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

HTML

PDF (PC)

2866

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
[1] SRINIVAS N, DEB K. Multiobjective optimization using nondominated sorting in genetic algorithms[J]. Evolutionary Computation, 1994, 2(3):221-248.
[2] ZITZLER E, LAUMANNS M, THIELE L. SPEA2:improving the performance of the strength pareto evolutionary algorithm[J]. Lecture Notes in Computer Science, 2004, 3242(4):742-751.
[3] DEB K, JAIN H. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I:solving problems with box constraints[J]. IEEE Transactions on Evolutionary Computation, 2014, 18(4):577-601.
[4] ZITZLER E, KÜNZLI S. Indicator-based selection in multiobjective search[J]. Lecture Notes in Computer Science, 2004, 3242:832-842.
[5] BEUME N, NAUJOKS B, EMMERICH M. SMS-EMOA:multiobjective selection based on dominated hypervolume[J]. European Journal of Operational Research, 2007, 181(3):1653-1669.
[6] BADER J, ZITZLER E. HypE:an algorithm for fast hypervolume-based many-objective optimization[J]. Evolutionary Computation, 2011, 19(1):45
[7] ZHANG Q, LI H. MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Trans Evol Comput, 2007, 11(6):712-731.
[8] LI H, ZHANG Q. Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2009, 13(2):284-302.
[9] CHENG R, JIN Y, OLHOFER M, et al. A reference vector guided evolutionary algorithm for many-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2016, 20(5):773-791.
[10] QI Y, MA X, LIU F, et al. MOEA/D with adaptive weight adjustmen[J]. Evolutionary Computation, 2014, 22(2):231-264.
[11] ZHOU A, ZHANG Q. Are all the subproblems equally important? resource allocation in decomposition-based multiobjective evolutionary algorithms[J]. IEEE Transactions on Evolutionary Computation, 2016, 20(1):52-64.
[12] TRIVEDI A, SRINIVASAN D, SANYAL K, et al. A survey of multiobjective evolutionary algorithms based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2017, 21(3):440-462.
[13] SATO H. Analysis of inverted PBI and comparison with other scalarizing functions in decomposition based MOEAs[J]. Journal of Heuristics, 2015, 21(6):819-849.
[14] ISHIBUCHI H, AKEDO N, NOJIMA Y. A study on the specification of a scalarizing function in MOEA/D for many-objective knapsack problems[J]. Proc of Learning and Intelligent Optimization 7(LION 7), 2013, 7997:231-246.
[15] DEB K, THIELE L, LAUMANNS M.Scalable test problems for evolutionary multiobjective optimization[C]//Evolutionary Multiobjective Optimization. London:Springer London Ltd, 2005:105-145.
[16] LI K, DEB K, ZHANG Q, et al. An evolutionary many-objective optimization algorithm based on dominance and decomposition[J]. IEEE Transactions on Evolutionary Computation, 2015, 19(5):694-716.
[17] ZITZLER E, THIELE L. Multiobjective evolutionary algorithms:a comparative case study and the strength Pareto approach[J]. IEEE Transactions on Evolutionary Computation, 1999, 3(4):257-271.
[18] RUSSO L M S, FRANCISCO A P. Quick hypervolume[J]. IEEE Transactions on Evolutionary Computation, 2012, 18(4):481-502.
[19] ZITZLER E, THIELE L, LAUMANNS M, et al. Performance assessment of multiobjective optimizers:an analysis and review[J]. IEEE Transactions on Evolutionary Computation, 2003, 7(2):117-132.
[1] 唐超兰, 谢义. 6061铝合金铣削工艺参数多目标优化[J]. 广东工业大学学报, 2020, 37(05): 87-93.
[2] 胡德卿, 熊锐, 吴坚, 谢火志, 潘浩坤. 基于滚流比的某汽油发动机进气道优化设计和研究[J]. 广东工业大学学报, 2019, 36(01): 87-92.
[3] 唐俊杰, 陈璟华, 邱明晋. 基于动态模糊混沌粒子群算法的含电动汽车微电网多目标优化调度研究[J]. 广东工业大学学报, 2018, 35(03): 100-106.
[4] 黄美华, 温洁嫦, 何勇. 求解多目标背包问题的改进人工鱼群算法[J]. 广东工业大学学报, 2016, 33(05): 44-48.
[5] 高鹰, 余琦, 刘外喜. 应用云模型和Favour排序的多目标优化算法[J]. 广东工业大学学报, 2014, 31(3): 14-20.
[6] 许欢, 温洁嫦. 差分进化算法在物流配送路径优化中的应用[J]. 广东工业大学学报, 2013, 30(4): 61-64.
[7] 谢桂芩，杨玉华，涂井先. 带有时间窗的虚拟场站接驳补货车辆路径问题[J]. 广东工业大学学报, 2013, 30(1): 61-67.
[8] 谢桂芩, 涂井先. 分区域多目标进化算法在协同车辆路径问题中的应用[J]. 广东工业大学学报, 2011, 28(4): 38-44.
[9] 张金凤 , 陈蔚丽. 多目标进化算法在物流配送中心选址中的应用[J]. 广东工业大学学报, 2010, 27(4): 76-80.
[10] 刘玉兰;. 下层带扰动参数的二层多目标优化问题的灵敏度分析[J]. 广东工业大学学报, 2009, 26(2): 11-.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发