广东工业大学学报 ›› 2018, Vol. 35 ›› Issue (04): 37-44.doi: 10.12052/gdutxb.170147

• 综合研究 • 上一篇    下一篇

MOEA/D聚合函数的二次泛化及其优化性能分析

周怡璐, 王振友, 李叶紫, 李锋   

  1. 广东工业大学 应用数学学院, 广东 广州 510520
  • 收稿日期:2017-11-06 出版日期:2018-07-09 发布日期:2018-05-24
  • 通信作者: 李锋(1977-),男,讲师,主要研究方向为算法设计与分析,E-mail:lfgdutnews@126.com E-mail:lfgdutnews@126.com
  • 作者简介:周怡璐(1992-),女,硕士研究生,主要研究方向为算法设计与分析、最优化理论与方法.
  • 基金资助:
    广州市科技计划项目（201707010435）；广东省研究生教育创新改革资助项目（2014JGXM-MS17）

A Quadratic Scalarizing Function in MOEA/D and its Performance on Multi and Many-Objective Optimization

Zhou Yi-lu, Wang Zhen-you, Li Ye-zi, Li Feng   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2017-11-06 Online:2018-07-09 Published:2018-05-24

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摘要： 基于分解的多目标进化算法（Multi-objective Evolutionary Algorithm Based on Decomposition，MOEA/D）是多目标优化算法的一个重要分支，多目标优化的关键问题是如何在算法的收敛性和散布性之间达到良好的平衡.目前主流算法的聚合函数存在着不同的优缺点，尤其是当使用切比雪夫方法选择个体时，经常出现个体偏离权重现象，个体和权重间得不到很好的粘合.本文基于此提出了一种新的聚合函数方法，提高了MOEA/D的性能.该聚合函数的函数形式为二次函数，种群个体在该函数下的等高线是一条二次曲线（本文称双曲线函数方法，Hyperbola Function Method，HYB），是对目前存在的聚合函数的一种泛化形式.该HYB方法相比PBI （Penalty-based Boundary Intersection）方法更强调收敛性，能更容易地在收敛性散布性之间达到平衡.本文测试了MOKP问题及DTLZ系列等测试函数，并与其他算法进行了实验对比，结果显示HYB方法更稳定有效且种群在收敛速度上有一定的提高.

关键词: 多目标优化, 基于分解的多目标进化算法, 聚合函数

Abstract: Multi-objective Evolutionary Algorithm Based on decomposition (MOEA/D) is an important branch. Achieving balance between convergence and diversity is a key issue in evolutionary multi-objective optimization. There are more or less deficiencies and shortcomings in the mainstream scalarizing functions. When using Tchebycheff to choose individuals, individuals often deviate from the weight and can not combine well with weight. On this basis, a new scalarizing function which improves performance of MOEA/D is presented. The scalarizing function is a quadratic function and its contour line is also a quadratic function (In this paper it is called Hyperbola function method, which is HYB.), which is a generalization to the current scalarizing functions. Comparing with PBI, this algorithm has better convergence and the balance between convergence and diversity is easily obtained. After testing MOKP and series of DTLZ and comparing with other algorithms, HYB is shown to be stable and effective and to improve the speed of convergence.

Key words: multi-objective optimization, multi-objective evolutionary algorithm based on decomposition (MOEA/D), scalarizing functions

中图分类号: 

  • TP301.6
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