A comparative study of different algorithms and scalarization techniques for constructing the Pareto front of multiobjective optimization problems

Abstract

This paper presents an analysis and comparison of various algorithms applied to different scalarization methods for multiobjective optimization problems (MOPs). At first, some theoretical results are provided on the relation between (weakly) efficient solutions of an MOP and optimal solutions of the related numerical method. Moreover, we consider some deficiencies in different scalarization approaches given in the literature and try to fill some gaps in these works. Hence, by considering appropriate limitations, we provide sufficient conditions for (ε-)properly efficient and (ε-)efficient solutions of an MOP via scalarization techniques. Then, an algorithm for approximating the Pareto front of MOPs is presented. The main purpose of this algorithm is to generate efficient points on the Pareto front with a uniform distribution. One advantage of this algorithm, compared to some other algorithms, is that in each iteration of the algorithm, more than one efficient point located on the Pareto border can be generated. The new algorithm is implemented by applying the modified Pascoletti–Serafini, the unified direction, and the modified normal boundary intersection scalarization techniques, and then the procedures are considered on different test problems including (non-)convex and discrete Pareto fronts. The capability of the numerical method is shown by comparing the results with the algorithms in the literature. To compare the algorithms, measures of coverage and spacing metric indicators are used.

Keywords:

• Multiobjective optimization
• efficient solution
• Pareto front
• scalarized problem

Mathematics Subject Classification:

• 90C29

Disclosure statement

No potential conflict of interest was reported by the author(s).