An Efficient Constrained Global optimization Method through Adaptively Adjusting Predicted Feasible Region and Its Application in Buckling Design of Stiffened Cylindrical Shell with Variable Ribs

Abstract

Surrogate-based optimization methods are popular in tackling expensive problems due to their high efficiency. When constrained problems are encountered, obtaining the feasible global optimum becomes quite challenging due to the inaccuracy of constraint surrogates. In this study, an efficient constrained global optimization method based on Kriging surrogate models is proposed. In the proposed method, the feasible region predicted by the constraint surrogates is adaptively adjusted by checking the feasibility of the infill point, which is obtained through minimizing the lower confidence bound (LCB) of the objective prediction subject to the adjusted constraints. Specifically, the candidate infill region is initialized to the predicted feasible region without considering the uncertainty from constraint surrogates. Then, the feasibility of the infill point is checked by expensive evaluation. If the infill point is infeasible, the candidate infill region is shrunk to obtain the next infill point. Otherwise, it is extended to incorporate other promising regions that potentially contain a better solution. Through the shrink-and-extend strategy, both the feasible and infeasible points in the vicinity of the global optimum are infilled, which is beneficial to improving the surrogates’ accuracy on the feasible region boundary. In order to verify the effectiveness of the proposed method, it is first compared with three state-of-the-art algorithms on thirteen benchmark mathematical problems and on two engineering problems. Besides, the proposed method is also applied to the buckling design of stiffened cylindrical shell with variable ribs under constraints of strength and weight to demonstrate its applicability.