[1]华一村,刘奇奇,郝矿荣,等.非规则Pareto前沿面多目标进化优化算法研究综述[J].郑州大学学报(工学版),2021,42(01):1-8.[doi:10.13705/j.issn.1671-6833.2021.01.001]
　HUA Yicun,LIU Qiqi,HAO Kuangrong,et al.A Survey of Evolutionary Algorithms for Multi-objective Optimization Problems with Irregular Pareto Fronts[J].Journal of Zhengzhou University (Engineering Science),2021,42(01):1-8.[doi:10.13705/j.issn.1671-6833.2021.01.001]
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非规则Pareto前沿面多目标进化优化算法研究综述()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
42
期数:
2021年01期
页码:
1-8
栏目:
出版日期:
2021-03-14

文章信息/Info

Title:
A Survey of Evolutionary Algorithms for Multi-objective Optimization Problems with Irregular Pareto Fronts
作者:
华一村1; 刘奇奇2; 郝矿荣1; 金耀初1; 2
1.东华大学 信息科学与技术学院，上海 201620; 2.萨里大学 计算机科学系，英国 萨里 GU2 7XH
Author(s):
HUA Yicun1;  LIU Qiqi2;  HAO Kuangrong1;  JIN Yaochu1; 2
1.College of Information Science and Technology, Donghua University, Shanghai 201620, China; 2.Department of Computer Science, University of Surrey, Surrey GU2 7XH, U.K.
关键词:
多目标优化;  进化算法;  非规则Pareto前沿面;  综述
Keywords:
multi-objective optimization;  evolutionary algorithm;  irregular Pareto front;  survey
分类号:
TP301
DOI:
10.13705/j.issn.1671-6833.2021.01.001
文献标志码:
A
摘要:
现实中多目标优化问题的Pareto前沿面往往是不连续的，退化的等非规则的形式。传统的针对规则Pareto前沿面的进化算法无法很好地解决这类问题。因此，针对具有非规则Pareto前沿面的多目标优化问题的进化算法逐渐成为进化计算领域的研究热点。本文对现有的针对非规则Pareto前沿面的进化算法进行分类综述，分析各类算法的特点和缺陷，并给出未来的发展方向。
Abstract:
In reality, the Pareto fronts of multi-objective optimization problems are often irregular. Evolutionary algorithms for such problems have gradually become a hot topic. This paper provides a survey of the existing evolutionary algorithms for the multi-objective optimization problems with irregular Pareto fronts, gives a general mathematical description of the multi-objective optimization problems, and introduces the relevant definitions in the research field such as dominated and non-dominated solutions. It suggests a taxonomy of the typical multi-objective optimization test problems with irregular Pareto fronts, as well as the actual multi-objective optimization test problems with irregular Pareto fronts such as car crash test problem. The existing evolutionary algorithms for multi-objective optimization problems with irregular Pareto fronts are divided into four categories: the methods of adjusting the reference vectors according to the population distribution, the fixed reference vectors merging other auxiliary methods, the methods of reference points, and the methods of clustering and partitioning. Their strengths and weaknesses are discussed. Although evolutionary algorithms for multi-objective optimization problems with irregular Pareto fronts have achieved certain success, existing algorithms generally perform well only on some irregular Pareto front problems. Algorithms that can work efficiently on all kinds of irregular Pareto front problems are yet to be developed. High dimensional, dynamic and the data-driven multi-objective problems with irregular Pareto fronts remain to be solved. More intelligent evolutionary algorithms that can identify and handle multiple types of multi-objective optimization problems with irregular Pareto fronts are the focus of future research. Hybrid approaches, transfer learning or multi-task learning and optimization combined with evolutionary computation are possible solutions.

参考文献/References:

[1] 雷德明, 严新平. 多目标智能优化方法及其应用[M]. 北京: 科学出版社, 2009.

