[1]邢文来,吴润秀,肖人彬,等.决策变量分组优化的多目标萤火虫算法[J].智能系统学报,2025,20(4):838-857.[doi:10.11992/tis.202406005]
XING Wenlai,WU Runxiu,XIAO Renbin,et al.A multi-objective firefly algorithm with group optimization of decision variables[J].CAAI Transactions on Intelligent Systems,2025,20(4):838-857.[doi:10.11992/tis.202406005]
点击复制
XING Wenlai,WU Runxiu,XIAO Renbin,et al.A multi-objective firefly algorithm with group optimization of decision variables[J].CAAI Transactions on Intelligent Systems,2025,20(4):838-857.[doi:10.11992/tis.202406005]
决策变量分组优化的多目标萤火虫算法
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
20
期数:
2025年第4期
页码:
838-857
栏目:
学术论文—机器学习
出版日期:
2025-08-05
- Title:
- A multi-objective firefly algorithm with group optimization of decision variables
- Keywords:
- multi-objective optimization problems; multi-objective firefly algorithm; variable grouping; learning behaviour; mutation operator; archive truncation; convergence speed; optimization accuracy
- 分类号:
- TP18
- 文献标志码:
- 2025-2-26
- 摘要:
- 多目标萤火虫算法采用整体维度更新策略，常因某几维变量上优化效果不佳，导致算法收敛速度慢和寻优精度低。针对上述问题，本文提出基于决策变量分组优化的多目标萤火虫算法(multi-objective firefly algorithm with group optimization of decision variables, MOFA-GD)。引入决策变量分组机制，根据各变量对算法性能的不同影响，将整体决策变量划分成收敛性变量组和多样性变量组；设计决策变量分组优化模型，利用学习行为优化收敛性变量组，加快种群收敛速度，非均匀变异算子优化多样性变量组，避免种群过早收敛，逐渐减小的变异幅度引导种群局部开发，提升算法寻优精度；采用档案截断策略维护外部档案，精准删除拥挤个体，从而保持外部档案的多样性。实验结果表明：MOFA-GD表现出优秀的收敛速度和寻优精度，获得了均匀分布的Pareto解集。本文所提算法为求解多目标优化问题提供了一种高效且可靠的解决方案。
- Abstract:
- Multi-objective firefly algorithm adopts an overall dimension update strategy, which often results in slow convergence and poor optimization accuracy due to inadequate optimization effects on certain dimensions. To address these problems, this paper proposes a multi-objective firefly algorithm with group optimization of decision variables(MOFA-GD). Firstly, it introduces a decision variable grouping mechanism, dividing the entire set of decision variables into a convergence variable group and a diversity variable group based on different impacts of each variable on the algorithm’s performance. Secondly, it designs a decision variable grouping optimization model, utilizing learning behavior to optimize the convergence variable group to accelerate the population’s convergence speed, while using a non-uniform mutation operator to optimize the diversity variable group to prevent premature convergence. A gradually decreasing mutation amplitude guides local exploitation by the population, thereby enhancing the algorithm’s optimization accuracy. Finally, it adopts an archive truncation strategy to maintain the external archive, accurately removing crowded individuals to preserve diversity of the external archive. Experimental results show that MOFA-GD demonstrates excellent convergence speed and optimization accuracy, achieving a uniformly distributed Pareto optimal solution set. The proposed algorithm provides a high-efficiency and reliable solution for solving multi-objective optimization problems.
- 参考文献/References:
-
[1] FARAG M A, EL-SHORBAGY M A, MOUSA A A, et al. A new hybrid metaheuristic algorithm for multiobjective optimization problems[J]. International journal of computational intelligence systems, 2020, 13(1): 920-940.
[2] BAROCIO E, REGALADO J, CUEVAS E, et al. Modified bio-inspired optimisation algorithm with a centroid decision making approach for solving a multi-objective optimal power flow problem[J]. IET generation, transmission & distribution, 2017, 11(4): 1012-1022.
[3] 李昌响, 赵嘉, 韩龙哲, 等. 多通道CNN-BiLSTM的短时温度预测[J]. 江西师范大学学报(自然科学版), 2023, 47(3): 325-330.
LI Changxiang, ZHAO Jia, HAN Longzhe, et al. The short-time temperature prediction for multi-channel CNN-BiLSTM[J]. Journal of Jiangxi Normal University (natural science edition), 2023, 47(3): 325-330.
[4] 李松, 吴润秀, 康平, 等. 基于自适应剪辑与概率参数的Tri-Training算法[J]. 江西师范大学学报(自然科学版), 2023, 47(5): 490-496.
LI Song, WU Runxiu, KANG Ping, et al. The ADP-Tri-Training: Tri-Training with adaptive editing and probability parameters[J]. Journal of Jiangxi Normal University (natural science edition), 2023, 47(5): 490-496.
