Many-objective Evolutionary Algorithm Based on Multi-subpopulation and Density Estimation for Load Distribution of Cold Rolling
ZHAO Zhi-wei1,2, LIU Yue2, XIONG Zhi-jian1, YANG Xiu-wei1
1. Department of Computer Science and Technology, Tangshan University, Tangshan, Hebei 063000, China
2. Institute of Electrical Engineering, North China University of Science and Technology, Tangshan, Hebei 063000, China
Abstract：A many-objective evolutionary algorithm based on multi-subpopulation and density estimation is proposed. The sub-populations are divided by reference vectors, and the degree of approaching the Pareto front is improved by the convergence mechanism. In addition, the individual density is evaluated by calculating the euclidean distance between individual and reference vector, in order to maintaining the diversity of the solution set. The results of numerical simulation indicate that the convergence and diversity of the solution set obtained by the proposed algorithm is obviously better than the comparison algorithms. Finally, the load distribution is optimized by the proposed algorithm for many-objective optimization. The optimized load distribution scheme can reduce energy consumption by 2.2%, and improves product quality.
赵志伟, 刘月, 熊志坚, 杨秀伟. 基于多子种群和密度估计的高维多目标进化算法的冷轧负荷分配[J]. 计量学报, 2022, 43(1): 65-71.
ZHAO Zhi-wei, LIU Yue, XIONG Zhi-jian, YANG Xiu-wei. Many-objective Evolutionary Algorithm Based on Multi-subpopulation and Density Estimation for Load Distribution of Cold Rolling. Acta Metrologica Sinica, 2022, 43(1): 65-71.
［1］ 刘彬, 刘泽仁, 赵志彪, 等. 基于速度交流的多种群多目标粒子群算法研究［J］. 计量学报, 2020, 41(08): 1002-1011.
Liu B, Liu Z R, Zhao Z B, et al. Research on multi-population multi-objective particle swarm optimization algorithm based on velocity communication［J］. Acta Metrologica Sinica, 2020, 41(08): 1002-1011.
［2］ Liu X F, Zhan Z H, Gao Y, et al. Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization［J］. IEEE Transactions on Evolutionary Computation, 2018, 23(4): 587-602.
［3］ Wang H, Jiao L, Yao X. Two_Arch2: An improved two-archive algorithm for many-objective optimization［J］. IEEE Transactions on Evolutionary Computation, 2014, 19(4): 524-541.
［4］ Elarbi M, Bechikh S, Gupta A, et al. A new decomposition-based NSGA-II for many-objective optimization［J］. IEEE transactions on systems, man, and cybernetics: systems, 2017, 48(7): 1191-1210.
［5］ 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.
［6］ Asafuddoula M, Ray T, Sarker R. A decomposition-based evolutionary algorithm for many objective optimization［J］. IEEE Transactions on Evolutionary Computation, 2014, 19(3): 445-460.
［7］ Cheng R, Jin Y C, Olhofer M, et al. A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization［J］. IEEE Transactions on Evolutionary Computation, 2016, 20(5): 773-791.
［8］ Huband S, Hingston P , Barone L, et al. A review of multiobjective test problems and a scalable test problem toolkit［J］. IEEE Transactions on Evolutionary Computation, 2006, 10(5): 477-506.
［9］ 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.
［10］ Deb K, Pratap A, Agarwal S, et al. A fast and elitist multi-objective genetic algorithm: NSGA-II［J］. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
［11］ Zitzler E, Künzli S. Indicator-based selection in multiobjective search［C］//International conference on parallel problem solving from nature. Springer, Berlin, Heidelberg, 2004: 832-842.
［12］ 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.
［13］ Derrac J, García S, Molina D, et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms［J］. Swarm and Evolutionary Computation, 2011, 1(1): 3-18.
［14］ 魏立新, 王恒, 孙浩, 等. 基于改进深度信念网络训练的冷轧轧制力预报［J］. 计量学报, 2021, 42(07): 906-912.
Wei L X , Wang H, Sun H , et al. Research on Cold Rolling Force Prediction Model Based on Improved Deep Belief Network［J］. Acta Metrologica Sinica, 2021, 42(07): 906-912.
［14］ 魏立新, 张宇, 孙浩, 等. 基于改进OS-ELM的冷连轧在线轧制力预报［J］. 计量学报, 2019, 40(01): 113-118.
Wei L X , Zhang Y , Sun H , et al. Online cold rolling prediction based on improved OS-ELM［J］. Acta Metrologica Sinica, 2019, 40(1): 111-116.
［15］ 赵新秋, 赵利娟, 杨景明, 等. 基于万有引力算法的铝热连轧规程优化设计［J］.计量学报, 2015, 36(05): 517-520.
Zhao X Q, Zhao L J, Yang J M , et al. Aluminum strip hot rolling schedule optimization design based on the gravitational search algorithm［J］. Acta Metrologica Sinica, 2015, 36(05): 517-520.
［16］ 赵志伟. 基于反向学习的差分进化算法的冷轧负荷分配［J］. 计量学报, 2017, 38(04): 453-458.
Zhao Z W . A Differential Evolution Algorithm Based on Opposite Learning in Load Distribution for Cold Rolling［J］. Acta Metrologica Sinica, 2017, 38(4): 453-458.
［17］ Hu Z Y, Wei Z H, Ma X M, et al. Multi-parameter deep-perception and many-objective autonomous-control of rolling schedule on high speed cold tandem mill［J］. ISA transactions, 2020, 102: 193-207.
［18］ Hu Z Y , Yang J M , Zhao Z W, et al. Multi-objective optimization of rolling schedules on aluminum hot tandem rolling［J］. International Journal of Advanced Manufacturing Technology, 2016, 85(1-4):85-97.
2022, Vol. 43 
