考虑可再生能源的多目标柔性流水车间调度问题
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摘要
为了节能减排、保护环境,针对可再生能源的柔性流水车间调度问题(FFSP-RE),提出集成低碳调度策略的快速非支配排序遗传算法。根据可再生能源的发电特性建立了可再生能源供电模型,在此基础上构建了FFSP-RE的数学优化模型;给出快速非支配排序遗传算法,其中提出基于操作的编码方法,设计了考虑可再生能源特性的低碳调度策略,线性次序交叉和基于位置交叉采用随机选择方法,变异算子采用反转逆序法,根据拥挤度和非支配等级选择进入下一代种群的个体;通过多个数值实验证明了所提算法能够有效求解FFSP-RE,可再生能源能够在保证完工时间的前提下有效降低碳排放量。
Aiming at the Flexible Flow Shop Scheduling Problem with Renewable Energy(FFSP-RE),a Non-dominated Sorting Genetic Algorithm-Ⅱ(NSGA-Ⅱ)integrated low carbon scheduling strategy was proposed.According to the power generation characteristics of renewable energy,the power supplied model by renewable energy was established,and the optimization model of FFSP-RE was formulated.The general process of NSGA-Ⅱ was proposed,and the operation-based encoding method was employed.The position-based crossover and the liner order crossover operators were chosen randomly to fully explore the solution space,and the reverse operator was employed to mutate the population.The offspring and the parents were combined and those dominated more were selected to enter the next generation.A comprehensive experiment was conducted,and the results showed that the proposed algorithm could solve FFSP-RE effectively and efficiently.The low-carbon scheduling algorithm could reduce carbon emission effectively under the premise of makespan optimization.
Aiming at the Flexible Flow Shop Scheduling Problem with Renewable Energy(FFSP-RE),a Non-dominated Sorting Genetic Algorithm-Ⅱ(NSGA-Ⅱ)integrated low carbon scheduling strategy was proposed.According to the power generation characteristics of renewable energy,the power supplied model by renewable energy was established,and the optimization model of FFSP-RE was formulated.The general process of NSGA-Ⅱ was proposed,and the operation-based encoding method was employed.The position-based crossover and the liner order crossover operators were chosen randomly to fully explore the solution space,and the reverse operator was employed to mutate the population.The offspring and the parents were combined and those dominated more were selected to enter the next generation.A comprehensive experiment was conducted,and the results showed that the proposed algorithm could solve FFSP-RE effectively and efficiently.The low-carbon scheduling algorithm could reduce carbon emission effectively under the premise of makespan optimization.
引文
[1] SHI Dan.The Effectiveness of energy-saving and emission reductionduring the 12th Five-Year-Plan and the mission in next period[J].China Energy,2015,37(9):4-10,42(in Chinese).[史丹.“十二五”节能减排的成效与“十三五”的任务[J].中国能源,2015,37(9):4-10,42.]
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[4] SU Zhixiong,YI Junmin.Genetic algorithm with forwardbackward scheduling approach for hybrid flow shop problems[J].Computer Integrated Manufacturing Systems,2016,22(4):1059-1069(in Chinese).[苏志雄,伊俊敏.基于正逆序策略的混合流水车间遗传调度算法[J].计算机集成制造系统,2016,22(4):1059-1069.]
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[7] MANSOURI S A,AKTAS E,BESIKCI U.Green scheduling of a two-machine flowshop:Trade-off between makespan and energy consumption[J].European Journal of Operational Research,2015,248(3):772-788.
[8] NAGASAWA K,IKEDA Y,IROHARA T.Robust flow shop scheduling with random processing times for reduction of peak power consumption[J].Simulation Modelling Practice&Theory,2015,59(1):102-113.
[9] LUO Hao,DU Bing,HUANG G Q,et al.Hybrid flow shop scheduling considering machine electricity consumption cost[J].International Journal of Production Economics,2013,146(2):423-439.
