连铸机开浇炉次与时间决策的多目标优化
|
摘要
针对连铸机开浇决策中的炉次选择、排序与开浇时间确定的多目标优化问题,以炼钢厂生产批量计划执行情况的总惩罚、生产线积压金属量、优质铁水非有效利用量最小为目标函数,构建了连铸机开浇炉次与时间决策的多目标优化模型。针对该模型特点设计了改进的非支配排序遗传算法,以预选池内选择的炉次序号为基因的编码方式减小模型解的无效搜索空间,采取调整传统精英解集的计算顺序、限定计算拥挤距离个体数目的改进措施来减轻计算负荷,利用对Pareto解进行模糊选优的方法确定最终优化解。以某钢厂的生产实例数据测试表明,该模型有利于连铸生产炉次浇铸周期的稳定控制,算法效率优于传统的非支配排序遗传算法和强度Pareto进化算法。
For the integrated decision making of charge selection and sequencing in the batch plan as well as the casting start time for continuous casters,a multi-objective optimization model was developed.The objectives were set to minimize the penalty of production batch plan implementation in steel plans,the amount of metal stocked in production line and the non-effective usage amount of high quality hot metal.According to the characteristics of model,an improved solving multi-objective evolutionary algorithm was derived based on Non-dominated Sorting Genetic Algorithm-Ⅱ(NSGA-Ⅱ).The chromosome was represented with the serial number of all charges in the charge batching pool to decrease the invalid searching space of solution.To reduce the computational complexity,the computation order of elitist solution in classical NSGA-Ⅱ was modified and the crowding distance calculation times for individuals were restricted.A fuzzy selection method was employed to choose the final solution among Pareto solutions.Computational tests on the real operation data of a steel plant showed that the proposed multi-objective optimization model was conducive to the stable control of charge's casting cycle on continuous casters,and the modified algorithm was better than the classical NSGAⅡ and Strength Pareto Evolutionary Algorithm-Ⅱ(SPEA-Ⅱ).
For the integrated decision making of charge selection and sequencing in the batch plan as well as the casting start time for continuous casters,a multi-objective optimization model was developed.The objectives were set to minimize the penalty of production batch plan implementation in steel plans,the amount of metal stocked in production line and the non-effective usage amount of high quality hot metal.According to the characteristics of model,an improved solving multi-objective evolutionary algorithm was derived based on Non-dominated Sorting Genetic Algorithm-Ⅱ(NSGA-Ⅱ).The chromosome was represented with the serial number of all charges in the charge batching pool to decrease the invalid searching space of solution.To reduce the computational complexity,the computation order of elitist solution in classical NSGA-Ⅱ was modified and the crowding distance calculation times for individuals were restricted.A fuzzy selection method was employed to choose the final solution among Pareto solutions.Computational tests on the real operation data of a steel plant showed that the proposed multi-objective optimization model was conducive to the stable control of charge's casting cycle on continuous casters,and the modified algorithm was better than the classical NSGAⅡ and Strength Pareto Evolutionary Algorithm-Ⅱ(SPEA-Ⅱ).
引文
[1]ZHANG Wenxue,LI Tieke.Integration of continuous-casting and hot-rolling rolling plan based on dynamic constraint satisfaction[J].Computer Integrated Manufacturing Systems,2011,17(10):2177-2184(in Chinese).[张文学,李铁克.基于动态约束满足的连铸热轧一体化滚动计划[J].计算机集成制造系统,2011,17(10):2177-2184.]
[2]DONG Hongyu,HUANG Min,LP W H,et al.On the integrated charge planning with flexible jobs in primary steelmaking processes[J].International Journal of Production Research,2010,48(21):6499-6535.
[3]DONG Hongyu,HUANG Min,LP W H,et al.Improved variable neighbourhood search for integrated tundish planning in primary steelmaking processes[J].International Journal of Production Research,2012,50(20):5747-5761.
[4]YU Chunyue,QU Rongxia.Multi-objective order planning model and algorithm for integrated steel production[J].Control Theory and Applications,2009,26(12):1452-1454.
