SCGOSR: Surrogate-based constrained global optimization using space reduction

Abstract

Global optimization problems with computationally expensive objective and constraints are challenging. In this work, we present a new kriging-based constrained global optimization algorithm SCGOSR that can find global optima with fewer objective and constraint function evaluations. In SCGOSR, we propose a multi-start constrained optimization algorithm that can capture approximately local optimal points from kriging and select the promising ones for updating. In addition, according to two different penalty functions, two subspaces are created to construct local surrogate models and speed up the local search. Subspace1 is the neighborhood of the presented best solution, and Subspace2 is a region that covers several promising samples. The proposed multi-start constrained optimization is carried out alternately in Subspace1, Subspace2 and the global space. With iterations going on, kriging models of the costly objective and constraints are dynamically updated. In order to guarantee the balance between local and global search, the estimated mean square error of kriging is used to explore the unknown design space. Once SCGOSR gets stuck in a local valley, the algorithm will focus on the sparsely sampled regions. After comparison with 6 surrogate-based optimization algorithms on 13 representative cases, SCGOSR shows noticeable advantages in handling computationally expensive black-box problems.