[1]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]
Copy

Hierarchical multi-objective firefly algorithm for large-scale sparse optimization

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 21 Number of periods: 2026 2 Page number: 461-475 Column: 学术论文—智能系统 Public date: 2026-03-05
Title:
Hierarchical multi-objective firefly algorithm for large-scale sparse optimization
Author(s):
QIU Ziyu1; 2;  ZHAO Jia1; 2;  WANG Ben3;  ZHANG Yiying4;  WANG Hui1; 2;  LU Fangzhou5;  FAN Tanghuai1; 2
1. School of Information Engineering, Jiangxi University of Water Resources and Electric Power, Nanchang 330099, China;
2. Jiangxi Province Engineering Research Center for Intelligent Processing and Early Warning Technology of Water Conservancy Big Data, Nanchang 330099, China;
3. NARI Group Corporation, Nanjing 211000, China;
4. College of Artificial Intelligence, Tianjin University of Science and Technology, Tianjin 300457, China;
5. State Grid Electric Power Research Institute, Nanjing 210003, China
Keywords:
firefly algorithm; multi-objective optimization; large-scale sparse optimization; sparsity; feature selection; Relief algorithm; hierarchical population; convergence
CLC:
TP18
DOI:
10.11992/tis.202505018
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.
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
Similar References:

Memo

-

Last Update: 1900-01-01

Copyright © CAAI Transactions on Intelligent Systems