[10] LIU Xiang,ZOU Fengxing,ZHANG Xiangping,et al.Hybrid flow-shop scheduling problem based on saving energy[C]//Proceedings of the 27th Chinese Control Conference.Beijing:Beihang University Press,2008:48-53(in Chinese).[刘向,邹逢兴,张湘平,等.面向节能的混合流水车间调度方法的研究[C]//第二十七届中国控制会议论文集.北京:北京航空航天大学出版社,2008:48-53.]
[11] DAI Ming,TANG Dunbing,GIRET A,et al.Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm[J].Robotics and Computer-Integrated Manufacturing,2013,29(5):418-429.
[12] ZENG Lingli.Mathematical modeling and algorithm for dynamic scheduling in process industry system for energy saving[D].Changsha:National University of Defense Technology,2009(in Chinese).[曾令李.面向节能的流程工业系统动态调度建模及算法研究[D].长沙:国防科学技术大学,2009.]
[13] ZHOU Yanwei.Research of multi-objective flow shop scheduling based on fast non-dominated sorting genetic algorithm[D].Guangzhou:South China University of Technology,2015(in Chinese).[周严伟.基于快速非支配排序遗传算法的多目标流水车间调度研究[D].广州:华南理工大学,2015.]
[14] ZHANG Liping.Modeling and optimization of flow shop scheduling problem based on energy saving[D].Hangzhou:Zhejiang University of Technology,2013(in Chinese).[张立萍.面向节能的流水车间调度建模与优化[D].杭州:浙江工业大学,2013.]
[15] ROJAS J,MORA C,MERINO M,et al.Some implications of the use of renewable energy in production scheduling[C]//Proceedings of the 2015International Conference on Operations Excellence and Service Engineering.Orlando,Fla.,USA:IEOM Society,2015.
[16] WANG Chengshan,WU Zhen,LI Peng.Research on key technologies of microgrid[J].Transactions of China Electrotechnical Society,2014,29(2):1-12(in Chinese).[王成山,武震,李鹏.微电网关键技术研究[J].电工技术学报,2014,29(2):1-12.]
[17] XING Wen.Optimization allocation and benefit analysis of energy-intensive enterprises microgrid based on load control[D].Xiangtan:Xiangtan University,2016(in Chinese).[邢文.基于负荷控制的高耗能企业微网优化配置及效益分析[D].湘潭:湘潭大学,2016.]
[18] HU Zhen.Benefit optimization of power generation and consumption in energy intensive enterprise based on demand response[D].Xiangtan:Xiangtan University,2016(in Chinese).[胡真.基于需求响应的高耗能企业发用电效益优化[D].湘潭:湘潭大学,2016.]
[19] LI Nengxue.The load scheduling for users based on demand response and benefit analysis[D].Xiangtan:Xiangtan University,2016(in Chinese).[李能学.基于需求响应的大用户负荷调度及效益分析[D].湘潭:湘潭大学,2016.]
[20] LI Ming,YANG Lieluan,WANG Weizhou,et al.High-energy enterprises for Gansu power grid to participate in renewable energy consumption“Dutch-net-source”coordinated control[J].Electric Power,2015,48(12):115-121(in Chinese).[李明,杨烈銮,王维洲,等.针对甘肃电网的高载能企业参与可再生能源消纳“荷—网—源”协调控制[J].中国电力,2015,48(12):115-121.]
[21] CHEN Runze,SUN Hongbin,YIN Hongyang.Analysis on the mode and benefit of high power enterprises participation in power system dispatching[J].Automation of Electric Power Systems,2015,39(17):168-175(in Chinese).[陈润泽,孙宏斌,晋宏杨.高载能企业参与电力系统调度的模式与效益分析[J].电力系统自动化,2015,39(17):168-175.]
[22]WANG Xiaoqing,DING Hongwei,Qiu Minmin,et al.A low-carbon production scheduling system considering renewable energy[C]//Peoceedings of the IEEE International Conference on Service Operations,Logistics,&Informatics.Washington,D.C.,USA:IEEE,2011:101-106.
