A NONLINEAR SCALARIZATION METHOD FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

摘要

This paper presents population-based linear and nonlinear scalarization method for solving multi-objective optimization problems (MOPs). Firstly, we extend the weighted sum method by generating a set of different weights and solving a series of corresponding scalar optimization problems. This mechanism obtains an approximation of all Pareto solutions. However, the extended weighted sum method only works for convex MOPs. For nonconvex MOPs, nonlinear scalarization mechanisms have to be considered. Therefore, the weighted sum method is additionally extended to nonlinear case and a nonlinear scalarization method for nonconvex MOPs is proposed. It turns out that the proposed method not only works for nonconvex MOPs but also for MOPs with disconnected Pareto frontiers. Comprehensively numerical experiments are presented with the results and analysis showing that the proposed methods are efficient in solving various kinds of MOPs.