A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming

• 作者: Min Jiang Rui Shen Zhiqing Meng
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 数学
• 关键词: MULTI-OBJECTIVE Programming PENALTY Function Objective PARAMETERS CONSTRAINT PENALTY Parameter PARETO Weakly-Efficient Solution
• 年，卷（期）: 2014,（6）
• 页码范围: 331-339
• 页数: 9页
• 分类号: O1

摘要

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.