[1]裘梓榆,赵嘉,王奔,等.面向大规模稀疏优化的分层多目标萤火虫算法[J].智能系统学报,2026,21(2):461-475.[doi:10.11992/tis.202505018]
QIU Ziyu,ZHAO Jia,WANG Ben,et al.Hierarchical multi-objective firefly algorithm for large-scale sparse optimization[J].CAAI Transactions on Intelligent Systems,2026,21(2):461-475.[doi:10.11992/tis.202505018]
点击复制
QIU Ziyu,ZHAO Jia,WANG Ben,et al.Hierarchical multi-objective firefly algorithm for large-scale sparse optimization[J].CAAI Transactions on Intelligent Systems,2026,21(2):461-475.[doi:10.11992/tis.202505018]
面向大规模稀疏优化的分层多目标萤火虫算法
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
21
期数:
2026年第2期
页码:
461-475
栏目:
学术论文—智能系统
出版日期:
2026-03-05
- Title:
- Hierarchical multi-objective firefly algorithm for large-scale sparse optimization
- Keywords:
- firefly algorithm; multi-objective optimization; large-scale sparse optimization; sparsity; feature selection; Relief algorithm; hierarchical population; convergence
- 分类号:
- TP18
- 摘要:
- 针对多目标萤火虫算法在处理大规模稀疏多目标优化问题中存在的Pareto最优解稀疏性维持困难以及种群难以收敛的问题，提出了一种得分引导与特征选择的分层多目标萤火虫算法(hierarchical multi-objective firefly algorithm based on score guidance and feature selection, HLsMOFA)。该算法提出得分引导的初始化策略，计算决策变量初始得分，生成稀疏性状态的初始种群；构建特征选择的得分更新机制，引入Relief算法计算特征权重，在每次迭代时结合特征纯度共同更新决策变量得分，进一步维持Pareto最优解的稀疏特性；设计分层学习模式，将萤火虫种群按比例进行分层，减少移动过程中个体受全吸引模型影响而产生的振荡，提升算法在大规模决策空间中的收敛性能。实验结果表明，HLsMOFA较选择的对比算法具有更好的收敛性与多样性。
- Abstract:
- Aiming at the problem that the multi-objective firefly algorithm is difficult to maintain the sparsity of Pareto optimal solutions and the population is difficult to converge in dealing with large-scale sparse multi-objective optimization problems, a hierarchical multi-objective firefly algorithm with score guidance and feature selection (HLsMOFA) is proposed. The algorithm proposes a score-guided initialization strategy, calculates the initial score of the decision variable, and generates the initial population of the sparse state. The score updating mechanism of feature selection is constructed, and the Relief algorithm is introduced to calculate the feature weight. At each iteration, the decision variable score is jointly updated with the feature purity to further maintain the sparse characteristics of the Pareto optimal solutions. A hierarchical learning model is designed to stratify the firefly population proportionally, reduce the oscillation caused by the influence of the full attraction model during the movement process, and improve the convergence performance of the algorithm in a large-scale decision space. The experimental results show that HLsMOFA has better convergence and diversity than the selected comparison algorithm.
