Comparison of Partition Evaluation Measures in an Adaptive Partitioning Algorithm for Global Optimization

Abstract

An adaptive partitioning algorithm with random search is proposed to locate the global optimum of multimodal functions. Partitioning algorithms divide the feasible region into nonoverlapping partitions in order to restrict and direct the search to the most promising region expected to contain the global optimum. In such a scheme a partition evaluation measure is required to assess sub-regions in order to re-partition the most promising sub-region and intensify the search within that area. This study provides computational results on several classes of partition evaluation measures used in the assessment of samples taken from all partitions. Among the partition evaluation classes used in our comparison are fuzzy, statistical, and deterministic interval estimation measures. Performance in terms of solution quality is reported on an extensive set of 77 test functions collected from the literature.