[23] SHI Lishan.Construct a new power system compatible with the characteristics of renewable energy resources[J].Power System and Clean Energy,2009,25(4):1-4(in Chinese).[史立山.构建适应可再生能源资源特点的新型电力体系[J].电网与清洁能源,2009,25(4):1-4.]
[24] LAN Lan.Analysis of characteristics and economic for new energy power generation[D].Beijing:North China Electric Power University,2014(in Chinese).[蓝澜.新能源发电特性与经济性分析研究[D].北京:华北电力大学,2014.]
[25] WANG Chengshan,ZHOU Yue.Review on demonstration projects of microgrid[J].Distribution&Utilization,2015(1):16-21(in Chinese).[王成山,周越.微电网示范工程综述[J].供用电,2015(1):16-21.]
[26] XU Hua,ZHANG Ting.Improved discrete particle swarm algorithm for solving flexible flow shop scheduling problem[J].Journal of Computer Applications,2015,35(5):1342-1347,1352(in Chinese).[徐华,张庭.改进离散粒子群算法求解柔性流水车间调度问题[J].计算机应用,2015,35(5):1342-1347,1352.]
[27] LI Li,GUO Shaoyan,ZHANG Yaqin.Research on the quantity relationship between the cement product varietyand energy consumption and CO2emissions[J].Development Orientation of Building Materials,2010(1):29-35(in Chinese).[李黎,郭少衍,张雅钦.水泥产品品种及能耗与CO_2排放量的数量关系研究[J].建材发展导向,2010(1):29-35.]
[28] WANG Shuting.Studies on Permutation flow shop scheduling using genetic algorithm variable neighborhood search[D].Wuhan:Huazhong University of Science and Technology,2013(in Chinese).[王书婷.基于遗传变邻域算法的置换流水车间调度问题研究[D].武汉:华中科技大学,2013.]
[29] WU Xiuli,CUI Qi,YU Jianjun.Improved genetic algorithm variable neighborhood search for solving hybrid flow shop scheduling problem[J].Computer Integrated Manufacturing Systems,2017,23(9):1917-1927(in Chinese).[吴秀丽,崔琪,余建军.变邻域改进遗传算法求解混合流水车间调度问题[J].计算机集成制造系统,2017,23(9):1917-1927.]
[30] DAI Min,TANG Dunbing,ADRIANA G,et al.Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm[J].Robotics and Computer-Integrated Manufacturing,2013,29(5):418-429.
[31] WANG Shengyao,WANG Ling,XU Ye,et al.An estimation of distribution algorithm for solving hybrid flow-shop scheduling problem[J].Acta Automatick Sinica,2012,38(3):437-443(in Chinese).[王圣尧,王凌,许烨,等.求解混合流水车间调度问题的分布估计算法[J].自动化学报,2012,38(3):437-443.]
[2] Energy Information Administration.International energy outlook 2009[EB/OL].[2017-04-21].http://www.eia.doe.gov/oiaf/ieo/index.html.
[3] FANG Kan,UHAN N,ZHAO Fu,et al.A New approach to scheduling in manufacturing for power consumption and carbon footprint reduction[J].Journal of Manufacturing Systems,2011,30(4):234-240.
[4] SU Zhixiong,YI Junmin.Genetic algorithm with forwardbackward scheduling approach for hybrid flow shop problems[J].Computer Integrated Manufacturing Systems,2016,22(4):1059-1069(in Chinese).[苏志雄,伊俊敏.基于正逆序策略的混合流水车间遗传调度算法[J].计算机集成制造系统,2016,22(4):1059-1069.]
[5] LIU Chang,LI Dong,PENG Hui,et al.EDA algorithm with correlated variables for solving hybrid flow-shop scheduling problem[J].Computer Integrated Manufacturing Systems,2015,21(4):1032-1039(in Chinese).[刘昶,李冬,彭慧,等.求解混合流水车间调度问题的变量相关EDA算法[J].计算机集成制造系统,2015,21(4):1032-1039.]