- 参考文献/References:
-
[1] HUA Yicun, LIU Qiqi, HAO Kuangrong, et al. A survey of evolutionary algorithms for multi-objective optimization problems with irregular pareto fronts[J]. IEEE/CAA journal of automatica sinica, 2021, 8(2): 303-318
[2] HAN Fei, CHEN Wentao, LING Qinghua, et al. Multi-objective particle swarm optimization with adaptive strategies for feature selection[J]. Swarm and evolutionary computation, 2021, 62: 100847
[3] KUMAR S, TEJANI G G, PHOLDEE N, et al. Multi-objective passing vehicle search algorithm for structure optimization[J]. Expert systems with applications, 2021, 169: 114511
[4] LI Wentao, ZHOU Haoxiang, XU Weihua, et al. Interval dominance-based feature selection for interval-valued ordered data[J]. IEEE transactions on neural networks and learning systems, 2022, 34(10): 6898-6912
[5] JIN Yaochu, SENDHOFF B. Pareto-based multiobjective machine learning: an overview and case studies[J]. IEEE transactions on systems, man, and cybernetics, part C (applications and reviews), 2008, 38(3): 397-415
[6] WANG Liping, PAN Xiaotian, SHEN Xiao, et al. Balancing convergence and diversity in resource allocation strategy for decomposition-based multi-objective evolutionary algorithm[J]. Applied soft computing, 2021, 100: 106968
[7] 曹嘉乐, 杨磊, 田井林, 等. 面向高维多目标优化的双阶段双种群进化算法[J]. 计算机工程与应用, 2024, 60(9): 159-171 CAO Jiale, YANG Lei, TIAN Jinglin, et al. Dual-stage dual-population evolutionary algorithm for many-objective optimization[J]. Computer engineering and applications, 2024, 60(9): 159-171
[8] 谢承旺, 潘嘉敏, 郭华, 等. 一种采用混合策略的大规模多目标进化算法[J]. 计算机学报, 2024, 47(1): 69-89 XIE Chengwang, PAN Jiamin, GUO Hua, et al. A large scale multi-objective evolutionary algorithm adopting hybrid strategies[J]. Chinese journal of computers, 2024, 47(1): 69-89
[9] 鲁昶. 基于进化算法的大规模稀疏多目标优化问题求解[D]. 合肥: 安徽大学, 2020. LU Chang. Solving large-scale sparse multi-objective optimization problems by evolutionary algorithms[D]. Hefei: Anhui University, 2020.
[10] MA Yilin, HAN Ruizhu, WANG Weizhong. Portfolio optimization with return prediction using deep learning and machine learning[J]. Expert systems with applications, 2021, 165: 113973
[11] HAZIMEH H, MAZUMDER R, SAAB A. Sparse regression at scale: branch-and-bound rooted in first-order optimization[J]. Mathematical programming, 2022, 196(1): 347-388
[12] SU Yansen, JIN Zhongxiang, TIAN Ye, et al. Comparing the performance of evolutionary algorithms for sparse multi-objective optimization via a comprehensive indicator [research frontier][J]. IEEE computational intelligence magazine, 2022, 17(3): 34-53
[13] 李东旭. 求解复杂稀疏多目标优化问题的进化算法研究[D]. 合肥: 安徽大学, 2022. LI Dongxu. Research on evolutionary algorithms for solving complex sparse multi-objective optimization problems[D]. Hefei: Anhui University, 2022.
[14] 金忠祥. 面向稀疏多目标优化的性能评价指标研究[D]. 合肥: 安徽大学, 2022. JIN Zhongxiang. Research on performance evaluation indicator for sparse multi-objective optimization[D]. Hefei: Anhui University, 2022.
[15] ANTONIO L M, COELLO C A C. Use of cooperative coevolution for solving large scale multiobjective optimization problems[C]// Proceedings of the 2013 IEEE Congress on Evolutionary Computation. Cancun: IEEE, 2013: 2758-2765.
[16] ZILLE H, ISHIBUCHI H, MOSTAGHIM S, et al. A framework for large-scale multiobjective optimization based on problem transformation[J]. IEEE transactions on evolutionary computation, 2017, 22(2): 260-275
[17] TIAN Ye, ZHENG Xiutao, ZHANG Xingyi, et al. Efficient large-scale multiobjective optimization based on a competitive swarm optimizer[J]. IEEE transactions on cybernetics, 2019, 50(8): 3696-3708
[18] HE Cheng, CHENG Ran, YAZDANI D. Adaptive offspring generation for evolutionary large-scale multiobjective optimization[J]. IEEE transactions on systems, man, and cybernetics: systems, 2020, 52(2): 786-798
[19] TIAN Ye, ZHANG Xingyi, WANG Chao, et al. An evolutionary algorithm for large-scale sparse multiobjective optimization problems[J]. IEEE transactions on evolutionary computation, 2019, 24(2): 380-393
[20] 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, 2020, 51(6): 3115-3128
[21] TANG Jun, LIU Gang, PAN Qingtaso. A review on representative swarm intelligence algorithms for solving optimization problems: applications and trends[J]. IEEE/CAA journal of automatica sinica, 2021, 8(10): 1627-1643
[22] YANG Xinshe. Multiobjective firefly algorithm for continuous optimization[J]. Engineering with computers, 2013, 29(2): 175-184
[23] 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
[24] 刘丹, 邢文来, 张莹莹, 等. 纵横交叉和螺旋移动的萤火虫算法[J]. 江西科学, 2025, 43(2): 321-329 LIU Dan, XING Wenlai, ZHANG Yingying, et al. Firefly algorithm with vertical horizontal crossover and spiral movement[J]. Jiangxi science, 2025, 43(2): 321-329
[25] THENG D, BHOYAR K K. Feature selection techniques for machine learning: a survey of more than two decades of research[J]. Knowledge and information systems, 2024, 66(3): 1575-1637
[26] KIRA K, RENDELL L A. A practical approach to feature selection[M]. San Francisco: Morgan Kaufmann, 1992.
