CN106055836A

CN106055836A - Multi-target optimization method for casting sequence selection, ranking and casting time policy of continuous casting machine

Info

Publication number: CN106055836A
Application number: CN201610478277.4A
Authority: CN
Inventors: 郑忠; 龚永民; 龙建宇; 高小强; 呼万哲
Original assignee: Chongqing University
Current assignee: Chongqing University
Priority date: 2016-06-27
Filing date: 2016-06-27
Publication date: 2016-10-26
Anticipated expiration: 2036-06-27
Also published as: CN106055836B

Abstract

The present invention provides a multi-objective optimization method for the selection, sorting and decision-making of pouring times of continuous casting units, which includes the following steps: establishing the total penalty based on the implementation of the production batch plan of the steelmaking plant, the amount of backlogged metal in the production line, and the high-quality A multi-objective optimization model composed of constraint equations such as the objective function and relevant process requirements to minimize the non-effective utilization of molten iron; obtain the production batch plan of the steel plant, encode and initialize the population based on the selection of the furnace sequence number; decode and Calculate the fitness value and obtain the initial solution set; perform non-dominated sorting and crowding distance sorting; select some individuals in the population as parents; crossover and mutate the parents; decode the calculation results and calculate fitness; determine the elite solution set, Calculate the crowding distance and sort; output the elite solution set, select the maximum satisfaction plan and transmit it to the steelmaking-continuous casting production operation control system. The invention is beneficial to the stable control of the casting cycle of continuous casting production heats, and the algorithm efficiency is superior to the traditional non-dominated sorting genetic algorithm and the intensity pareto evolution algorithm.

Description

Multi-objective optimization of pouring times selection, sorting and pouring time decision in continuous casting unit method

技术领域technical field

本发明涉及钢铁生产控制技术领域，具体涉及一种连铸机组浇炉次选择、排序与开浇时间决策的多目标优化方法。The invention relates to the technical field of iron and steel production control, in particular to a multi-objective optimization method for selection, sorting and decision-making of pouring times of a continuous casting unit.

背景技术Background technique

连铸生产中待开浇次的炉次构成与开浇时间决策问题，既是确定连铸机具体开浇作业计划问题，也是制定合理炼钢连铸生产作业计划的前提，其核心任务是从批量计划预选池内选择合适的炉次作为计划期连铸机待开浇次中的选定炉次(包括炉次选择及排序)，并确定各炉次间是否连浇及开浇时间。目前，针对该问题，钢厂基本上是依靠人工经验进行决策，决策结果的科学性和有效性难以保证。连铸开浇的炉次与时间决策问题是典型的多目标多约束的优化决策问题，因此，研究该问题的多目标优化建模及求解方法有重要的现实意义和理论价值。In the continuous casting production, the composition of furnaces to be started and the decision-making time of the casting time are not only the problem of determining the specific casting operation plan of the continuous casting machine, but also the premise of formulating a reasonable steelmaking and continuous casting production operation plan. The core task is to start from the batch Select the appropriate heats in the planning pre-selection pool as the selected heats in the continuous casting machine to be poured during the planning period (including furnace selection and sorting), and determine whether continuous casting between each heat and the start-up time. At present, in response to this problem, steel mills basically rely on manual experience to make decisions, and it is difficult to guarantee the scientificity and effectiveness of the decision-making results. The heat number and time decision-making problem of continuous casting is a typical multi-objective and multi-constrained optimization decision-making problem. Therefore, it is of great practical significance and theoretical value to study the multi-objective optimization modeling and solution method of this problem.

近年来，关于炼钢-连铸生产计划调度领域的多目标问题相关研究主要集中在炼钢-连铸的生产批量计划制定，以及生产调度方面。In recent years, research on multi-objective problems in the field of steelmaking-continuous casting production planning and scheduling mainly focuses on the production batch planning and production scheduling of steelmaking-continuous casting.

