自组织映射更新的双种群约束多目标狼群算法

doi:10.3778/j.issn.1002-8331.2504-0270

摘要/Abstract

摘要： 为克服多目标狼群算法无法处理约束条件、种群聚集导致其过早陷入局部最优以及更新机制落后致使种群优质信息丢失的缺陷，提出自组织映射更新的双种群约束多目标狼群算法(CMOWPA-S)。该算法构建一种双种群结构，主种群采用约束支配原则确保种群始终在可行域内，辅助种群则不考虑约束条件以增加算法发现优质解的可能性，保证算法在约束条件下的有效性；提出二元优化狩猎策略，奔袭过程加入精英狼辅助头狼召唤狼群，围攻过程引入莱维飞行策略，提升算法逃脱局部最优的能力；设计基于自组织映射的种群更新机制，通过自组织映射提取种群邻域信息以产生优质后代，确保种群优质信息的传递，最后采用环境选择策略淘汰冗余种群。为验证算法性能，在14个模拟约束多目标问题上与4种经典、5种新型约束多目标优化算法比较，在10个真实约束多目标问题上与5种新型约束多目标优化算法比较。实验结果表明，CMOWPA-S能有效解决约束目标优化问题，避免陷入局部最优且获得种群多样性较好的解。

关键词: 狼群算法, 约束优化, 多目标优化, 双种群, 自组织映射

Abstract: To address the shortcomings of conventional multi-objective wolf pack algorithms, including their inability to handle constraints, premature convergence caused by population clustering, and outdated update mechanisms leading to loss of high-quality solutions, this paper proposes a self-organizing map updated dual-population constrained multi-objective wolf pack algorithm (CMOWPA-S). The algorithm constructs a dual-population structure where the main population employs constrained dominance principles to ensure operation within feasible regions, while the auxiliary population disregards constraints to enhance solution quality discovery. A dual-optimization hunting strategy is introduced: elite wolves assist the leader in summoning the pack during the raid phase, and Lévy flight strategy is incorporated in the siege phase to improve local optimum escape capability. A self-organizing map-based population update mechanism is designed to extract neighborhood information for generating superior offspring, ensuring the inheritance of high-quality solutions. Environmental selection strategies are implemented to eliminate redundant populations. To verify the performance of the algorithm, it is compared with 4 classic and 5 emerging constrained multi-objective optimization algorithms on 14 simulated constrained multi-objective problems, and with 5 new constrained multi-objective optimization algorithms on 10 real constrained multi-objective problems. The experimental results show that CMOWPA-S can effectively solve constrained objective optimization problems, avoid falling into local optima, and obtain solutions with good population diversity.

Key words: wolf pack algorithm, constrained optimization, multi-objective optimization, dual-population, self-organizing map

康水平, 唐光清, 樊棠怀, 王晖, 吕莉. 自组织映射更新的双种群约束多目标狼群算法[J]. 计算机工程与应用, 2025, 61(23): 90-109.

KANG Shuiping, TANG Guangqing, FAN Tanghuai, WANG Hui, LYU Li. Dual-Population Constrained Multi-Objective Wolf Pack Algorithm with Self-Organizing Mapping Update[J]. Computer Engineering and Applications, 2025, 61(23): 90-109.

