A parallel constrained lower confidence bounding approach for computationally expensive constrained optimization problems

Abstract

Computationally expensive constrained optimization problems (COPs) are very common in real-world engineering designs. This work proposes a parallel constrained lower confidence bounding (PCLCB) approach to solve challenging optimization problems with computationally expensive objective and constraints. In the PCLCB approach, a two-phase constrained lower confidence bounding (CLCB) criterion is proposed to adaptively allocate infill sample points. In the first phase where no feasible solution exists, a lower confidence bounding (LCB) function of constraints is developed to search for feasible points and improve the accuracies of the Kriging models. After a feasible point is found, the CLCB criterion focuses on local search in the second phase to improve the obtained optimum. In this phase, the search is implemented in a limited region where points may be feasible. Furthermore, an enhanced Kriging believer strategy is presented to parallelize the CLCB criterion to generate a batch of candidate points at each iteration. The PCLCB approach is tested on sixteen numerical benchmark cases and compared with the state-of-the-art alternative methods. Results indicate that the performance of PCLCB is highly competitive to the recently published algorithms in terms of efficiency and effectiveness. To verify the capability of PCLCB in solving real-world engineering problems, the lightweight design of micro-aerial vehicle (MAV) fuselage is presented. The weight of the MAV fuselage obtained by the proposed approach is on average 3.5% less than that of the other alternative methods.