已有研究针对生产批量计划与炼钢-连铸多目标调度计划的制定问题是分别独立进行的，前者主要涉及浇次计划的制定或组浇计划及炉次计划的联合优化方法，不涉及连铸机上的炉次选择、排序及开浇时间确定问题，仅在批量计划中确定了浇次内炉数；后者的研究重点是多目标下的炼钢连铸调度计划的具体排程方法，通常假设连铸机各待开浇次的顺序及开浇时间为已知条件，回避了连铸机上可执行的浇次计划中待开浇炉次及开浇时间的确定是受到生产线上金属资源平衡等因素的影响，这极大简化了现实问题。这种分别研究的方法与现实生产需求之间存在明显差异，钢厂生产管理既需要全面考虑生产批量计划，又需要在兼顾现实生产约束的基础上同时对连铸机的组浇与开浇的多目标问题进行优化决策，即实质上是制定连铸机的浇次作业计划问题，并将此决策结果作为制定炼钢连铸作业计划排程的前提条件。然而，由于对该类问题重要性的认识欠缺，以及建模与求解的难度较大，导致生产实践中由调度员按人工经验来确定，由此给生产带来了大量的不确定性，影响了“有序、稳定、高效”的生产目标的实现。Existing studies have been carried out independently on the formulation of production batch planning and steelmaking-continuous casting multi-objective scheduling plan. For the problems of heat selection, sorting and pouring time determination on the casting machine, only the number of furnaces in the pouring time is determined in the batch plan; the research focus of the latter is the specific scheduling method of the steelmaking and continuous casting scheduling plan under the multi-objective, It is usually assumed that the sequence of pouring times and the starting time of the continuous casting machine are known conditions, avoiding the fact that the determination of the number of furnaces to be started and the starting time in the pouring plan that can be executed on the continuous casting machine is determined by the metal resources on the production line The influence of factors such as balance, which greatly simplifies the practical problem. There is a clear difference between this separate research method and the actual production demand. The production management of the steel plant not only needs to fully consider the production batch plan, but also needs to take into account the actual production constraints. Optimizing decision-making based on multi-objective problems is essentially the problem of formulating the casting operation plan of the continuous casting machine, and the decision result is taken as the precondition for formulating the steelmaking and continuous casting operation planning schedule. However, due to the lack of understanding of the importance of this type of problem, and the difficulty of modeling and solving, the scheduler is determined by manual experience in production practice, which brings a lot of uncertainty to production and affects It has achieved the production goal of "orderly, stable and efficient".

发明内容Contents of the invention

为了克服上述现有技术中存在的缺陷，本发明的目的是提供一种连铸机组浇炉次选择、排序与开浇时间决策的多目标优化方法。In order to overcome the above-mentioned defects in the prior art, the object of the present invention is to provide a multi-objective optimization method for the selection, sequencing and decision-making of pouring times of continuous casting units.

为实现本发明的上述目的，本发明提供了一种连铸机组浇炉次选择、排序与开浇时间决策的多目标优化方法，其包括如下步骤：In order to achieve the above-mentioned purpose of the present invention, the present invention provides a multi-objective optimization method for selection, sorting and decision-making of pouring time of continuous casting units, which includes the following steps:

S1，控制器与钢厂的MES数据库连接，获取钢厂MES计划预选池中的生产批量计划，所述批量计划中包括分配到每台铸机上的浇次数量、浇次内各炉次所属钢种类别、断面规格及预定开浇时刻；S1, the controller is connected to the MES database of the steel plant to obtain the production batch plan in the pre-selected pool of the steel plant MES plan, the batch plan includes the number of pouring times allocated to each casting machine, the steel of each furnace in the pouring time Types, section specifications and scheduled pouring time;

S2，建立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的目标函数，所述目标函数为：S2, establishing an objective function that minimizes the total penalty for the implementation of the production batch plan of the steelworks, the amount of backlogged metal in the production line, and the non-effective utilization of high-quality molten iron. The objective function is:

min F＝{f₁,f₂,f₃} (1)min F＝{f ₁ ,f ₂ ,f ₃ } (1)

其中，in,

${f f}_{11} = = {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} (({ξ ξ}_{i i k k ((k k + + 11))}^{11} + + {ξ ξ}_{i i k k ((k k + + 11))}^{22})) \cdot \cdot {z z}_{i i k k} \cdot \cdot {z z}_{i i ((k k + + 11))} + + {Σ Σ}_{i i = = 11}^{I I} {d d}_{i i} \cdot \cdot (({K K}_{i i} - - {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k})) + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((| | {x x}_{{ik ik}^{d d}} - - {τ τ}_{{ik ik}^{d d}}^{d d a a t t e e} | | \cdot \cdot {ψ ψ}_{i i} + + {y the y}_{{ik ik}^{d d}} \cdot &Center Dot; {e e}_{i i})) - - - - - - ((22))$

f₂＝Q_O (3)f ₂ =Q _O (3)

${f f}_{33} = = {Q Q}_{E E.} \cdot \cdot {π π}^{p p} + + {Q Q}_{I I} \cdot \cdot {δ δ}^{p p} - - {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k} \cdot \cdot {v v}_{i i k k} \cdot \cdot {q q}_{i i} \cdot \cdot \frac{11}{11 - - η η} - - - - - - ((44))$

Q_O＝Q_E+Q_IV-Q_C-Q_L-Q_S (5)Q _O ＝Q _E +Q _IV -Q _C -Q _L -Q _S (5)

${Q Q}_{C C} = = {Σ Σ}_{i i = = 11}^{I I} {rq rq}_{i i} + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((m m i i n no (({τ τ}_{e e},, {x x}_{{ik ik}^{d d}} + + {τ τ}_{{ik ik}^{d d}})) - - {x x}_{{ik ik}^{d d}})) \cdot &Center Dot; ρ ρ \cdot &Center Dot; {wa w}_{{ik ik}^{d d}} \cdot &Center Dot; {ws ws}_{{ik ik}^{d d}} - - - - - - ((66))$

