An Improved Blind Kriging Surrogate Model for Design Optimization Problems

Abstract

Surrogate modeling techniques are widely employed in solving constrained expensive black-box optimization problems. Therein, Kriging is among the most popular surrogates in which the trend function is considered as a constant mean. However, it also encounters several challenges related to capturing the overall trend with a relatively limited number of function evaluations as well as searching feasible points with complex or discontinuous feasible regions. To address this above issue, this paper presents an improved surrogate blind Kriging (IBK) and a combined infill strategy to find the optimal solution. According to enhancing the prediction accuracy of metamodels of objective and constraints, the high-order effects of regression function in the blind Kriging are identified by promising a variable selection technique. In addition, an infill strategy is developed based on the probability of feasibility, penalization, and constrained expected improvement for updating blind Kriging metamodels of the objective and constraints. At each iteration, two infill sample points are allocated at the positions to achieve improvement in optimality and feasibility. The IBK metamodels are updated by the newly-added infill sample points, which leads the proposed framework search to rapidly converge to the optimal solution. The performance and applicability of the proposed model are tested on several numerical benchmark problems via comparing with other metamodel-based constrained optimization methods. The obtained results indicate that IBK generally has a greater efficiency performance and outperforms the competitors in terms of a limited number of function evaluations. Finally, IBK is successfully applied to structural design optimization. The optimization results show that IBK is able to find the best feasible design with fewer evaluation functions compared with other studies, and this demonstrates the effectiveness and practicality of the proposed model for solving the constrained expensive black-box engineering design optimization problems.