数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 702-720.doi: 10.1007/s10473-024-0218-8

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A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

N. HOSEINPOOR, M. GHAZNAVI*   

  1. Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
  • 收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2024-04-25 发布日期:2024-04-16
  • 通讯作者: *M. GHAZNAVI, E-mail: Ghaznavi@shahroodut.ac.ir

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

N. HOSEINPOOR, M. GHAZNAVI*   

  1. Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
  • Received:2022-11-20 Revised:2023-01-08 Online:2024-04-25 Published:2024-04-16
  • Contact: *M. GHAZNAVI, E-mail: Ghaznavi@shahroodut.ac.ir

摘要: In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends theobjective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

关键词: smultiobjective optimization, Pareto front, scalarization, objective-constraint approach, proper efficient solution

Abstract: In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends theobjective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

Key words: smultiobjective optimization, Pareto front, scalarization, objective-constraint approach, proper efficient solution

中图分类号: 

  • 90C29