[5]YU Chunyue,WANG Cheng’en.Multi-objective order-planning model and algorithm for integrated steel production[M].Control Theory&Applications,2009,26(12):1452-1454(in Chinese).[於春月,王成恩.钢铁一体化生产多目标合同计划建模与算法[J].控制理论与应用,2009,26(12):1452-1454.]
[6]LU Kebin,HUANG Kewei,ZHANG Ruiyou,et al.Multiobjective model and algorithm for charge design problem of steel-making[M].Journal of Central South University:Science and Technology,2009,40(S1):315-318(in Chinese).[卢克斌,黄可为,张瑞友,等.炼钢组炉问题的多目标优化模型与算法[M].中南大学学报:自然科学版,2009,40(S1):315-318.]
[7]NING Shushi,WANG Wei,PAN Xuejun.Integrated method of steel-making and continuous casting planning[J].Control Theory&Applications,2007,24(3):374-379(in Chinese).[宁树实,王伟,潘学军.一种炼钢-连铸生产计划一体化编制方法[J].控制理论与应用,2007,24(3):374-379.]
[8]TANG Lixin,GUAN Jing,HU Guofen.Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration[J].Computers&Industrial Engineering,2010,58(2):239-248.
[9]PANG Xinfu,YU Shengping,LUO Xiaochuan,et al.Hybrid job shop rescheduling method and its application for steelmaking-casting[J].System Engeering-Thory&Practice,2012,32(4):826-838(in Chinese).[庞新富,俞胜平,罗小川,等.混合Job shop炼钢—连铸重调度方法及其应用[J].系统工程理论与实践,2012,32(4):826-838.]
[10]WANG Gang,WANG Bin,WANG Bao,et al.Scheduling model for steelmaking-continuous casting process based on“furnace-caster matching”principle[J].Journal of University of Science and Technology Beijing,2013,35(8):1080-1092(in Chinese).[王刚,王彬,王宝,等.基于“炉机对应”原则的炼钢—连铸调度模型[J].北京科技大学学报,2013,35(8):1080-1092.]
[11]WANG Chuang,LIU Qing,WANG Bin,et al.Scheduling model of steelmaking-continuous casting processes in special steel plants[J].Journal of University of Science and Technology Beijing,2013,35(3):371-378(in Chinese).[王闯,刘青,王彬,等.特殊钢厂炼钢—连铸调度模型[J].北京科技大学学报,2013,35(3):371-378.]
[12]PANG Xinfu,YU Shengping,ZHENG Binglin,et al.Complete modification rescheduling method and its application for steelmaking and continuous casting[EB/OL].[2016-03-24].http://serv.yanchick.org/Books/Материалы%20конференций/ifac2008/data/papers/2705.pdf.
[13]YU Shengping,PAN Quanke.A rescheduling method for operation time delay disturbance in steelmaking and continuous casting production process[J].International Journal of Iron and Steel Research,2012,19(12):33-41.
[14]SUN Liangliang,WANG Xiuying.Application of mix optimization scheduling approach for steelmaking-continuous casting process based on actual steelmaking industry[J].International Journal of Iron and Steel Research,2013,20(10):1-9.
[15]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.
[16]TANG Lixin,WANG Mengguang,YANG Zihou.Model and algorithm of cast plan with unknown number of cast for steelmaking-continuous casting scheduling[J].Iron and Steel,1997,32(7):19-21(in Chinese).[唐立新,王梦光,杨自厚.炼钢一连铸对于浇次数未知的最优浇次计划模型与算法[J].钢铁,1997,32(7):19-21.]
[17]GONG Yongmin,ZHENG Zhong,LONG Jianyu,et al.An optimization model for casting start time decision of continuous caster in steel plant[J].Journal of Northeastern University:Natural Science,2016,37(2):203-207(in Chinese).[龚永民,郑忠,龙建宇,等.炼钢厂连铸机的开浇时间决策优化模型[J].东北大学学报:自然科学版,2016,37(2):203-207.]
