. This work proposes a method for automatic determination of regions of the search space of a given function. Those regions guarantee enclose one an optimum. Based on an initial sampling of the search space, an incremental convex hull algorithm is used to incrementally grow regions that enclose one optimum. After applying the method we can use any optimization algorithm on each of the determined region; comparing with genetic algorithms for multimodal functions, the proposed method eliminates the use of parameters like radius in fitness sharing.