[6] SONG Daili,ZHANG Jie.Batch scheduling problem of hybrid flow shop based on ant colony algorithm[J].Computer Integrated Manufacturing Systems,2013,19(7):1640-1647(in Chinese).[宋代立,张洁.蚁群算法求解混合流水车间分批调度问题[J].计算机集成制造系统,2013,19(7):1640-1647.]
[7] MANSOURI S A,AKTAS E,BESIKCI U.Green scheduling of a two-machine flowshop:Trade-off between makespan and energy consumption[J].European Journal of Operational Research,2015,248(3):772-788.
[8] NAGASAWA K,IKEDA Y,IROHARA T.Robust flow shop scheduling with random processing times for reduction of peak power consumption[J].Simulation Modelling Practice&Theory,2015,59(1):102-113.
[9] LUO Hao,DU Bing,HUANG G Q,et al.Hybrid flow shop scheduling considering machine electricity consumption cost[J].International Journal of Production Economics,2013,146(2):423-439.
[10] LIU Xiang,ZOU Fengxing,ZHANG Xiangping,et al.Hybrid flow-shop scheduling problem based on saving energy[C]//Proceedings of the 27th Chinese Control Conference.Beijing:Beihang University Press,2008:48-53(in Chinese).[刘向,邹逢兴,张湘平,等.面向节能的混合流水车间调度方法的研究[C]//第二十七届中国控制会议论文集.北京:北京航空航天大学出版社,2008:48-53.]
[11] DAI Ming,TANG Dunbing,GIRET A,et al.Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm[J].Robotics and Computer-Integrated Manufacturing,2013,29(5):418-429.
[12] ZENG Lingli.Mathematical modeling and algorithm for dynamic scheduling in process industry system for energy saving[D].Changsha:National University of Defense Technology,2009(in Chinese).[曾令李.面向节能的流程工业系统动态调度建模及算法研究[D].长沙:国防科学技术大学,2009.]
[13] ZHOU Yanwei.Research of multi-objective flow shop scheduling based on fast non-dominated sorting genetic algorithm[D].Guangzhou:South China University of Technology,2015(in Chinese).[周严伟.基于快速非支配排序遗传算法的多目标流水车间调度研究[D].广州:华南理工大学,2015.]
[14] ZHANG Liping.Modeling and optimization of flow shop scheduling problem based on energy saving[D].Hangzhou:Zhejiang University of Technology,2013(in Chinese).[张立萍.面向节能的流水车间调度建模与优化[D].杭州:浙江工业大学,2013.]
[15] ROJAS J,MORA C,MERINO M,et al.Some implications of the use of renewable energy in production scheduling[C]//Proceedings of the 2015International Conference on Operations Excellence and Service Engineering.Orlando,Fla.,USA:IEOM Society,2015.
[16] WANG Chengshan,WU Zhen,LI Peng.Research on key technologies of microgrid[J].Transactions of China Electrotechnical Society,2014,29(2):1-12(in Chinese).[王成山,武震,李鹏.微电网关键技术研究[J].电工技术学报,2014,29(2):1-12.]
[17] XING Wen.Optimization allocation and benefit analysis of energy-intensive enterprises microgrid based on load control[D].Xiangtan:Xiangtan University,2016(in Chinese).[邢文.基于负荷控制的高耗能企业微网优化配置及效益分析[D].湘潭:湘潭大学,2016.]
[18] HU Zhen.Benefit optimization of power generation and consumption in energy intensive enterprise based on demand response[D].Xiangtan:Xiangtan University,2016(in Chinese).[胡真.基于需求响应的高耗能企业发用电效益优化[D].湘潭:湘潭大学,2016.]
[19] LI Nengxue.The load scheduling for users based on demand response and benefit analysis[D].Xiangtan:Xiangtan University,2016(in Chinese).[李能学.基于需求响应的大用户负荷调度及效益分析[D].湘潭:湘潭大学,2016.]