${Q Q}_{L L} = = {Q Q}_{C C} \cdot &Center Dot; \frac{η η}{11 - - η η} - - - - - - ((77))$

${Q Q}_{S S} = = \frac{{Q Q}_{C C} \cdot &Center Dot; {τ τ}_{A A}}{(({τ τ}_{e e} - - {τ τ}_{s the s})) \cdot \cdot ((11 - - η η))} + + {Q Q}_{r r c c o o n no} - - - - - - ((88))$

(2)式表示被选炉次相互间钢种差异惩罚费用和交货期差异费用、未开浇的剩余炉次的惩罚费用、各炉次未准时开浇惩罚费用之和；The formula (2) represents the sum of the penalty fee for the steel type difference between the selected furnaces and the difference fee for the delivery date, the penalty fee for the remaining furnaces that have not started pouring, and the penalty fee for each furnace not being poured on time;

(3)式表示生产线积压金属量Q_o；The formula (3) represents the backlog of metal quantity Q _o in the production line;

(4)式表示优质铁水未有效利用量；The formula (4) represents the unutilized amount of high-quality molten iron;

(5)式表示积压金属量，是基于生产线的金属资源平衡而设置，分别由计划期进铁量Q_E，期初生产线上库存金属量Q_IV，连铸浇钢量Q_C，金属损耗量Q_L，有利于生产稳定的期末生产线安全库存金属量Q_S构成；Equation (5) represents the amount of backlog metal, which is set based on the balance of metal resources in the production line. It consists of iron intake Q _E in the planning period, metal inventory on the production line at the beginning of the period Q _IV , continuous casting steel pouring Q _C , and metal loss Q _L , which is conducive to stable production and constitutes the metal quantity Q _S of the production line safety stock at the end of the period;

(6)式表示各连铸机的浇钢量分别由上一计划期遗留任务的浇钢量和待开浇次中各炉次的浇钢量构成；Formula (6) indicates that the steel pouring amount of each continuous casting machine is composed of the steel pouring amount of the remaining tasks in the previous planning period and the steel pouring amount of each furnace in the pouring time to be started;

(7)式表示浇钢量对应的金属损耗量；The formula (7) represents the amount of metal loss corresponding to the amount of poured steel;

(8)式表示在生产线安全库存金属量，它需要在生产线平均库存金属量基础上加一个随机波动需求金属量Q_rcon；Equation (8) represents the safe stock metal quantity in the production line, which needs to add a random fluctuating demand metal quantity Q _rcon on the basis of the average stock metal quantity of the production line;

其中，符号的具体含义为：Among them, the specific meanings of the symbols are:

①、定义的符号与集合：①. Defined symbols and sets:

i:铸机序列号，i∈I，I为连铸机集合；i: serial number of the casting machine, i∈I, I is the set of continuous casting machines;

k:预选池各铸机的炉次序号，k∈K_i，K_ij为预选池铸机i浇次j炉次集合，K_i为预选池的连铸机i的全部炉次集合，k依据各铸机的预定开浇时间先后产生；k: Furnace sequence number of each casting machine in the pre-selection pool, k∈K _i , K _ij is the set of casting times j of casting machine i in the pre-selection pool, K _i is the set of all heats of continuous casting machine i in the pre-selection pool, and k is generated successively according to the scheduled start-up time of each casting machine;

k^d:待开浇炉次序号，为连铸机i的待开浇炉次集合，是铸机i预定最低开浇炉数；k ^d : the sequence number of the furnace to be poured, is the set of furnaces to be poured for continuous casting machine i, is the scheduled minimum number of pouring furnaces for casting machine i;

②、已知参数:②. Known parameters:

q_ik:铸机i炉次k的钢水重量；q _ik : weight of molten steel in caster i furnace k;

v_ik:预选池铸机i炉次k是否优质品种钢；v _ik : whether heat k of pre-selected pool casting machine is high-quality steel;

wa_ik:预选池铸机i炉次k的断面规格；wa _ik : cross-sectional specification of furnace i heat k of pre-selection pool casting machine;

:铸机i待开浇炉次k^d的断面规格； : cross-sectional specification of casting machine i to be poured k ^d ;

ws_ik:预选池铸机i炉次k的拉速；ws _ik : Casting speed of furnace k of pre-selection pool casting machine i;

:铸机i待开浇炉次k^d的拉速； : Casting speed of casting machine i to be poured k ^d ;

rq_i:铸机i上遗留任务的钢水重量；rq _i : the molten steel weight of the remaining tasks on casting machine i;

ρ:钢液密度；ρ: molten steel density;

