计算机科学 ›› 2024, Vol. 51 ›› Issue (8): 333-344.doi: 10.11896/jsjkx.230500046
程雪峰1, 董明刚1,2
CHENG Xuefeng1, DONG Minggang1,2
摘要: 动态多目标优化问题广泛存在于现实生活中,在环境发生变化后,进化算法需具备快速收敛、快速追踪帕累托最优前沿和维持多样性的能力。对于环境变化程度严重且变化频繁的情况,传统的预测方法无法有效获得帕累托最优前沿解。针对该问题,提出了一种基于循环神经网络(Recurrent Neural Networks,RNN)信息累积的动态多目标优化算法(IA-RNN)。首先,提出了一种基于RNN信息累积的非线性预测方法,利用RNN递归进行信息累积,提高了历史信息利用率,增强了预测的能力。其次,设计了一种基于个体的线性预测方法,利用参数矩阵对个体线性变化进行预测。线性预测与RNN非线性预测协同进化,可快速追踪帕累托最优前沿。最后,设计了一种基于最小二乘法的参数修正策略,通过当前环境的近似帕累托最优前沿解反向指导参数修正,减小了误差堆积的影响。将IA-RNN与5种代表性动态多目标优化算法在14个DF基准测试问题上进行比较。实验证明,IA-RNN算法的收敛性和多样性更优。
中图分类号:
[1]WANG D J,LIU F,JIN Y.A multi-objective evolutionary algorithm guided by directed search for dynamic scheduling[J].Computers & Operations Research,2017,79:279-290. [2]GUO Y N,CHENG J,LUO S,et al.Robust dynamic multi-objective vehicle routing optimization method[J].IEEE/ACM Transactions on Computational Biology and Bioinformatics,2017,15(6):1891-1903. [3]MASHWANI W K,SALHI A.Multiobjective evolutionary algorithm based on multimethod with dynamic resources allocation[J].Applied Soft Computing,2016,39:292-309. [4]QIAO J,ZHANG W.Dynamic multi-objective optimization control for wastewater treatment process[J].Neural Computing and Applications,2018,29:1261-1271. [5]HUANG L,SUH I H,ABRAHAM A.Dynamic multi-objective optimization basedon membrane computing for control of time-varying unstable plants[J].Information Sciences,2011,181(11):2370-2391. [6]DED K,RAO N U B,KARTHIK S.Dynamic multi-objective optimization and decision-making using modified NSGA-II:A case study on hydro-thermal power scheduling[C]//4th International Conference Evolutionary Multi-Criterion Optimization(EMO 2007).Matsushima,Japan:Springer Berlin Heidelberg,2007:803-817. [7]JIANG S,YANG S.A steady-state and generational evolutio-nary algorithm for dynamic multiobjective optimization[J].IEEE Transactions on Evolutionary Computation,2016,21(1):65-82. [8]ZHANG K,SHEN C,LIU X,et al.Multiobjective evolutionstrategy for dynamic multiobjective optimization[J].IEEE Transactions on Evolutionary Computation,2020,24(5):974-988. [9]PENG Z,ZHENG J,ZOU J,et al.Novel prediction and memory strategies for dynamic multiobjective optimization[J].Soft Computing,2015,19:2633-2653. [10]LIANG Z,ZHENG S,ZHU Z,et al.Hybrid of memory and prediction strategies for dynamic multiobjective optimization[J].Information Sciences,2019,485:200-218. [11]ZHOU A,JIN Y,ZHANG Q.A population prediction strategy for evolutionary dynamic multiobjective optimization[J].IEEE Transactions on Cybernetics,2013,44(1):40-53. [12]LI Q,ZOU J,YANG S,et al.A predictive strategy based on special points for evolutionary dynamic multi-objective optimization[J].Soft Computing,2019,23:3723-3739. [13]LIANG Z P,LI H C,WANG Z Q,et al.Dynamic multi-objective evolutionary algorithm with adaptive change response [J].Acta Automatica Sinica,2023,49(8):1688-1706. [14]SUN H,CAO A,HU Z,et al.A novelquantile-guided dual prediction strategies for dynamic multi-objective optimization[J].Information Sciences,2021,579:751-775. [15]ZHANG H,DING J,JIANG M,et al.Inverse gaussian process modeling for evolutionary dynamic multiobjective optimization[J].IEEE Transactions on Cybernetics,2021,52(10):11240-11253. [16]LIU R,CHEN Y,MA W,et al.A novel cooperative coevolu-tionary dynamic multi-objective optimization algorithm using a new predictive model[J].Soft Computing,2014,18:1913-1929. [17]MA X,YANG J,SUN H,et al.Multiregional co-evolutionary algorithm for dynamic multiobjective optimization[J].Information Sciences,2021,545:1-24. [18]JIANG M,HUNAG Z,QIU L,et al.Transfer learning-based dynamic multiobjective optimization algorithms[J].IEEE Transactions on Evolutionary Computation,2017,22(4):501-514. [19]ELMAN J L.Finding structure in time[J].Cognitive Science,1990,14(2):179-211. [20]RAMBABU R,VADAKKEPAT P,TAN K C,et al.A mixture-of-experts prediction framework for evolutionary dynamic multiobjective optimization[J].IEEE Transactions on Cybernetics,2019,50(12):5099-5112. [21]DEB K,PRATAP A,AGARWAL S,et al.A fast and elitistmultiobjective genetic algorithm:NSGA-II[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197. [22]GONG X,ZHANG T,CHEN C L P,et al.Research review for broad learning system:Algorithms,theory,and applications[J].IEEE Transactions on Cybernetics,2022,52:8922-8950. [23]WANG H,SONG G.Innovative NARX recurrent neural net-work model for ultra-thin shape memory alloy wire[J].Neurocomputing,2014,134:289-295. [24]MA X M,YANG J M,SUN H,et al.Dynamic multi-objective optimization algorithm based on multi-region center point prediction [J].Control and Decision,2022,37(10):2477-2486. [25]LI Z,TANAKA G.Multi-reservoir echo state networks with sequence resampling for nonlinear time-series prediction[J].Neurocomputing,2022,467:115-129. [26]JIANG S,YANG S,YAO X,et al.Benchmark Functions for the CEC′2018Competition on Dynamic Multiobjective Optimization[R].Newcastle University,2018. [27]ZHAO Q,YAN B,SHI Y,et al.Evolutionary dynamic multiobjective optimization via learning from historical search process[J].IEEE Transactions on Cybernetics,2021,52(7):6119-6130. [28]ZHOU A,JIN Y,ZHANG Q.A population prediction strategy for evolutionary dynamic multiobjective optimization[J].IEEE Transactions on Cybernetics,2013,44(1):40-53. [29]SIERRA M R,COELLO C A.Improving PSO-based multi-objective optimization using crowding,mutation and∈-dominance [C]//Evolutionary Multi-Criterion Optimization:Third International Conference(EMO 2005).Berlin Heidelberg:Springer,2005:505-519. [30]WILCOXON F.Individual comparisons by ranking methods[M].New York:Springer,1992:196-202. [31]TIAN Y,CHENG R,ZHANG X,et al.PlatEMO:A MATLAB platform for evolutionary multi-objective optimization[educational forum][J].IEEE Computational Intelligence Magazine,2017,12(4):73-87. [32]FRIEDMAN M.The use of ranks to avoid the assumption ofnormality implicit in the analysis of variance[J].Journal of the American Statistical Association,1937,32(200):675-701. |
|