Constraint Importance Mode Pursuing Sampling for Continuous Global Optimization

Many engineering design problems deal with global optimization of constrained black-box problems which is usually computation-intensive. Ref. [1] proposed a Mode-Pursuing Sampling (MPS) method for global optimization based on a sampling technique which systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire problem domain. In this paper, we propose a novel and more efficient sampling technique which greatly enhances the performance of the MPS method, especially in the presence of expensive constraints. The effective sampling of the search space is attained via biasing the sample points towards feasible regions and being away from the forbidden regions. This is achieved by utilizing the incrementally obtained information about the constraints, hence, it is called Constraint-importance Mode Pursuing Sampling (CiMPS). According to intensive comparisons and experimental verifications, the new sampling technique is found to be more efficient in solving constrained optimization problems compared to the original MPS method. To the best of our knowledge, this is the first metamodel-based global optimization method that directly aims at reducing the number of function evaluations for both expensive objective functions and constraints.