η:金属损耗系数；η: metal loss coefficient;

τ_s、τ_e:计划期开始时刻、结束时刻；τ _s , τ _e : the start time and end time of the planning period;

τ_A:全流程平均物流时间；τ _A : the average logistics time of the whole process;

:铸机i待开浇炉次k^d的浇铸周期； : Casting cycle of casting machine i to be poured k ^d ;

:铸机i炉次k的预定开浇时间； : Scheduled pouring time of heat number k of casting machine i;

e_i:铸机i炉次间断浇损失费用系数；e _i : cost coefficient of intermittent pouring loss of heat of casting machine i;

Q_rcon:随机波动需求金属量；Q _rcon : random fluctuation demand metal quantity;

δ^p、π^p、δ^p':遗留任务的优质品种钢比例、进铁与期初库存金属量的优质铁水比例；δ ^p , π ^p , δ ^p' : the proportion of high-quality steel for the remaining tasks, the proportion of high-quality molten iron between incoming iron and the amount of metal in stock at the beginning of the period;

ψ_i:准时开浇差异费用系数；ψ _i : difference cost coefficient for on-time pouring;

:相邻炉次间钢种差异引起的附加费用，若钢种代码相同0，仅属同钢种大类a₁，属不同钢种大类a₂； : the additional cost caused by the difference of steel grades between adjacent heats, if the codes of the steel grades are the same 0, it only belongs to the same steel grade a ₁ , and it belongs to the different steel grade a ₂ ;

:预定开浇时间差异附加费用，β₁为相邻炉次交货期差异的费用系数； : Additional charges for differences in scheduled pouring time, β ₁ is the cost coefficient of the difference in the delivery time of adjacent batches;

d_i:铸机i的炉次未被选做待开浇炉次延期损失费用系数；d _i : the heat of casting machine i is not selected as the delay loss cost coefficient of the heat to be poured;

M:惩罚因子，通过设置惩罚因子将非法解去除，M为足够大的正数，以确保解不满足约束时受到足够大的适应度值的惩罚；M: penalty factor, by setting the penalty factor to remove illegal solutions, M is a positive number large enough to ensure that the solution is punished with a sufficiently large fitness value when it does not meet the constraints;

:为量纲统一系数； : is the dimensional unity coefficient;

③、待求解的决策变量：③. Decision variable to be solved:

:铸机i被选做待开浇炉次k^d的开浇时刻； : Casting machine i is selected as the pouring start time of furnace time k ^d to be poured;

:二进制变量，1表示铸机i待开浇炉次k^d与其紧前炉次断浇，0表示与紧前炉次连浇； : Binary variable, 1 means caster i to be started pouring furnace k ^d and its immediately preceding furnace for interrupted pouring, 0 represents continuous pouring with the immediately preceding furnace;

z_ik:二进制变量，1表示预选池内铸机i内某炉次k被选中作为待开浇炉次，0表示某炉次k未被选中；z _ik : binary variable, 1 means that a furnace k in the casting machine i in the pre-selection pool is selected as the furnace to be poured, and 0 means that a furnace k is not selected;

S3，建立生产批量计划中预选池炉次与待开浇炉次关系的约束关系，金属资源平衡相关约束关系，连铸设备可用时间约束关系以及待开浇的炉次间的顺序及时间约束关系；S3. Establish the constraint relationship between the pre-selected pool heats and the heats to be poured in the production batch plan, the metal resource balance-related constraint relationship, the continuous casting equipment available time constraint relationship, and the order and time constraint relationship between the heats to be poured ;

S4，基于炉次序号选择进行编码并进行种群初始化；S4, select and encode based on the furnace sequence number and perform population initialization;

S5，解码并计算适应度值，获得初始解集，所述适应度函数为：S5, decode and calculate the fitness value to obtain the initial solution set, the fitness function is:

$\begin{matrix} min min & F f = = {{{f f}_{{eval eval}_{11}},, {f f}_{{eval eval}_{22}},, {f f}_{{eval eval}_{33}}}} \end{matrix} - - - - - - ((99))$

其中，in,

${f f}_{{eval eval}_{11}} = = {f f}_{11} - - - - - - ((1010))$

${f f}_{{eval eval}_{33}} = = {f f}_{33} + + M m \cdot \cdot m m a a x x {{{Q Q}_{D D.},, {Q Q}_{E E.} \cdot \cdot {π π}^{p p} + + {Q Q}_{I I V V} \cdot \cdot {δ δ}^{p p}}} - - - - - - ((1212))$

(9)式表示整个计算过程以求适应度函数的最小值为目标；Equation (9) expresses the whole calculation process to find the fitness function The minimum value of is the target;

(10)式表示适应度函数值等于目标函数值f₁；Equation (10) represents the fitness function value equal to the objective function value f ₁ ;

