极限学习决策网络指导的多目标粒子群算法

doi:10.3778/j.issn.1673-9418.2304026

摘要/Abstract

摘要： 在求解多目标优化问题时，粒子群优化算法通常采用预设的榜样选择方法和搜索策略，无法根据具体的寻优状态进行调整。面对不同的优化问题，不合适的搜索策略难以有效指导种群的进化，导致种群的搜索性能降低。为了解决以上问题，提出一种极限学习决策网络指导的多目标粒子群优化算法（ELDN-PSO）。首先，将多目标优化问题分解成若干标量子问题，并构建一个极限学习决策网络。网络将粒子的位置作为输入，根据当前寻优状态为每个粒子选择合适的搜索动作。将粒子在子问题上的适应度值变化作为强化学习的样本用于训练网络，并通过极限学习机提升训练速度。在优化的过程中，网络会根据寻优状态自动调整，在不同的搜索阶段为粒子选择合适的搜索策略。其次，多目标优化问题中存在一系列难以比较的非支配解，将每个解的领导能力量化成可进行比较的数值，从而更明确地为粒子选择合适的学习榜样。此外，使用一个外部档案储存较好的粒子，用于维护解集质量并指导种群的进化。在ZDT和DTLZ测试函数上进行对比实验，结果表明ELDN-PSO能够有效应对不同形状的Pareto前沿，提升种群的寻优速度以及解集的收敛性和多样性。

关键词: 粒子群优化, 极限学习机, 多目标优化, 目标分解, 加速系数

Abstract: When solving multi-objective optimization problems, particle swarm optimization algorithms usually employ preset example selection methods and search strategies, which cannot be adjusted according to specific optimization states. In the face of different optimization problems, inappropriate search strategies cannot effectively guide the population, resulting in low search performance of the population. To solve the above problems, a multi-objective particle swarm optimization algorithm guided by extreme learning decision network (ELDN-PSO) is proposed. First of all, the multi-objective optimization problem is decomposed into several scalar subproblems, and an extreme learning decision network is constructed. The network takes the particle position as input, and selects appropriate search actions for each particle according to the optimization state. The fitness change of a particle on the subproblem is obtained as the training sample for the reinforcement learning, and the training speed is improved by extreme learning machine. In the process of optimization, the network is automatically adjusted according to the optimization states, and it selects the appropriate search strategy for the particles at different search stages. Secondly, the non-dominated solutions in the multi-objective optimization problem are difficult to compare. Thus, the leadership of each solution is quantified into a comparable value, so that the examples are more clearly selected for the particles. In addition, an external archive is used to store better particles to maintain the quality of the solutions and guide the population. Comparative experiments are carried out on the ZDT and DTLZ test functions. The results show that ELDN-PSO can effectively cope with different Pareto front shapes, improving the optimization speed as well as the convergence and diversity of the solutions.

Key words: particle swarm optimization, extreme learning machine, multi-objective optimization, objective decomposition, acceleration coefficient

张一帆, 宋威. 极限学习决策网络指导的多目标粒子群算法[J]. 计算机科学与探索, 2024, 18(6): 1513-1525.

ZHANG Yifan, SONG Wei. Multi-objective Particle Swarm Optimization Algorithm Guided by Extreme Learning Decision Network[J]. Journal of Frontiers of Computer Science and Technology, 2024, 18(6): 1513-1525.