[27] KUMAR N, MANNA A K, SHAIKH A A, et al. Application of hybrid binary tournament-based quantum-behaved particle swarm optimization on an imperfect production inventory problem[J]. Soft Computing, 2021, 25(16): 11245-11267
[28] ZITZLER E, LAUMANNS M, THIELE L. SPEA2: Improving the strength pareto evolutionary algorithm[J]. TIK report, 2001, 103.
[29] 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 Jia, 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
[30] 赵嘉, 陈文平, 肖人彬, 等. 面向多峰优化问题的自主学习萤火虫算法[J]. 控制与决策, 2022(8): 1971-1980 ZHAO Jia, CHEN Wenping, XIAO Renbin, et al. Firefly algorithm based on self-learning for multi-peak optimization problem[J]. Control and decision, 2022(8): 1971-1980
[31] WANG Xiangyu, ZHANG Kai, WANG Jian, et al. An enhanced competitive swarm optimizer with strongly convex sparse operator for large-scale multiobjective optimization[J]. IEEE transactions on evolutionary computation, 2021, 26(5): 859-871
[32] TIAN Ye, LU Chang, ZHANG Xingyi, et al. A pattern mining-based evolutionary algorithm for large-scale sparse multiobjective optimization problems[J]. IEEE transactions on cybernetics, 2020, 52(7): 6784-6797
[33] QI Sheng, WANG Rui, ZHANG Tao, et al. A two-layer encoding learning swarm optimizer based on frequent itemsets for sparse large-scale multi-objective optimization[J]. IEEE/CAA journal of automatica sinica, 2024, 11(06): 1342-1357
[34] LI Yingwei, FENG Xiang, YU Huiqun. A dynamic knowledge-guided coevolutionary algorithm for large-scale sparse multiobjective optimization problems[J]. IEEE transactions on systems, man, and cybernetics: systems, 2024, 54(11): 7054-7064
[35] PONSICH A, JAIMES A L, COELLO C A C. A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications[J]. IEEE transactions on evolutionary computation, 2013, 17(3): 321-344
[36] LU Hui, ZHANG Qingfu, DENG Jingda, et al. A preference-based multiobjective evolutionary approach for sparse optimization[J]. IEEE transactions on neural networks and learning systems, 2018, 29(5): 1716-1731
[37] TIAN Ye, ZHU Weijian, ZHANG Xingyi, et al. A practical tutorial on solving optimization problems via PlatEMO[J]. Neurocomputing, 2023, 518: 190-205
[38] 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
- 相似文献/References:
-
[1]王? 艳,曾建潮.多目标微粒群优化算法综述[J].智能系统学报,2010,5(5):377.[doi:10.3969/j.issn.1673-4785.2010.05.001]
WANG Yan,ZENG Jian-chao.A survey of a multiobjective particle swarm optimization algorithm[J].CAAI Transactions on Intelligent Systems,2010,5():377.[doi:10.3969/j.issn.1673-4785.2010.05.001]
[2]郭丽萍,李向涛,谷文祥,等.改进的萤火虫算法求解阻塞流水线调度问题[J].智能系统学报,2013,8(1):33.[doi:10.3969/j.issn.1673-4785.201205012]
GUO Liping,LI Xiangtao,GU Wenxiang,et al.An improved firefly algorithm for the blocking flow shop scheduling problem[J].CAAI Transactions on Intelligent Systems,2013,8():33.[doi:10.3969/j.issn.1673-4785.201205012]
[3]陶新民,徐鹏,刘福荣,等.组合分布估计和差分进化的多目标优化算法[J].智能系统学报,2013,8(1):39.[doi:10.3969/j.issn.1673-4785.201208035]
