工程科学学报.第43卷.第3期：422-432.2021年3月 Chinese Journal of Engineering,Vol.43,No.3:422-432,March 2021 https://doi.org/10.13374/j.issn2095-9389.2020.02.19.004;http://cje.ustb.edu.cn 基于改进差分进化算法的加热炉调度方法 闫 祺，李文甲，王稼晨，马凌，赵军四 天津大学中低温热能高效利用教育部重点实验室，天津300350 ☒通信作者，E-mail:zhaojun@tju.edu.cn 摘要提出一种以燃料消耗量最小为优化目标的加热炉生产调度新方法.首先基于热力学第一定律分析了流入及流出加 热炉的各项能量，并对燃料消耗量的计算式进行了理论推导.进而根据加热炉区实际生产调度特点归纳各约束条件，以多台 加热炉总燃料消耗量最小为优化目标，构建调度优化数学模型.采用自适应差分进化算法搭配禁忌搜索算法进行综合求解， 并通过9组实际钢坯生产案例模拟验证了该算法的可行性和有效性.同时，为了探究加热炉燃料消耗量的影响因素，提出了 分别衡量加热炉区缓冲等待、炉内加热两部分时间同理想生产时间匹配程度的评价参数山和42，并分析了燃料消耗量对二 者的敏感性，结果表明：当连铸坯到达加热炉节奏与热轧工序出坯节奏之比由0.5增至2时，燃料消耗量对两评价参数的敏感 性逐渐减弱 关键词加热炉：调度优化：燃料消耗量：差分进化算法：敏感性分析 分类号TF087 Reheat furnace production scheduling based on the improved differential evolution algorithm YAN Qi.LI Wen-jia.WANG Jia-chen.MA Ling.ZHAO Jun Key Laboratory of Efficient Utilization of Low and Medium Grade Energy,Tianjin University,Tianjin 300350,China Corresponding author,E-mail:zhaojun@tju.edu.cn ABSTRACT The reheat furnace,located between the continuous caster and the hot rolling mill,plays the role of buffer coordination zone,and is one of the most important production equipment in the hot rolling process.As reheat furnaces were the largest energy- consumer group in the hot rolling process,their schedule optimization was of great importance to achieve high production efficiency and reduce energy consumption.In this paper,a new reheat furnace production scheduling method with the target of minimum fuel consumption was proposed.First,the energy inputs and outputs from the reheat furnace were analyzed based on the first law of thermodynamics,then the equation for calculating of the fuel consumption was derived.Second,various production constraints were summarized to consider the actual characteristics of the dispatching plan in reheat furnaces,and the mathematical model of scheduling optimization was constructed with the minimum fuel consumption set as the optimization objective.The adaptive differential evolution algorithm and the tabu search algorithm were applied to obtain the optimal solution.The differential evolution algorithm could dynamically adjust the scaling factor and the crossover rate according to the change of the fitness function value of each generation of individuals,and this adaptive strategy could balance the ability of development and exploration of the algorithm.After the model was validated with actual production data,the feasibility and effectiveness of the algorithm were verified by nine groups of actual billet production cases.Furthermore,to explore the influencing factors of energy consumption of reheat furnace,two evaluation parameters,u and 42,were defined to quantify the matching degree of time series of the buffer waits and the heating processes to ideal production in 收稿日期：2020-02-19 基金项目：国家重点研发计划资助项目(2018YFB0605901)基于改进差分进化算法的加热炉调度方法 闫    祺，李文甲，王稼晨，马    凌，赵    军苣 天津大学中低温热能高效利用教育部重点实验室，天津 300350 苣通信作者，E-mail：zhaojun@tju.edu.cn 摘    要    提出一种以燃料消耗量最小为优化目标的加热炉生产调度新方法. 首先基于热力学第一定律分析了流入及流出加 热炉的各项能量，并对燃料消耗量的计算式进行了理论推导. 进而根据加热炉区实际生产调度特点归纳各约束条件，以多台 加热炉总燃料消耗量最小为优化目标，构建调度优化数学模型. 采用自适应差分进化算法搭配禁忌搜索算法进行综合求解， 并通过 9 组实际钢坯生产案例模拟验证了该算法的可行性和有效性. 同时，为了探究加热炉燃料消耗量的影响因素，提出了 分别衡量加热炉区缓冲等待、炉内加热两部分时间同理想生产时间匹配程度的评价参数 μ1 和 μ2，并分析了燃料消耗量对二 者的敏感性，结果表明：当连铸坯到达加热炉节奏与热轧工序出坯节奏之比由 0.5 增至 2 时，燃料消耗量对两评价参数的敏感 性逐渐减弱. 关键词    加热炉；调度优化；燃料消耗量；差分进化算法；敏感性分析 分类号    TF087 Reheat  furnace  production  scheduling  based  on  the  improved  differential  evolution algorithm YAN Qi，LI Wen-jia，WANG Jia-chen，MA Ling，ZHAO Jun苣 Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, Tianjin University, Tianjin 300350, China 苣 Corresponding author, E-mail: zhaojun@tju.edu.cn ABSTRACT    The reheat furnace, located between the continuous caster and the hot rolling mill, plays the role of buffer coordination zone,  and  is  one  of  the  most  important  production  equipment  in  the  hot  rolling  process.  As  reheat  furnaces  were  the  largest  energy￾consumer group in the hot rolling process, their schedule optimization was of great importance to achieve high production efficiency and reduce  energy  consumption.  In  this  paper,  a  new  reheat  furnace  production  scheduling  method  with  the  target  of  minimum  fuel consumption  was  proposed.  First,  the  energy  inputs  and  outputs  from  the  reheat  furnace  were  analyzed  based  on  the  first  law  of thermodynamics, then the equation for calculating of the fuel consumption was derived. Second, various production constraints were summarized to consider the actual characteristics of the dispatching plan in reheat furnaces, and the mathematical model of scheduling optimization was constructed with the minimum fuel consumption set as the optimization objective. The adaptive differential evolution algorithm  and  the  tabu  search  algorithm  were  applied  to  obtain  the  optimal  solution.  The  differential  evolution  algorithm  could dynamically adjust the scaling factor and the crossover rate according to the change of the fitness function value of each generation of individuals, and this adaptive strategy could balance the ability of development and exploration of the algorithm. After the model was validated  with  actual  production  data,  the  feasibility  and  effectiveness  of  the  algorithm  were  verified  by  nine  groups  of  actual  billet production cases. Furthermore, to explore the influencing factors of energy consumption of reheat furnace, two evaluation parameters, μ1 and μ2 , were defined to quantify the matching degree of time series of the buffer waits and the heating processes to ideal production in 收稿日期: 2020−02−19 基金项目: 国家重点研发计划资助项目（2018YFB0605901） 工程科学学报，第 43 卷，第 3 期：422−432，2021 年 3 月 Chinese Journal of Engineering, Vol. 43, No. 3: 422−432, March 2021 https://doi.org/10.13374/j.issn2095-9389.2020.02.19.004; http://cje.ustb.edu.cn