[5] LIAGKOURAS K, METAXIOTIS K. Enhancing the performance of MOEAs: an experimental presentation of a new fitness guided mutation operator[J]. Journal of experimental & theoretical artificial intelligence, 2017, 29(1): 91-131.
[6] XIAO Renbin. Four development stages of collective intelligence[J]. Frontiers of information technology & electronic engineering, 2024, 25(7): 903-916.
[7] MIRJALILI S, SAREMI S, MIRJALILI S M, et al. Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization[J]. Expert systems with applications, 2016, 47: 106-119.
[8] AKBARI R, HEDAYATZADEH R, ZIARATI K, et al. A multi-objective artificial bee colony algorithm[J]. Swarm and evolutionary computation, 2012, 2: 39-52.
[9] YANG Xinse. Nature-inspired metaheuristic algorithms[M]. Frome: Luniver press, 2008.
[10] YANG Xinshe. Multiobjective firefly algorithm for continuous optimization[J]. Engineering with computers, 2013, 29(2): 175-184.
[11] 谢承旺, 肖驰, 丁立新, 等. HMOFA: 一种混合型多目标萤火虫算法[J]. 软件学报, 2018, 29(4): 1143-1162.
XIE Chengwang, XIAO Chi, DING Lixin, et al. HMOFA: a hybrid multi-objective firefly algorithm[J]. Journal of software, 2018, 29(4): 1143-1162.
[12] ZHAO Jia, CHEN Dandan, XIAO Renbin, et al. Multi-strategy ensemble firefly algorithm with equilibrium of convergence and diversity[J]. Applied soft computing, 2022, 123: 108938.
[13] 赵嘉, 胡秋敏, 肖人彬, 等. 求解大规模稀疏优化问题的高维多目标萤火虫算法[J]. 控制与决策., 2024, 39(12): 3989-3996.
ZHAO Jia, HU Qiumin, XIAO Renbin, et al. Many-objective firefly algorithm for solving large-scale sparse optimization problems[J]. Control and decision., 2024, 39(12): 3989-3996.
[14] LYU Li, ZHAO Jia, WANG Jiayuan, et al. Multi-objective firefly algorithm based on compensation factor and elite learning[J]. Future generation computer systems, 2019, 91: 37-47.
[15] 赵嘉, 陈丹丹, 肖人彬, 等. 一种基于最大最小策略和非均匀变异的萤火虫算法[J]. 智能系统学报, 2022, 17(1): 116-130.
ZHAO Jia, CHEN Dandan, XIAO Renbin, et al. A heterogeneous variation firefly algorithm with maximin strategy[J]. CAAI transactions on intelligent systems, 2022, 17(1): 116-130.
[16] 陈娟, 赵嘉, 肖人彬, 等. 基于动态反向学习和莱维飞行的双搜索模式萤火虫算法[J]. 信息与控制, 2023, 52(5): 607-615.
CHEN Juan, ZHAO Jiao, XIAO Renbin, et al. Double search mode firefly algorithm based on dynamic reverse learning and levy flight[J]. Information and control, 2023, 52(5): 607-615.
[17] ZHAO Jia, CHEN Dandan, XIAO Renbin, et al. Multi-objective firefly algorithm with adaptive region division[J]. Applied soft computing, 2023, 147: 110796.
[18] WANG Hui, WANG Wenjun, CUI Laizhong, et al. A hybrid multi-objective firefly algorithm for big data optimization[J]. Applied soft computing, 2018, 69: 806-815.
[19] ZHAO Jia, LV Siyu, XIAO Renbin, et al. Hierarchical learning multi-objective firefly algorithm for high-dimensional feature selection[J]. Applied soft computing, 2024, 165: 112042.
[20] MA Xiaoliang, LIU Fang, QI Yutao, et al. A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables[J]. IEEE transactions on evolutionary computation, 2016, 20(2): 275-298.
[21] ZHAO Xinchao, GAO Xiaoshan, HU Zechun. Evolutionary programming based on non-uniform mutation[J]. Applied mathematics and computation, 2007, 192(1): 1-11.
[22] ZITZLER E, LAUMANNS M. THIELE L. SPEA2: improving the strength pareto evolutionary algorithm for multi-objective optimization [C]//Proceedings of the Evolutionary Methods for Design, Optimization and Control. Barcelona: IEEE, 2002: 19-26.
[23] 赵嘉, 谢智峰, 吕莉, 等. 深度学习萤火虫算法[J]. 电子学报, 2018, 46(11): 2633-2641.
ZHAO Jia, XIE Zhifeng, LV Li, et al. Firefly algorithm with deep learning[J]. Acta electronica sinica, 2018, 46(11): 2633-2641.
[24] ZHAO Jia, CHEN Wenping, XIAO Renbin, et al. Firefly algorithm with division of roles for complex optimal scheduling[J]. Frontiers of information technology & electronic engineering, 2021, 22(10): 1311-1333.
