A new algorithm for finding Pareto optimal points of multiobjective optimization problems

Document Type : Original Article

Authors

1 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.

2 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

3 Assistant Professor-Shahrood University of Technology

Abstract

In this paper, a modified scalarization technique for finding Pareto optimal points of multiobjective optimization problems is provided. The proposed method is a combination of the normal constraint and elastic constraint method. First, we introduce the optimization problem of the modified method and then we present an algorithm for obtaining the set of Pareto points. Thereafter, the relationship between optimal solutions of this scalarization problem and (weakly, properly) efficient solutions of the multiobjective optimization problems are analyzed. Indeed, some necessary conditions for (weak, proper) efficiency are presented. All the provided results are established without any convexity assumption. Furthermore, we propose a new algorithm for approximating the Pareto front of multiobjective optimization problems. We solve some test problems by applying the suggested algorithm and compare the results with some existing methods, including the epsilon-constraint method, the Pascolleti-Serafini method and the NBI method. The obtained results highlight the efficiency of our approach in comparison with examined methods.

Keywords

References

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