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

作     者：N.HOSEINPOOR M.GHAZNAVI N.HOSEINPOOR;M.GHAZNAVI

作者机构：Faculty of Mathematical SciencesShahrood University of TechnologyShahroodIran 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2024年第44卷第2期

页      面：702-720页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

主　　题：multiobjective optimization Pareto front scalarization objective-constraint approach proper efficient solution 

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 the objective-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.