[18]KIM S,WHITT W.Statistical analysis with Little’s Law[J].Operations Research,2013,61(4):1031-1040.
[19]VON LUCKEN C,BARAN B,BRIZUELA C.A survey on multi-objective evolutionary algorithms for many-objective problems[J].Computational Optimization Applications,2014,58(3):707-756.
[20]ZHAO Zhen,LIU Gang,YAN Junwei,et al.Genetic algorithm for large-scale scheduling of parallel machines based on double linearl inkedlist encoding[J].Computer Integrated Manufacturing Systems,2011,17(2):301-309(in Chinese).[赵振,刘钢,严隽薇,等.基于双线性链表编码的并行机大规模调度遗传算法[J].计算机集成制造系统,2011,17(2):301-309.]
[21]WANG Yong,CAI Zixing,ZHOU Yuren,et al.Constrained optimization evolutionary algorithms[J].Journal of Software,2009,20(1):11-29(in Chinese).[王勇,蔡自兴,周育人,等.约束优化进化算法[J].软件学报,2009,20(1):11-29.]
[22]SOUSA T,MORAIS H,VALE Z,et al.A multi-objective optimization of the active and reactive resource scheduling at a distribution level in a smart grid context[J].Energy,2015,85:236-250.
[23]ZITZLE R E,LANUMANNS M,T HIELE L.SPEA2:improving the strength pareto evolutionary algorithm for multi objective optimization[EB/OL].[2016-03-24].http://www.kddresearch.org/Courses/Spring-2007/CIS830/Handouts/P8.pdf.
[24]GONG Maoguo,JIAO Licheng,YANG Dongdong,et al.Research on evolutionary multi-objective optimization algorithms[J].Journal of Software,2009,20(2):271-289(in Chinese).[公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289.]
[2]DONG Hongyu,HUANG Min,LP W H,et al.On the integrated charge planning with flexible jobs in primary steelmaking processes[J].International Journal of Production Research,2010,48(21):6499-6535.
[3]DONG Hongyu,HUANG Min,LP W H,et al.Improved variable neighbourhood search for integrated tundish planning in primary steelmaking processes[J].International Journal of Production Research,2012,50(20):5747-5761.
[4]YU Chunyue,QU Rongxia.Multi-objective order planning model and algorithm for integrated steel production[J].Control Theory and Applications,2009,26(12):1452-1454.
[5]YU Chunyue,WANG Cheng’en.Multi-objective order-planning model and algorithm for integrated steel production[M].Control Theory&Applications,2009,26(12):1452-1454(in Chinese).[於春月,王成恩.钢铁一体化生产多目标合同计划建模与算法[J].控制理论与应用,2009,26(12):1452-1454.]
[6]LU Kebin,HUANG Kewei,ZHANG Ruiyou,et al.Multiobjective model and algorithm for charge design problem of steel-making[M].Journal of Central South University:Science and Technology,2009,40(S1):315-318(in Chinese).[卢克斌,黄可为,张瑞友,等.炼钢组炉问题的多目标优化模型与算法[M].中南大学学报:自然科学版,2009,40(S1):315-318.]
[7]NING Shushi,WANG Wei,PAN Xuejun.Integrated method of steel-making and continuous casting planning[J].Control Theory&Applications,2007,24(3):374-379(in Chinese).[宁树实,王伟,潘学军.一种炼钢-连铸生产计划一体化编制方法[J].控制理论与应用,2007,24(3):374-379.]
[8]TANG Lixin,GUAN Jing,HU Guofen.Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration[J].Computers&Industrial Engineering,2010,58(2):239-248.
[9]PANG Xinfu,YU Shengping,LUO Xiaochuan,et al.Hybrid job shop rescheduling method and its application for steelmaking-casting[J].System Engeering-Thory&Practice,2012,32(4):826-838(in Chinese).[庞新富,俞胜平,罗小川,等.混合Job shop炼钢—连铸重调度方法及其应用[J].系统工程理论与实践,2012,32(4):826-838.]