[20] LI Ming,YANG Lieluan,WANG Weizhou,et al.High-energy enterprises for Gansu power grid to participate in renewable energy consumption“Dutch-net-source”coordinated control[J].Electric Power,2015,48(12):115-121(in Chinese).[李明,杨烈銮,王维洲,等.针对甘肃电网的高载能企业参与可再生能源消纳“荷—网—源”协调控制[J].中国电力,2015,48(12):115-121.]
[21] CHEN Runze,SUN Hongbin,YIN Hongyang.Analysis on the mode and benefit of high power enterprises participation in power system dispatching[J].Automation of Electric Power Systems,2015,39(17):168-175(in Chinese).[陈润泽,孙宏斌,晋宏杨.高载能企业参与电力系统调度的模式与效益分析[J].电力系统自动化,2015,39(17):168-175.]
[22]WANG Xiaoqing,DING Hongwei,Qiu Minmin,et al.A low-carbon production scheduling system considering renewable energy[C]//Peoceedings of the IEEE International Conference on Service Operations,Logistics,&Informatics.Washington,D.C.,USA:IEEE,2011:101-106.
[23] SHI Lishan.Construct a new power system compatible with the characteristics of renewable energy resources[J].Power System and Clean Energy,2009,25(4):1-4(in Chinese).[史立山.构建适应可再生能源资源特点的新型电力体系[J].电网与清洁能源,2009,25(4):1-4.]
[24] LAN Lan.Analysis of characteristics and economic for new energy power generation[D].Beijing:North China Electric Power University,2014(in Chinese).[蓝澜.新能源发电特性与经济性分析研究[D].北京:华北电力大学,2014.]
[25] WANG Chengshan,ZHOU Yue.Review on demonstration projects of microgrid[J].Distribution&Utilization,2015(1):16-21(in Chinese).[王成山,周越.微电网示范工程综述[J].供用电,2015(1):16-21.]
[26] XU Hua,ZHANG Ting.Improved discrete particle swarm algorithm for solving flexible flow shop scheduling problem[J].Journal of Computer Applications,2015,35(5):1342-1347,1352(in Chinese).[徐华,张庭.改进离散粒子群算法求解柔性流水车间调度问题[J].计算机应用,2015,35(5):1342-1347,1352.]
[27] LI Li,GUO Shaoyan,ZHANG Yaqin.Research on the quantity relationship between the cement product varietyand energy consumption and CO2emissions[J].Development Orientation of Building Materials,2010(1):29-35(in Chinese).[李黎,郭少衍,张雅钦.水泥产品品种及能耗与CO_2排放量的数量关系研究[J].建材发展导向,2010(1):29-35.]
[28] WANG Shuting.Studies on Permutation flow shop scheduling using genetic algorithm variable neighborhood search[D].Wuhan:Huazhong University of Science and Technology,2013(in Chinese).[王书婷.基于遗传变邻域算法的置换流水车间调度问题研究[D].武汉:华中科技大学,2013.]
[29] WU Xiuli,CUI Qi,YU Jianjun.Improved genetic algorithm variable neighborhood search for solving hybrid flow shop scheduling problem[J].Computer Integrated Manufacturing Systems,2017,23(9):1917-1927(in Chinese).[吴秀丽,崔琪,余建军.变邻域改进遗传算法求解混合流水车间调度问题[J].计算机集成制造系统,2017,23(9):1917-1927.]
[30] DAI Min,TANG Dunbing,ADRIANA G,et al.Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm[J].Robotics and Computer-Integrated Manufacturing,2013,29(5):418-429.
[31] WANG Shengyao,WANG Ling,XU Ye,et al.An estimation of distribution algorithm for solving hybrid flow-shop scheduling problem[J].Acta Automatick Sinica,2012,38(3):437-443(in Chinese).[王圣尧,王凌,许烨,等.求解混合流水车间调度问题的分布估计算法[J].自动化学报,2012,38(3):437-443.]