(11)式表示适应度函数值等于目标函数值f₂加上违反积压金属量关系约束的惩罚与开浇时间超越计划期的惩罚之和；Equation (11) represents the fitness function value It is equal to the sum of the objective function value f ₂ plus the penalty for violating the relationship constraints of the backlog metal quantity and the penalty for the pouring time exceeding the planned period;

(12)式表示适应度函数值等于目标函数值f₃与计划用优质铁水超出所能供应优质铁水所受惩罚之和；Equation (12) represents the fitness function value It is equal to the sum of the objective function value f ₃ and the penalty for planning to use high-quality molten iron beyond the supply of high-quality molten iron;

S6，对所述初始解集中的解进行非支配排序与拥挤距离排序；S6, performing non-dominated sorting and crowding distance sorting on the solutions in the initial solution set;

S7，选择步骤S6中种群中的一部分个体作为父代；S7, selecting a part of individuals in the population in step S6 as the parent generation;

S8，对步骤S7选出的父代按铸机分段的双亲双子多点交叉，以及按铸机分段取点随机变异，确保染色体特征与真实生产炉次序号特征的一致性；S8, for the parent generation selected in step S7 according to the multi-point crossover of the parent and child of the casting machine segment, and randomly mutating the points selected according to the casting machine segment, to ensure the consistency of the chromosome characteristics and the real production furnace sequence number characteristics;

S9，对步骤S8计算后的结果解码并计算适应度，所述适应度函数为步骤S5中的适应度函数；S9, decoding the result calculated in step S8 and calculating fitness, the fitness function being the fitness function in step S5;

S10，确定精英解集，限制计算拥挤距离个体数量，计算拥挤距离与排序；S10, determine the elite solution set, limit the number of individuals for calculating the crowding distance, calculate the crowding distance and sort;

S11，判断是否达到最大迭代次数，如果是，执行步骤S12，否则，执行步骤S7；S11, judging whether the maximum number of iterations is reached, if yes, execute step S12, otherwise, execute step S7;

S12，输出精英解集，用模糊选优方法选出最大满意度方案作为连铸开浇炉次时间决策方法；S12, output the elite solution set, and use the fuzzy optimal selection method to select the maximum satisfaction scheme as the decision-making method for the continuous casting furnace time;

S13，将最大满意度方案传输给炼钢-连铸生产运行控制系统，该系统按照所述最大满意度方案实现对各台连铸机上的待开浇炉次的选择、排序和开浇时间决策的有效生产运行控制。S13, the maximum satisfaction plan is transmitted to the steelmaking-continuous casting production operation control system, and the system realizes the selection, sorting and casting time decision of the heats to be started on each continuous casting machine according to the maximum satisfaction plan Effective production operation control.

本发明的连铸机开浇炉次与时间决策的多目标优化方法通过对钢厂连铸机开浇炉次与时间决策问题的分析，在综合考虑生产批量计划中的炉次与待开浇炉次的相互关系、金属资源平衡、连铸设备资源状况、炉次时间顺序等现实影响因素的基础上，建立了连铸开浇炉次与时间决策的多目标优化模型，并以非支配排序遗传算法(Non-dominatedSorting Genetic Algorithm,NSGAII)为基础设计了改进算法(Improved NSGAII，INSGAII)进行模型求解，提高了计算速度和准确性。The multi-objective optimization method of the continuous casting machine casting furnace and time decision-making method of the present invention is through the analysis of the continuous casting machine casting furnace and time decision-making problem in the steel plant, considering the furnace number and the time to be poured in the production batch plan comprehensively Based on the actual influencing factors such as the relationship between heats, metal resource balance, continuous casting equipment resource status, and time sequence of heats, a multi-objective optimization model for continuous casting casting heats and time decisions was established, and the non-dominated order Based on the genetic algorithm (Non-dominated Sorting Genetic Algorithm, NSGAII), an improved algorithm (Improved NSGAII, INSGAII) is designed to solve the model, which improves the calculation speed and accuracy.

本发明的附加方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

附图说明Description of drawings

本发明的上述和/或附加的方面和优点从结合下面附图对实施例的描述中将变得明显和容易理解，其中：The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

图1是本发明方法的算法流程图；Fig. 1 is the algorithm flowchart of the inventive method;

图2是本发明一种优选实施方式中基于炉次序号选择的编码示意图；Fig. 2 is a schematic diagram of encoding based on furnace sequence number selection in a preferred embodiment of the present invention;

图3是本发明一种优选实施方式中精英解集截断原理图；Fig. 3 is a schematic diagram of elite solution set truncation in a preferred embodiment of the present invention;

图4是本发明一种优选实施方式中模型决策适应度最小值进化过程Fig. 4 is the evolution process of the minimum value of model decision-making fitness in a preferred embodiment of the present invention

图5是本发明一种优选实施方式中决策甘特图；Fig. 5 is a decision-making Gantt chart in a preferred embodiment of the present invention;

图6是图5所示实例中人工决策的甘特图。FIG. 6 is a Gantt chart of human decision-making in the example shown in FIG. 5 .