参考文献

[1] 崔瑀欣, 陆中, 周伽. 基于多目标人工蜂鸟算法的研制保证等级分配[J]. 航空学报, 2025, 46(4): 300-311.
CUI Y X, LU Z, ZHOU J. Development assurance level assignment based on multi-objective artificial hummingbird algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(4): 300-311.
[2] HE Q, WANG L. An effective co-evolutionary particle swarm optimization for constrained engineering design problems[J]. Engineering Applications of Artificial Intelligence, 2007, 20(1): 89-99.
[3] 侯艳, 任丙飞, 滕少华, 等. 带罐约束的多目标短期炼油调度优化研究[J]. 江西师范大学学报 (自然科学版), 2023, 47(3): 307-316.
HOU Y, REN B F, TENG S H, et al. The multi-objective short-term scheduling optimization with charging-tank-switch-overlap constraint in refinery[J]. Journal of Jiangxi Normal University (Natural Science Edition), 2023, 47(3): 307-316.
[4] ZAFAR M N, MOHANTA J C. Methodology for path planning and optimization of mobile robots: a review[J]. Procedia Computer Science, 2018, 133: 141-152.
[5] 米永强, 高岳林. 求解约束优化问题的改进粒子群优化算法[J]. 江西师范大学学报(自然科学版), 2015, 39(1): 59-63.
MI Y Q, GAO Y L. The improved particle swarm optimization algorithm for solving constrained optimization problems[J]. Journal of Jiangxi Normal University (Natural Science Edition), 2015, 39(1): 59-63.
[6] ANDERSEN E D, ANDERSEN K D. Presolving in linear programming[J]. Mathematical Programming, 1995, 71(2): 221-245.
[7] EDDY S R. What is dynamic programming?[J]. Nature Biotechnology, 2004, 22(7): 909-910.
[8] AMARI S I. Backpropagation and stochastic gradient descent method[J]. Neurocomputing, 1993, 5(4/5): 185-196.
[9] SADEGHIAN Z, AKBARI E, NEMATZADEH H, et al. A review of feature selection methods based on meta-heuristic algorithms[J]. Journal of Experimental & Theoretical Artificial Intelligence, 2025, 37(1): 1-51.
[10] BLUM C. Ant colony optimization: introduction and recent trends[J]. Physics of Life Reviews, 2005, 2(4): 353-373.
[11] WANG D S, TAN D P, LIU L. Particle swarm optimization algorithm: an overview[J]. Soft Computing, 2018, 22(2): 387-408.
[12] MIRJALILI S, LEWIS A. The whale optimization algorithm[J]. Advances in Engineering Software, 2016, 95: 51-67.
[13] YENIAY ?. Penalty function methods for constrained optimization with genetic algorithms[J]. Mathematical and Computational Applications, 2005, 10(1): 45-56.
[14] JIAO R W, ZENG S Y, LI C H. A feasible-ratio control technique for constrained optimization[J]. Information Sciences, 2019, 502: 201-217.
[15] DEB K, AGRAWAL S, PRATAP A, et al. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II[C]//Proceedings of the International Conference on Parallel Problem Solving from Nature. Berlin, Heidelberg: Springer, 2000: 849-858.
[16] MAVROTAS G. Effective implementation of the ε-constraint method in Multi-Objective mathematical programming problems[J]. Applied Mathematics and Computation, 2009, 213(2): 455-465.
[17] ZHANG Q F, LI H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731.
[18] FAN Z, LI H, WEI C M, et al. An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems[C]//Proceedings of the 2016 IEEE Symposium Series on Computational Intelligence. Piscataway: IEEE, 2017: 1-8.
[19] YU Q Q, YANG C, DAI G M, et al. A novel penalty function-based interval constrained multi-objective optimization algorithm for uncertain problems[J]. Swarm and Evolutionary Computation, 2024, 88: 101584.
[20] 吴虎胜, 张凤鸣, 吴庐山. 一种新的群体智能算法: 狼群算法[J]. 系统工程与电子技术, 2013, 35(11): 2430-2438.
WU H S, ZHANG F M, WU L S. New swarm intelligence algorithm: wolf pack algorithm[J]. Systems Engineering and Electronics, 2013, 35(11): 2430-2438.
[21] CHEN Y B, MEI Y S, YU J Q, et al. Three-dimensional unmanned aerial vehicle path planning using modified wolf pack search algorithm[J]. Neurocomputing, 2017, 266: 445-457.
[22] 杨聿壬, 郭江宇, 靳文兵, 等. 基于改进离散狼群算法的火力分配[J]. 火力与指挥控制, 2024, 49(5): 67-73.