[10]WANG Gang,WANG Bin,WANG Bao,et al.Scheduling model for steelmaking-continuous casting process based on“furnace-caster matching”principle[J].Journal of University of Science and Technology Beijing,2013,35(8):1080-1092(in Chinese).[王刚,王彬,王宝,等.基于“炉机对应”原则的炼钢—连铸调度模型[J].北京科技大学学报,2013,35(8):1080-1092.]
[11]WANG Chuang,LIU Qing,WANG Bin,et al.Scheduling model of steelmaking-continuous casting processes in special steel plants[J].Journal of University of Science and Technology Beijing,2013,35(3):371-378(in Chinese).[王闯,刘青,王彬,等.特殊钢厂炼钢—连铸调度模型[J].北京科技大学学报,2013,35(3):371-378.]
[12]PANG Xinfu,YU Shengping,ZHENG Binglin,et al.Complete modification rescheduling method and its application for steelmaking and continuous casting[EB/OL].[2016-03-24].http://serv.yanchick.org/Books/Материалы%20конференций/ifac2008/data/papers/2705.pdf.
[13]YU Shengping,PAN Quanke.A rescheduling method for operation time delay disturbance in steelmaking and continuous casting production process[J].International Journal of Iron and Steel Research,2012,19(12):33-41.
[14]SUN Liangliang,WANG Xiuying.Application of mix optimization scheduling approach for steelmaking-continuous casting process based on actual steelmaking industry[J].International Journal of Iron and Steel Research,2013,20(10):1-9.
[15]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.
[16]TANG Lixin,WANG Mengguang,YANG Zihou.Model and algorithm of cast plan with unknown number of cast for steelmaking-continuous casting scheduling[J].Iron and Steel,1997,32(7):19-21(in Chinese).[唐立新,王梦光,杨自厚.炼钢一连铸对于浇次数未知的最优浇次计划模型与算法[J].钢铁,1997,32(7):19-21.]
[17]GONG Yongmin,ZHENG Zhong,LONG Jianyu,et al.An optimization model for casting start time decision of continuous caster in steel plant[J].Journal of Northeastern University:Natural Science,2016,37(2):203-207(in Chinese).[龚永民,郑忠,龙建宇,等.炼钢厂连铸机的开浇时间决策优化模型[J].东北大学学报:自然科学版,2016,37(2):203-207.]
[18]KIM S,WHITT W.Statistical analysis with Little’s Law[J].Operations Research,2013,61(4):1031-1040.
[19]VON LUCKEN C,BARAN B,BRIZUELA C.A survey on multi-objective evolutionary algorithms for many-objective problems[J].Computational Optimization Applications,2014,58(3):707-756.
[20]ZHAO Zhen,LIU Gang,YAN Junwei,et al.Genetic algorithm for large-scale scheduling of parallel machines based on double linearl inkedlist encoding[J].Computer Integrated Manufacturing Systems,2011,17(2):301-309(in Chinese).[赵振,刘钢,严隽薇,等.基于双线性链表编码的并行机大规模调度遗传算法[J].计算机集成制造系统,2011,17(2):301-309.]
[21]WANG Yong,CAI Zixing,ZHOU Yuren,et al.Constrained optimization evolutionary algorithms[J].Journal of Software,2009,20(1):11-29(in Chinese).[王勇,蔡自兴,周育人,等.约束优化进化算法[J].软件学报,2009,20(1):11-29.]
[22]SOUSA T,MORAIS H,VALE Z,et al.A multi-objective optimization of the active and reactive resource scheduling at a distribution level in a smart grid context[J].Energy,2015,85:236-250.
[23]ZITZLE R E,LANUMANNS M,T HIELE L.SPEA2:improving the strength pareto evolutionary algorithm for multi objective optimization[EB/OL].[2016-03-24].http://www.kddresearch.org/Courses/Spring-2007/CIS830/Handouts/P8.pdf.
[24]GONG Maoguo,JIAO Licheng,YANG Dongdong,et al.Research on evolutionary multi-objective optimization algorithms[J].Journal of Software,2009,20(2):271-289(in Chinese).[公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289.]