具体实施方式detailed description

下面详细描述本发明的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，仅用于解释本发明，而不能理解为对本发明的限制。Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

炼钢厂通常具有执行不同类型任务(品种规格等)的多种类、多型号的连铸机。生产批量计划是由上层管理部门的生产指挥中心ERP按铸机以预定浇次的形式周期性地下达到钢厂MES(Manufacturing Execution System，MES)的计划预选池(简称预选池)，其信息通常包括分配到每台铸机上的浇次数量，浇次内各炉次所属钢种类别、断面规格及预定开浇时刻等，属于粗计划，在本实施方式中，断面规格为钢材的宽度尺寸与厚度尺寸。炼钢厂在制定炼钢-连铸生产调度计划之前，首先需要进行连铸开浇炉次与时间的决策。即需要根据批量计划信息、一段时期(简称计划期)内的预计进铁量、期初生产线的库存金属量、连铸设备任务状态等现实因素，具体决策从预选池内的各铸机的批量计划中选择哪些炉次作为本计划期的待开浇炉次，并决策各待开浇炉次是否与其前一炉次连浇及各炉次的开浇时刻。这种直接针对炉次进行连铸机浇铸任务安排的调度执行方式，更有利于发挥连铸机的连浇能力，实现钢厂的多目标管理要求。Steelworks usually have multiple types and models of continuous casting machines performing different types of tasks (species, etc.). The production batch plan is periodically undergrounded by the production command center ERP of the upper management department in the form of scheduled pouring times to the planned pre-selection pool (referred to as the pre-selection pool) of the steel plant MES (Manufacturing Execution System, MES), and its information usually includes The number of pouring times allocated to each casting machine, the type of steel to which each furnace belongs in the pouring time, the section specification and the scheduled start time of pouring, etc. belong to the rough plan. In this embodiment, the section specification is the width and thickness of the steel size. Before the steelmaking-continuous casting production scheduling plan is formulated, the steelmaking plant first needs to make a decision on the number and time of continuous casting casting. That is to say, it is necessary to make specific decisions from the batch planning of each casting machine in the pre-selection pool based on realistic factors such as batch planning information, expected iron intake within a certain period (referred to as the planning period), the amount of metal in stock in the production line at the beginning of the period, and the task status of continuous casting equipment. Select which heats are to be poured in this planning period, and decide whether each heat to be poured is continuous pouring with the previous heat and the pouring time of each heat. This method of scheduling and executing the casting task arrangement of the continuous casting machine directly for the furnace is more conducive to exerting the continuous casting ability of the continuous casting machine and realizing the multi-objective management requirements of the steel plant.

本发明方法可设置以下前提条件：①可根据进入预选池内的批量计划信息，按相同目标铸机所有炉次的预定开浇时间的先后顺序，进行炉次编号，以此区分每台连铸机上待确定的炉次基本信息；②计划期内，各铸机上的待开浇炉次仅在预选池内具有相同目标铸机的炉次中选取；③当预选池内存在未被选做在本计划期开浇的炉次时，可留作该铸机紧后计划期继续决策。The method of the present invention can set the following preconditions: ① According to the batch plan information entering the pre-selection pool, according to the order of the scheduled pouring time of all the furnaces of the same target casting machine, the numbering of the furnaces can be carried out, so as to distinguish each continuous casting machine. The basic information of the heats to be determined; ② During the planning period, the heats to be poured on each casting machine are only selected from the heats with the same target casting machine in the pre-selected pool; When the pouring furnace is started, it can be reserved for the casting machine's subsequent planning period to continue to make decisions.

优化目标：主要从有利于生产计划的有序进行及铁水等金属资源能有效利用的角度进行设计。以违反生产批量计划的惩罚、生产线上的积压金属量、优质铁水未有效利用量的最小化为优化的多目标。其中，对生产批量计划的违反惩罚主要涉及准时制要求下预选池内炉次的重新选择与排序问题，可借鉴组浇与准时制(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)惩罚方式来量化描述其执行效果；生产线上的积压金属量体现了计划期内的金属资源平衡关系，其量化表达式可描述为:[积压金属量]＝[期初在线库存金属量]+[累计进铁量]-[累计浇钢量]-[累计金属损耗量]-[期末在线安全库存金属量]，在线安全库存金属量有利于生产的稳定；优质铁水未有效利用量反映了钢厂需要将有限优质铁水资源用于生产优质品种钢的管理要求。Optimization objective: Design mainly from the perspectives that are conducive to the orderly progress of production planning and the effective utilization of metal resources such as molten iron. The multi-objective optimization is to minimize the penalty for violating the production batch plan, the backlog of metal on the production line, and the unutilized amount of high-quality molten iron. Among them, the punishment for violation of the production batch plan mainly involves the reselection and sequencing of heats in the pre-selection pool under the requirement of just-in-time system, which can be used for reference (Tang Lixin, Wang Mengguang, Yang Zihou. The optimal casting plan model and algorithm[J]. Iron and Steel, 1997,32(7):19-21) Quantitatively describe its execution effect by means of punishment; the backlog of metal on the production line reflects the balance of metal resources in the planning period Relationship, its quantitative expression can be described as: [backlog metal amount] = [beginning online inventory metal amount] + [accumulative iron intake amount] - [accumulative steel pouring amount] - [accumulative metal loss amount] - [period-end online safety stock metal quantity], online safety stock metal quantity is conducive to the stability of production; the unutilized amount of high-quality hot metal reflects the management requirements that steel mills need to use limited high-quality hot metal resources to produce high-quality steel.