参考文献

[1] 王丽萍, 任宇, 邱启仓, 等. 多目标进化算法性能评价指标研究综述[J]. 计算机学报, 2021, 44(8): 1590-1619.
WANG L P, REN Y, QIU Q C, et al. Survey on performance indicators for multi-objective evolutionary algorithms[J]. Chinese Journal of Computers, 2021, 44(8): 1590-1619.
[2] MOHAPATRA P, NAYAK A, KUMAR S K, et al. Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm[J]. International Journal of Production Research, 2015, 53(6): 1712-1735.
[3] LIU S C, ZHAN Z H, TAN K C, et al. A multiobjective framework for many-objective optimization[J]. IEEE Transactions on Cybernetics, 2022, 52(12): 13654-13668.
[4] 王金杰, 李炜. 混合互信息和粒子群算法的多目标特征选择方法[J]. 计算机科学与探索, 2020, 14(1): 83-95.
WANG J J, LI W. Multi-objective feature selection method based on hybrid MI and PSO algorithm[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(1): 83-95.
[5] 宋威, 华子彧. 融入社会影响力的粒子群优化算法[J]. 计算机科学与探索, 2020, 14(11): 1908-1919.
SONG W, HUA Z Y. Particle swarm optimization with social influence[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(11): 1908-1919.
[6] 王晓艳, 曹德欣. 基于进化能力的多策略粒子群优化算法[J]. 计算机工程与应用, 2023, 59(5): 78-86.
WANG X Y, CAO D X. Multi-strategy particle swarm optimization algorithm based on evolution ability[J]. Computer Engineering and Applications, 2023, 59(5): 78-86.
[7] 李湘喆, 顾磊, 马丽, 等. 余弦自适应混沌被囊体种群优化算法[J]. 计算机工程与应用, 2023, 59(2): 65-75.
LI X Z, GU L, MA L, et al. Chaotic tunicate swarm algorithm based on cosine adaptive[J]. Computer Engineering and Applications, 2023, 59(2): 65-75.
[8] 徐泽, 杨伟, 张文强, 等. 基于连锁环网与改进离散粒子群算法的多目标配电网重构[J]. 电力系统保护与控制, 2021, 49(6): 114-123.
XU Z, YANG W, ZHANG W Q, et al. Multi-objective distribution network reconfiguration based on chain loops and improved binary particle swarm optimization[J]. Power System Protection and Control, 2021, 49(6): 114-123.
[9] MARTINEZ S Z, COELLO C A C. A multi-objective particle swarm optimizer based on decomposition[C]//Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Jul 12-16, 2011. New York: ACM, 2011: 69-76.
[10] LIN Q, LI J, DU Z, et al. A novel multi-objective particle swarm optimization with multiple search strategies[J]. European Journal of Operational Research, 2015, 247(3): 732-744.
[11] DAI C, WANG Y, YE M. A new multi-objective particle swarm optimization algorithm based on decomposition[J]. Information Sciences, 2015, 325: 541-557.
[12] HU Y, ZHANG Y, GONG D. Multiobjective particle swarm optimization for feature selection with fuzzy cost[J]. IEEE Transactions on Cybernetics, 2021, 51(2): 874-888.
[13] LI L, CHANG L, GU T, et al. On the norm of dominant difference for many-objective particle swarm optimization[J]. IEEE Transactions on Cybernetics, 2021, 51(4): 2055-2067.
[14] WU B, HU W, HU J, et al. Adaptive multiobjective particle swarm optimization based on evolutionary state estimation[J]. IEEE Transactions on Cybernetics, 2021, 51(7): 3738-3751.
[15] XIANG Y, ZHOU Y, CHEN Z, et al. A many-objective particle swarm optimizer with leaders selected from historical solutions by using scalar projections[J]. IEEE Transactions on Cybernetics, 2020, 50(5): 2209-2222.
[16] WU B, HU W, HE Z, et al. A many-objective particle swarm optimization based on virtual Pareto front[C]//Proceedings of the 2018 IEEE Congress on Evolutionary Computation, Rio de Janeiro, Jul 8-13, 2018. Piscataway: IEEE, 2018: 1-8.
[17] HUANG G B, ZHU Q Y, SIEW C K. Extreme learning machine: theory and applications[J]. Neurocomputing, 2006, 70(1): 489-501.
[18] ZITZLER E, DEB K, THIELE L. Comparison of multi-objective evolutionary algorithms: empirical results[J]. Evolutionary Computation, 2000, 8(2): 173-195.
[19] KENNEDY J, EBERHART R. Particle swarm optimization[C]//Proceedings of the 1995 IEEE International Conference on Neural Networks, Perth, Nov 27-Dec 1, 1995. Piscataway: IEEE, 1995: 1942-1948.
[20] SHI Y, EBERHART R. A modified particle swarm optimizer[C]//Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, May 4-9, 1998. Piscataway: IEEE, 1998: 69-73.
[21] HUANG G B, ZHU Q Y, SIEW C K. Extreme learning machine: a new learning scheme of feedforward neural networks[C]//Proceedings of the 2004 IEEE International Joint Conference on Neural Networks, Budapest, Jul 25-29, 2004. Piscataway: IEEE, 2004: 985-990.
[22] HUANG G B, CHEN L, SIEW C K. Universal approximation using incremental constructive feedforward networks with random hidden nodes[J]. IEEE Transactions on Neural Networks, 2006, 17(4): 879-892.
[23] HUANG G B, ZHOU H, DING X, et al. Extreme learning machine for regression and multiclass classification[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2012, 42(2): 513-529.
[24] WIDROW B, GREENBLATT A, KIM Y, et al. The No-Prop algorithm: a new learning algorithm for multilayer neural networks[J]. Neural Networks, 2013, 37: 182-188.
[25] ZHANG Q, LI H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731.
[26] SHI Y, EBERHART R C. Parameter selection in particle swarm optimization[C]//Proceedings of the 7th International Conference on Evolutionary Programming, San Diego, Mar 25-27, 1998. Berlin, Heidelberg: Springer, 1998: 591-600.
[27] MENG A, LI Z, YIN H, et al. Accelerating particle swarm optimization using crisscross search[J]. Information Sciences, 2016, 329: 52-72.
[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] DE FARIAS L, ARAUJO A. A decomposition-based many-objective evolutionary algorithm updating weights when required[J]. Swarm and Evolutionary Computation, 2022, 68: 100980.
[30] TIAN Y, SI L, ZHANG X, et al. Local model-based Pareto front estimation for multiobjective optimization[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(1): 623-634.
[31] DEB K, THIELE L, LAUMANNS M, et al. Scalable multi-objective optimization test problems[C]//Proceedings of the 2002 IEEE Congress on Evolutionary Computation, Honolulu, May 12-17, 2002. Piscataway: IEEE, 2002: 825-830.
[32] ZITZLER E, THIELE L, LAUMANNS M, et al. Performance assessment of multiobjective optimizers: an analysis and review[J]. IEEE Transactions on Evolutionary Computation, 2003, 7(2): 117-132.
[33] 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.
[34] LIN Q, LIU S, ZHU Q, et al. Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2018, 22(1): 32-46.
[35] SUN L, LI K. Adaptive operator selection based on dynamic Thompson sampling for MOEA/D[C]//Proceedings of the 16th International Conference on Parallel Problem Solving from Nature, Leiden, Sep 5-9, 2020. Cham: Springer, 2020: 271-284.
[36] LIU Y, ISHIBUCHI 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.
[37] TIAN Y, ZHU W, ZHANG X, et al. A practical tutorial on solving optimization problems via PlatEMO[J]. Neuro-computing, 2023, 518: 190-205.