TAO Xinmin,XU Peng,LIU Furong,et al.Multi objective optimization algorithm composed of estimation of distribution and differential evolution[J].CAAI Transactions on Intelligent Systems,2013,8():39.[doi:10.3969/j.issn.1673-4785.201208035]
[4]莫愿斌,马彦追,郑巧燕,等.单纯形法的改进萤火虫算法及其在非线性方程组求解中的应用[J].智能系统学报,2014,9(6):747.[doi:10.3969/j.issn.1673-4785.201309075]
MO Yuanbin,MA Yanzhui,ZHENG Qiaoyan,et al.Improved firefly algorithm based on simplex method and its application in solving non-linear equation groups[J].CAAI Transactions on Intelligent Systems,2014,9():747.[doi:10.3969/j.issn.1673-4785.201309075]
[5]朱书伟,周治平,张道文.融合并行混沌萤火虫算法的K-调和均值聚类[J].智能系统学报,2015,10(6):872.[doi:10.11992/tis.201505043]
ZHU Shuwei,ZHOU Zhiping,ZHANG Daowen.K-harmonic means clustering merged with parallel chaotic firefly algorithm[J].CAAI Transactions on Intelligent Systems,2015,10():872.[doi:10.11992/tis.201505043]
[6]秦全德,程适,李丽,等.人工蜂群算法研究综述[J].智能系统学报,2014,9(2):127.[doi:10.3969/j.issn.1673-4785.201309064]
QIN Quande,CHENG Shi,LI Li,et al.Artificial bee colony algorithm: a survey[J].CAAI Transactions on Intelligent Systems,2014,9():127.[doi:10.3969/j.issn.1673-4785.201309064]
[7]张伟,乔俊飞.神经网络的污水处理过程多目标优化控制方法[J].智能系统学报,2016,11(5):594.[doi:10.11992/tis.201512022]
ZHANG Wei,QIAO Junfei.Multi-objective optimization control for wastewatertreatment processing based on neural network[J].CAAI Transactions on Intelligent Systems,2016,11():594.[doi:10.11992/tis.201512022]
[8]屠传运,陈韬伟,余益民,等.膜系统下的一种多目标优化算法[J].智能系统学报,2017,12(5):678.[doi:10.11992/tis.201706013]
TU Chuanyun,CHEN Taowei,YU Yimin,et al.Multi-objective optimization algorithm based on membrane system[J].CAAI Transactions on Intelligent Systems,2017,12():678.[doi:10.11992/tis.201706013]
[9]魏伟一,文雅宏.一种精英反向学习的萤火虫优化算法[J].智能系统学报,2017,12(5):710.[doi:10.11992/tis.201706014]
WEI Weiyi,WEN Yahong.Firefly optimization algorithm utilizing elite opposition-based learning[J].CAAI Transactions on Intelligent Systems,2017,12():710.[doi:10.11992/tis.201706014]
[10]孟勤超,杨翠丽,乔俊飞.基于改进SPEA2算法的给水管网多目标优化设计[J].智能系统学报,2018,13(1):118.[doi:10.11992/tis.201701012]
MENG Qinchao,YANG Cuili,QIAO Junfei.Multi-objective optimization design of water distribution systems based on improved SPEA2 algorithm[J].CAAI Transactions on Intelligent Systems,2018,13():118.[doi:10.11992/tis.201701012]
[11]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.[doi:10.11992/tis.202106018]
ZHAO Jia,CHEN Dandan,XIAO Renbin,et al.A heterogeneous variation firefly algorithm with maximin strategy[J].CAAI Transactions on Intelligent Systems,2022,17():116.[doi:10.11992/tis.202106018]
备注/Memo
收稿日期:2025-5-22。
基金项目:国家自然科学基金项目（62466037， 62463021）.
作者简介:裘梓榆，硕士研究生，主要研究方向为群智能算法。获得“华为杯”第二十届中国研究生数学建模竞赛三等奖、2024江西省研究生数学建模竞赛二等奖。E-mail：280174135@qq.com。;赵嘉，教授，博士，主要研究方向为智能计算与计算智能、模式识别与大数据挖掘。主持国家自然科学基金项目3项，发表学术论文150余篇，出版专著1部。E-mail：zhaojia925@163.com。
通讯作者:赵嘉. E-mail：zhaojia925@163.com
更新日期/Last Update:
1900-01-01