YANG Y R, GUO J Y, JIN W B, et al. Weapon target assignment based on improved discrete wolf pack algorithm[J]. Fire Control & Command Control, 2024, 49(5): 67-73.
[23] 潘星宇, 邹雨澄, 肖人彬, 等. 面向集装箱装船排箱优化调度问题的交互感知狼群算法[J]. 南昌工程学院学报, 2021, 40(4): 77-84.
PAN X Y, ZOU Y C, XIAO R B, et al. An interactive perception wolf pack algorithm for shipping order optimization of containers[J]. Journal of Nanchang Institute of Technology, 2021, 40(4): 77-84.
[24] 赵嘉, 吕丰, 肖人彬, 等. 自适应分组和拥挤距离更新的多目标狼群算法[J]. 控制与决策, 2024, 39(11): 3772-3780.
ZHAO J, LV F, XIAO R B, et al. Multi-objective wolf pack algorithm based on adaptive grouping strategy and crowding distance[J]. Control and Decision, 2024, 39(11): 3772-3780.
[25] 马永杰, 云文霞. 遗传算法研究进展[J]. 计算机应用研究, 2012, 29(4): 1201-1206.
MA Y J, YUN W X. Research progress of genetic algorithm[J]. Application Research of Computers, 2012, 29(4): 1201-1206.
[26] HE C, LI M, ZHANG C X, et al. A self-organizing map approach for constrained multi-objective optimization problems[J]. Complex & Intelligent Systems, 2022, 8(6): 5355-5375.
[27] KOHONEN T. The self-organizing map[J]. Proceedings of the IEEE, 1990, 78(9): 1464-1480.
[28] MA Z W, WANG Y. Evolutionary constrained multiobjective optimization: test suite construction and performance comparisons[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(6): 972-986.
[29] KUMAR A, WU G H, ALI M Z, et al. A benchmark-suite of real-world constrained multi-objective optimization problems and some baseline results[J]. Swarm and Evolutionary Computation, 2021, 67: 100961.
[30] COELLO C A C, CORTéS N C. Solving multiobjective optimization problems using an artificial immune system[J]. Genetic Programming and Evolvable Machines, 2005, 6(2): 163-190.
[31] 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.
[32] 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.
[33] 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.
[34] LI K, DEB K, ZHANG Q F, et al. An evolutionary many-objective optimization algorithm based on dominance and decomposition[J]. IEEE Transactions on Evolutionary Computation, 2015, 19(5): 694-716.
[35] FAN Z, LI W J, CAI X Y, et al. Push and pull search for solving constrained multi-objective optimization problems[J]. Swarm and Evolutionary Computation, 2019, 44: 665-679.
[36] MING F, GONG W Y, LI D C, et al. A competitive and cooperative swarm optimizer for constrained multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(5): 1313-1326.
[37] QIAO K J, YU K J, QU B Y, et al. Dynamic auxiliary task-based evolutionary multitasking for constrained multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(3): 642-656.
[38] SUN R Q, ZOU J, LIU Y, et al. A multistage algorithm for solving multiobjective optimization problems with multiconstraints[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(5): 1207-1219.
[39] MING F, GONG W Y, WANG L, et al. Constrained multiobjective optimization via multitasking and knowledge transfer[J]. IEEE Transactions on Evolutionary Computation, 2024, 28(1): 77-89.
[40] ZOU J, SUN R Q, LIU Y, 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.
[41] TIAN Y, CHENG R, ZHANG X Y, et al. PlatEMO: a MATLAB platform for evolutionary multi-objective optimization[J]. IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87.
[42] ZHAO J, CHEN F J, XIAO R B, et al. Multi-modal multi-objective wolf pack algorithm with circumferential scouting and intra-niche interactions[J]. Swarm and Evolutionary Computation, 2025, 93: 101842.
[43] 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 J, HU Q M, XIAO R B, et al. Many-objective firefly algorithm for solving large-scale sparse optimization problems[J]. Control and Decision, 2024, 39(12): 3989-3996.