[2] ZHANG C J, TAN K C, LEE L H, et al. Adjust weight vectors in MOEA/D for bi-objective optimi-zation problems with discontinuous Pareto fronts[J]. Soft computing-a fusion of foundations, methodologies and applications, 2018, 22(12):3997-4012.
[3] ISHIBUCHI H, MASUDA H, NOJIMA Y. Pareto fronts of many-objective degenerate test problems[J]. IEEE transactions on evolutionary computation, 2016, 20(5):807-813.
[4] JAIN H, DEB K. An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach[J]. IEEE transactions on evolutionary computation, 2014, 18(4):602-622.
[5] HUA Y, JIN Y, HAO K. A clustering-based adaptive evolutionary algorithm for multiobjective optimization with irregular Pareto fronts[J]. IEEE transactions on cybernetics, 2019, 49(7): 2758-2770.
[6] BADER J, ZITZLER E. HypE: an algorithm for fast hypervolume-based many-objective optimization[J]. Evolutionary computation, 2011, 19(1):45-76.
[7] QI Y T, MA X L, LIU F, et al. MOEA/D with adaptive weight adjustment[J]. Evolutionary computation, 2014, 22(2):231-264.
[8] ANTONIO L M, COELLO C A C. Coevolutionary multiobjective evolutionary algorithms: survey of the state-of-the-art[J]. IEEE transactions on evolutionary computation, 2018, 22 (6):851-865.
[9] DAS I, DENNIS J E. Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems[J]. SIAM journal on optimization, 1998, 8(3):631-657.
[10] WANG H D, HE S, YAO X. Nadir point estimation for many-objective optimization problems based on emphasized critical regions[J]. Soft computing, 2017, 21(9):2283-2295.
[11] DEB K, THIELE L, LAUMANNS M, et al. Scalable test problems for evolutionary multiobjective optimization[J]. Evolutionary multiobjective optimization, 2005:105-145.
[12] JAIN H, DEB K. An improved adaptive approach for elitist nondominated sorting genetic algorithm for many-objective optimization[J] Evolutionary multi-criterion optimization, 2013, 7811:307-321.
[13] HUBAND S, BARONE L, WHILE L, et al. A scalable multi-objective test problem toolkit[J]. Lecture notes in computer science, 2005, 3410:280-295.
[14] CHENG R, LI M Q, TIAN Y, et al. A benchmark test suite for evolutionary many-objective optimization[J]. Complex & intelligent systems, 2017, 3(1):67-81.
[15] ZHANG Q F, ZHOU A, ZHAO S Z, et al. Multiobjective optimization test instances for the CEC 2009 special session and competition[J]. Mechanical engineering,2008,8:16283.
[16] YU G, CHAI T Y, LUO X C. Multiobjective production planning optimization using hybrid evolutionary algorithms for mineral processing[J]. IEEE transactions on evolutionary computation, 2011, 15(4):487-514.
[17] SAXENA D K, DURO J A, TIWARI A, et al. Objective reduction in many-objective optimization: linear and nonlinear algorithms[J]. IEEE transactions on evolutionary computation, 2013, 17(1):77-99.
[18] CHENG R, JIN Y C, NARUKAWA K. Adaptive reference vector generation for inverse model based evolutionary multiobjective optimization with degenerate and disconnected Pareto fronts[J]. Evolutionary multi-criterion optimization, 2015, 9018:127-140.
[19] CHENG R, JIN Y C, 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.
[20] XU H, ZENG W H, ZHANG D, et al. MOEA/HD: a multiobjective evolutionary algorithm based on hierarchical decomposition[J]. IEEE transactions on cybernetics, 2019, 49(2): 517-526.
[21] CAI X Y, MEI Z, FAN Z. A decomposition-based many-objective evolutionary algorithm with two types of adjustments for direction vectors[J]. IEEE transactions on cybernetics, 2018, 48(8)：2335-2348.
[22] JIANG S Y, YANG S X. An improved multiobjective optimization evolutionary algorithm based on decomposition for complex Pareto fronts[J]. IEEE transactions on cybernetics, 2016, 46(2):421-437.
[23] LIANG Z P, HOU W J, HUANG X, et al. Two new reference vector adaptation strategies for many-objective evolutionary algorithms[J]. Information sciences, 2019, 483:332-349.
[24] WANG R, PURSHOUSE R C, FLEMING P J. Preference-inspired co-evolutionary algorithms using weight vectors[J]. European journal of operational research, 2015, 243(2):423-441.
[25] GU F, LIU H L, TAN K C. A multiobjective evolutionary algorithm using dynamic weight design method[J]. International journal of innovative computing, information and control, 2012, 8(5B): 3677-3688.