约束条件：主要包括预选池内炉次与待开浇炉次的相互关系、金属资源平衡关系、连铸设备可用时间、炉次时间顺序关系等。Constraint conditions: mainly include the relationship between the heats in the pre-selected pool and the heats to be poured, the balance of metal resources, the availability time of continuous casting equipment, and the time sequence relationship of heats, etc.

为便于描述，定义模型求解涉及的主要符号如下：For the convenience of description, the main symbols involved in defining the solution of the model are as follows:

(1)符号与集合(1) Symbols and sets

j:预选池浇次序号，j_i∈J_i,J_i为预选池的连铸机i的浇次集合；j: the pouring sequence number of the pre-selection pool, j _i ∈ J _i , where J _i is the set of pouring times of the continuous casting machine i in the pre-selection pool;

(2)已知参数，其中括号内为单位或者取值，(2) Known parameters, where the units or values in brackets,

q_ik:铸机i炉次k的钢水重量(t)；q _ik : molten steel weight (t) of caster i furnace k;

mark_ik:预选池铸机i炉次k的钢种代码；mark _ik : the code of the steel grade of heat number k of pre-selection pool casting machine i;

stye_ik:预选池铸机i炉次k的钢种大类；stye _ik : the steel category of pre-selection pool caster i heat k;

v_ik:预选池铸机i炉次k是否优质品种钢(1为是，0为否)；v _ik : whether heat k of pre-selection pool caster i is high-quality steel (1 means yes, 0 means no);

wa_ik:预选池铸机i炉次k的断面规格(m²)；wa _ik : cross-sectional specification of furnace i heat k of pre-selection pool casting machine (m ² );

:铸机i待开浇炉次k^d的断面规格(m²)； : cross-sectional specification of casting machine i to be poured k ^d (m ² );

ws_ik:预选池铸机i炉次k的拉速(m·min^-1)；ws _ik : Casting speed of caster i heat k in the pre-selection pool (m min ^-1 );

:铸机i待开浇炉次kd的拉速(m·min^-1)； : Casting speed of casting machine i to be poured kd (m min ^-1 );

rq_i:铸机i上遗留任务的钢水重量(t)；rq _i : the molten steel weight (t) of the task left on casting machine i;

Rgrade_i:铸机i上遗留任务的钢种代码；Rgrade _i : the steel grade code of the task left on casting machine i;

rs_i:铸机i上遗留任务的浇铸速度(m·min^-1)；rs _i : the casting speed of the remaining tasks on casting machine i (m min ^-1 );

ra_i:铸机i上遗留任务的断面规格(m²)；ra _i : cross-sectional specification of the task left on casting machine i (m ² );

ρ:钢液密度(t·m^-3)；ρ: density of molten steel (t·m ^-3 );

η:金属损耗系数(t·t^-1)；η: metal loss coefficient (t t ^-1 );

τ_s、τ_e:计划期开始、结束时刻(min)；τ _s , τ _e : start and end time of the planning period (min);

τ_A:全流程平均物流时间(min)；τ _A : average logistics time of the whole process (min);

τ_ik:为预选池铸机i炉次k的浇铸周期(min)，τ_ik＝q_i/ρ·wa_ik·ws_ik；τ _ik : is the casting period (min) of heat k of the pre-selection pool casting machine i, τ _ik =q _i /ρ·wa _ik ·ws _ik ;

:铸机i待开浇炉次k^d的浇铸周期(min)； : Casting cycle of casting machine i to be poured k ^d (min);

:铸机i炉次间最小间隔时间(min)； : minimum interval time between heats of casting machine i (min);

:铸机i炉次k的预定开浇时间(min)； : Scheduled pouring time of heat number k of casting machine i (min);

:铸机i最大可用时间(min)； : Maximum available time of casting machine i (min);

:铸机i浇次间最早可用作业时间(min)； : The earliest available working time between pouring times of casting machine i (min);

e_i:铸机i炉次间断浇损失费用系数(CNY·Time^-1)；e _i : cost coefficient of intermittent pouring loss of casting machine i heat (CNY·Time ^-1 );

