Metamodel-Based Optimization for Problems With Expensive Objective and Constraint Functions

Current metamodel-based design optimization methods rarely deal with problems of not only expensive objective functions but also expensive constraints. In this work, we propose a novel metamodel-based optimization method, which aims directly at reducing the number of evaluations for both objective function and constraints. The proposed method builds on existing mode pursuing sampling method and incorporates two intriguing strategies: (1) generating more sample points in the neighborhood of the promising regions, and (2) biasing the generation of sample points toward feasible regions determined by the constraints. The former is attained by a discriminative sampling strategy, which systematically generates more sample points in the neighborhood of the promising regions while statistically covering the entire space, and the latter is fulfilled by utilizing the information adaptively obtained about the constraints. As verified through a number of test benchmarks and design problems, the above two coupled strategies result in significantly low number of objective function evaluations and constraint checks and demonstrate superior performance compared with similar methods in the literature. To the best of our knowledge, this is the first metamodel-based global optimization method, which directly aims at reducing the number of evaluations for both objective function and constraints.