多目标优化问题的Pascoletti-Serafini标量化方法  

The Pascoletti-Serafini scalarization scheme for multiobjective optimization problems

作　　者：唐莉萍[1,2] 杨新民 高英 Liping Tang;Xinmin Yang;Ying Gao

机构地区：[1]重庆工商大学数学与统计学院,重庆400047 [2]重庆工商大学社会经济应用统计重庆市重点实验室,重庆400047 [3]重庆师范大学数学科学学院,重庆401331

出　　处：《中国科学：数学》2020年第9期1249-1270,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11991024,11971084,11701057和11771064);重庆市自然科学基金(批准号:cstc2018jcyjyszxX0009和cstc2019jcyj-zdxmX0016);重庆市高等学校巴渝学者青年学者计划;重庆市教育委员会科学技术研究计划(批准号:KJQN201800806)资助项目。

摘　　要：非线性标量化方法是研究非凸多目标优化问题的一个重要途径.目前Pascoletti-Serafini标量化方法是处理非凸多目标优化问题的有力工具之一.但绝大部分结果是针对多目标优化问题的弱有效解和有效解建立的.因此,本文深入研究Akbari等(2018)提出的3类改进的Pascoletti-Serafini标量化方法,主要考虑在什么条件下可以建立非凸多目标优化问题真有效解的非线性标量化刻画.通过限制相应标量化问题中的参数范围,获得了非凸多目标优化问题弱有效解、有效解和真有效解的充分和必要条件.此外,举例说明了主要结果.The nonlinear scalarization technique is an important approach to study nonconvex multiobjective optimization problems. At present, Pascoletti-Serafini scalarization scheme is one of the powerful tools to deal with nonconvex multiobjective optimization problems. However, most of these results are established for weak efficiency and efficiency to multiobjective optimization problems. Consequently, this paper is devoted to further investigation on the modifications of the Pascoletti-Serafini method, which are proposed by Akbari et al.(2018).We are interested in establishing relationships between(weakly, properly) efficient solutions of a general nonconvex multiobjective optimization problem and optimal solutions of the related scalarized problem under appropriate assumptions. For this purpose, necessary and sufficient conditions to(weakly, properly) efficient solutions of a general nonconvex multiobjective optimization problem are achieved via restricting the ranges of the parameters involved in the corresponding scalarization problem. Furthermore, some examples are given to illustrate our main results.

关 键 词：多目标优化 Pascoletti-Serafini方法 真有效解 非线性标量化 

分 类 号：O224[理学—运筹学与控制论]