A New Partition-Based Random Search Method for Deterministic Optimization Problems

Abstract

The Nested Partition (NP) method is efficient in large-scale optimization problems. The most promising region is identified and partitioned iteratively. To guarantee the global convergence, a backtracking mechanism is introduced. Nevertheless, if inappropriate partitioning rules are used, lots of backtracking occur reducing largely the algorithm efficiency. A new partition-based random search method is developed in this paper. In the proposed method, all generated regions are stored for further partitioning and each region has a partition speed related to its posterior probability of being the most promising region. Promising regions have higher partition speeds while non-promising regions are partitioned slowly. The numerical results show that the proposed method finds the global optimum faster than the pure NP method if numerous high-quality local optima exist. It can also find all the identical global optima, if exist, in the studied case.