[26] LIU Q Q, JIN Y C, HEIDERICH M, et al. Adaptation of reference vectors for evolutionary for evolutionary many-objective optimization of problems with irregular Pareto fronts[C]// 2019 IEEE Congress on Evolutionary Computation (CEC). New York: IEEE, 2019:1726-1733.
[27] LIU H L, CHEN L, ZHANG Q F, et al. Adaptively allocating search effort in challenging many-objective optimization problems[J]. IEEE transactions on evolutionary computation, 2018, 22(3)：433-448.
[28] HE X Y, ZHOU Y R, CHEN Z F, et al. Evolutionary many-objective optimization based on dynamical decomposition[J]. IEEE transactions on evolutionary computation, 2019, 23(3): 361-375.
[29] LIU Y P, ISHIUCHI H, MASUYAMA N, et al. Adapting reference vectors and scalarizing functions by growing neural gas to handle irregular Pareto fronts[J]. IEEE transactions on evolutionary computation, 2020, 24(3):439-453.
[30] GE H, ZHAO M D, SUN L, et al. A many-objective evolutionary algorithm with two interacting processes: cascade clustering and reference point incremental learning[J]. IEEE transactions on evolutionary computation, 2019, 23(4)：572-586.
[31] LI H, DENG J D, ZHANG Q F, et al. Adaptive epsilon dominance in decomposition-based multiobjective evolutionary algorithm[J]. Swarm and evolutionary computation, 2019, 45：52-67.
[32] LI M Q, YANG S X, LIU X H. Pareto or non-Pareto: bi-criterion evolution in multi-objective optimization[J]. IEEE transactions on evolutionary computation, 2016, 20(5):645-665.
[33] CAI X Y, YANG Z X, FAN Z, et al. Decomposition-based-sorting and angle-based-selection for evolutionary multiobjective and many-objective optimization[J]. IEEE transactions on cybernetics, 2017, 47(9):2824-2837.
[34] LIU C,ZHAO Q,YAN B, et al. Adaptive sorting-based evolutionary algorithm for many-objective optimization[J]. IEEE transactions on evolutionary computation, 2019, 23(2):247-257.
[35] DAS S S, ISLAM M M, ARAFAT N A. Evolutionary algorithm using adaptive fuzzy dominance and reference point for many-objective optimization[J]. Swarm and evolutionary computation, 2019, 44: 1092-1107.
[36] LIU Y P, GONG D W, SUN X Y, et al. Many-objective evolutionary optimization based on reference points[J]. Applied soft computing, 2017, 50：344-355.
[37] TIAN Y, CHENG R, ZHANG X Y, et al. An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility[J]. IEEE transactions on evolutionary computation, 2018, 22(4):609-622.
[38] CAI X Y, SUN H R, ZHU C Y, et al. Locating the boundaries of Pareto fronts: a many-objective evolutionary algorithm based on corner solution search[EB/OL]. (2018-06-08)[2020-09-15]. https://arxiv.org/abs/1806.02967.
[39] WANG Z K, ZHANG Q F, LI H, et al. On the use of two reference points in decomposition based multiobjective evolutionary algorithms[J]. Swarm and evolutionary computation, 2017, 34: 89-102.
[40] ZHOU Y R, XIANG Y, CHEN Z F, et al. A scalar projection and angle-based evolutionary algorithm for many-objective optimization problems[J]. IEEE transactions on cybernetics, 2019, 49(6): 2073-2084.
[41] XIANG Y, ZHOU Y R, YANG X W, et al. A many-objective evolutionary algorithm with Pareto-adaptive reference points[J]. IEEE transactions on evolutionary computation, 2020, 24(1):99-113.
[42] LIN Q Z, LIU S B, WONG K C, et al. A clustering-based evolutionary algorithm for many-objective optimization problems[J]. IEEE transactions on evolutionary computation, 2019, 23(3): 391-405.
[43] DENYSIUK R, COSTA L, ESPwidth=4,height=12,dpi=110RITO SANTO I. Clustering-based selection for evolutionary many-objective optimization[C]// International Conference on Parallel Problem Solving from Nature.Berlin: Springer, 2014:538-547.
[44] 封文清,巩敦卫. 基于在线感知Pareto前沿划分目标空间的多目标进化优化[J].自动化学报, 2020,46(8):1628-1643.
[45] PAN L Q, HE C, TIAN Y, et al. A region division based diversity maintaining approach for many-objective optimization[J]. Integrated computer-aided engineering, 2017, 24(3): 279-296.
[46] CAI X Y, MEI Z W, FAN Z, et al. A constrained decomposition approach with grids for evolutionary multiobjective optimization[J]. IEEE transactions on evolutionary computation, 2018, 22(4): 564-577.
[47] 汪慎文,杨锋,徐亮,等. 离散差分进化算法求解共享单车调度问题[J].郑州大学学报(工学版),2019,40(4):48-53.
[48] 梁静,刘睿,瞿博阳,等.进化算法在大规模优化问题中的应用综述[J].郑州大学学报(工学版),2018,39(3):15-21.

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更新日期/Last Update: 2021-03-15