A Novel Sequential Multi-Objective Optimization Using Anchor Points in the Design Space of Global Variables

Multi-objective problems are encountered in many engineering applications and multi-objective optimization (MOO) approaches have been proposed to search for Pareto solutions. Due to the nature of searching for multiple optimal solutions, the computational efforts of MOO can be a serious concern. To improve the computational efficiency, a novel efficient sequential MOO (S-MOO) approach is proposed in this work, in which anchor points in the design space for global variables are fully utilized and a data set for global solutions is generated to guide the search for Pareto solutions. Global variables refer to those shared by more than one objective or constraint, while local variables appear only in one objective and corresponding constraints. As a matter of fact, it is the existence of global variables that leads to couplings among the multiple objectives. The proposed S-MOO breaks the couplings among multiple objectives (and constraints) by distinguishing the global variables, and thus all objectives are optimized in a sequential manner within each iteration while all iterations can be processed in parallel. The computational cost per produced Pareto point is reduced and a well-spread Pareto front is obtained. Six numerical and engineering examples including two three-objective problems are tested to demonstrate the applicability and efficiency of the proposed approach.