[25] TIAN Ye, CHENG Ran, ZHANG Xingyi, et al. PlatEMO: a MATLAB platform for evolutionary multi-objective optimization educational forum[J]. IEEE computational intelligence magazine, 2017, 12(4): 73-87.
[26] RAQUEL C R, NAVAL P C. An effective use of crowding distance in multiobjective particle swarm optimization[C]//Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation. Washington: ACM, 2005: 257-264.
[27] ZHANG Qingfu, LI Hui. MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE transactions on evolutionary computation, 2007, 11(6): 712-731.
[28] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE transactions on evolutionary computation, 2002, 6(2): 182-197.
[29] CORNE D W, JERRAM N R, KNOWLES J D, et al. PESA-II: region-based selection in evolutionary multiobjective optimization[C]//Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation. [S. l. : s. n. ], 2001: 283-290.
[30] ZHANG Xingyi, ZHENG Xiutao, CHENG Ran, et al. A competitive mechanism based multi-objective particle swarm optimizer with fast convergence[J]. Information sciences, 2018, 427: 63-76.
[31] 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.
[32] ELARBI M, BECHIKH S, GUPTA A, et al. A new decomposition-based NSGA-II for many-objective optimization[J]. IEEE transactions on systems, man, and cybernetics: systems, 2018, 48(7): 1191-1210.
[33] TIAN Ye, HE Cheng, CHENG Ran, et al. A multistage evolutionary algorithm for better diversity preservation in multiobjective optimization[J]. IEEE transactions on systems, man, and cybernetics: systems, 2021, 51(9): 5880-5894.
[34] LI Lianghao, HE Cheng, CHENG Ran, et al. A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization[J]. Swarm and evolutionary computation, 2022, 75: 101181.
[35] BACK T, PREUSS M, DEUTZ A, et al. Parallel problem solving from nature-PPSN XVI[M]. Cham: Springer International Publishing, 2020: 271-284.
[36] TIAN Ye, LU Chang, ZHANG Xingyi, et al. Solving large-scale multiobjective optimization problems with sparse optimal solutions via unsupervised neural networks[J]. IEEE transactions on cybernetics, 2021, 51(6): 3115-3128.
[37] HUA Yicun, JIN Yaochu, HAO Kuangrong. A clustering-based adaptive evolutionary algorithm for multiobjective optimization with irregular Pareto fronts[J]. IEEE transactions on cybernetics, 2019, 49(7): 2758-2770.
[38] RAY T, LIEW K M. A swarm metaphor for multiobjective design optimization[J]. Engineering optimization, 2002, 34(2): 141-153.
[39] TANABE R, ISHIBUCHI H. An easy-to-use real-world multi-objective optimization problem suite[J]. Applied soft computing, 2020, 89: 106078.
[40] DEB K. An efficient constraint handling method for genetic algorithms[J]. Computer methods in applied mechanics and engineering, 2000, 186(2/3/4): 311-338.
[41] PANICHELLA A. An improved Pareto front modeling algorithm for large-scale many-objective optimization[C]//Proceedings of the Genetic and Evolutionary Computation Conference. Boston : ACM, 2022: 565-573.
[42] MING Fei, GONG Wenyin, LI Dongcheng, et al. A competitive and cooperative swarm optimizer for constrained multiobjective optimization problems[J]. IEEE transactions on evolutionary computation, 2023, 27(5): 1313-1326.
[43] JIAO Ruwang, ZENG Sanyou, LI Changhe, et al. Handling constrained many-objective optimization problems via problem transformation[J]. IEEE transactions on cybernetics, 2021, 51(10): 4834-4847.
[44] QIAO Kangjia, YU Kunjie, QU Boyang, et al. An evolutionary multitasking optimization framework for constrained multiobjective optimization problems[J]. IEEE transactions on evolutionary computation, 2022, 26(2): 263-277.
[45] ZOU Juan, SUN Ruiqing, LIU Yuan, et al. A multipopulation evolutionary algorithm using new cooperative mechanism for solving multiobjective problems with multiconstraint[J]. IEEE transactions on evolutionary computation, 2024, 28(1): 267-280.
备注/Memo
收稿日期:2024-6-3。
基金项目:国家自然科学基金项目（62466037）；南昌市重大科技攻关项目（2024zdxm002, 2024zdxm010）.
作者简介:邢文来，硕士研究生，主要研究方向为群智能算法。E-mail：xwl9464@yeah.net。;吴润秀，教授，主要研究方向为群智能算法及应用、大数据与人工智能。发表学术论文30余篇。E-mail：wrx@nit.edu.cn。;肖人彬，教授，博士生导师，主要研究方向为群体智能、涌现计算、复杂系统建模与仿真。主持国家自然科学基金项目11项，获教育部自然科学奖1项、湖北省自然科学奖及科技进步奖4项。发表学术论文300余篇，出版学术专著和教材10余部。E-mail： rbxiao@hust.edu.cn。
通讯作者:吴润秀. E-mail：wrx@nit.edu.cn
更新日期/Last Update:
1900-01-01