A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method

This paper presents generalized scalarization methods for obtaining Pareto optimal solutions to multiobjective optimization problems (MOPs), which are not necessary linear nor convex. Several computational methods have been proposed for characterizing Pareto optimal solutions depending on the different methods to scalarize the MOPs. Among the many possible ways of scalarizing the MOPs, the weighting problem, the weighted 𝓁p-norm problem, the weighted minimax problem, the constraint problem and their variants have been studied as a means of characterizing Pareto optimal solutions of the MOPs. As generalizations of such existing scalarizing problems, new scalarizing problems, called the hyperplane problems are introduced. Then fully integrated methods for characterizing Pareto optimal solutions of the MOPs, called the hyperplane methods are developed. As an obvious advantage of the proposed methods, it is shown that all the existing scalarizing methods can be viewed as a special case of the hyperplane methods.