New decision-making methods for ranking of non-dominated points for multi-objective optimization problems

A multi-objective optimization problem (MOP) is a simultaneous optimization of more than one real-valued conflicting objective function subject to some constraints. Most MOP algorithms try to provide a set of Pareto optimal solutions which are equally good in terms of the objective functions. The set can be infinite, and hence, analysis and choice task of one or several solutions among the equally good solutions is hard for a decision maker (DM). In this paper, a new scalarization approach is proposed to select a Pareto optimal solution for convex MOPs such that the relative importance assigned to its objective functions is very close together. In addition, two decision-making methods are developed to analyze convex and non-convex MOPs based on evaluating a set of Pareto optimal solutions and the relative importance of the objective functions. These methods support the DM to rank the solutions and obtain one or several of them for real implementation without having any familiarity about MOPs.