Q_E、Q_IV:计划期进铁量与期初生产线上库存金属量(t)；Q _E , Q _IV : iron intake during the planning period and metal stock on the production line at the beginning of the period (t);

Q_rcon:随机波动需求金属量(t)；Q _rcon : random fluctuation demand metal quantity (t);

ψ_i:准时开浇差异费用系数(CNY·Charge^-1)；ψ _i : difference cost coefficient for on-time pouring (CNY·Charge ^-1 );

:相邻炉次间钢种差异引起的附加费用，若钢种代码相同0(CNY·Charge^-1)，仅属同钢种大类a₁(CNY·Charge^-1)，属不同钢种大类a₂(CNY·Charge^-1)； : Additional charges caused by differences in steel grades between adjacent furnaces. If the codes of the steel grades are the same 0 (CNY·Charge ^-1 ), it only belongs to the same steel category a ₁ (CNY·Charge ^-1 ), and it belongs to different steel grades Class a ₂ (CNY·Charge ^-1 );

:预定开浇时间差异附加费用，β₁为相邻炉次交货期差异的费用系数(CNY·Charge^-1)； : Additional charges for differences in scheduled pouring time, β ₁ is the cost coefficient (CNY·Charge ^-1 ) of the difference in the delivery time of adjacent batches;

d_i:铸机i的炉次未被选做待开浇炉次延期损失费用系数(CNY·Charge^-1)；d _i : The heat of casting machine i is not selected as the delay loss cost coefficient of the heat to be poured (CNY·Charge ^-1 );

(3)决策变量(3) Decision variable

:铸机i被选做待开浇炉次k^d的开浇时刻(min)； : casting machine i is selected as the pouring time (min) of furnace time k ^d to be poured;

z_ik:二进制变量，1表示预选池内铸机i内某炉次k被选中作为待开浇炉次，0表示某炉次k未被选中。z _ik : binary variable, 1 means that a heat k in the casting machine i in the pre-selection pool is selected as the heat to be poured, and 0 means that a certain heat k is not selected.

本发明提供了的连铸机开浇炉次与时间决策的多目标优化方法，如图1所示，包括如下步骤：The multi-objective optimization method for continuous casting machine pouring and time decision-making provided by the present invention, as shown in Figure 1, includes the following steps:

S1，控制器与钢厂的MES数据库连接，获取钢厂MES计划预选池中的生产批量计划，其中批量计划中包括分配到每台铸机上的浇次数量、浇次内各炉次所属钢种类别、断面规格及预定开浇时刻，基于炉次序号选择进行编码并进行种群初始化；S1, the controller is connected to the MES database of the steel plant to obtain the production batch plan in the pre-selection pool of the steel plant MES plan, where the batch plan includes the number of pouring times allocated to each casting machine, and the steel types of each furnace in the pouring time The category, section specification and scheduled pouring time are selected and coded based on the furnace sequence number and the population is initialized;

S2，按违反生产批量计划的总惩罚、生产线上的积压金属量、优质铁水未有效利用量的最小化为决策目标，建立连铸开浇炉次与时间决策的多目标优化函数，目标函数方程如下:S2, according to the total penalty for violation of the production batch plan, the amount of backlog metal on the production line, and the minimization of the unutilized amount of high-quality molten iron as the decision-making objectives, establish a multi-objective optimization function for continuous casting casting and time decision-making, and the objective function equation as follows:

min F＝{f₁,f₂,f₃} (1)min F＝{f ₁ ,f ₂ ,f ₃ } (1)

其中，in,

${f f}_{11} = = {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} (({ξ ξ}_{i i k k ((k k + + 11))}^{11} + + {ξ ξ}_{i i k k ((k k + + 11))}^{22})) \cdot &Center Dot; {z z}_{i i k k} \cdot &Center Dot; {z z}_{i i ((k k + + 11))} + + {Σ Σ}_{i i = = 11}^{I I} {d d}_{i i} \cdot &Center Dot; (({K K}_{i i} - - {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k})) + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((| | {x x}_{{ik ik}^{d d}} - - {τ τ}_{{ik ik}^{d d}}^{d d a a t t e e} | | \cdot \cdot {ψ ψ}_{i i} + + {y the y}_{{ik ik}^{d d}} \cdot &Center Dot; {e e}_{i i})) - - - - - - ((22))$

f₂＝Q_O (3)f ₂ =Q _O (3)

${f f}_{33} = = {Q Q}_{E E.} \cdot \cdot {π π}^{p p} + + {Q Q}_{I I} \cdot &Center Dot; {δ δ}^{p p} - - {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k} \cdot \cdot {v v}_{i i k k} \cdot \cdot {q q}_{i i} \cdot \cdot \frac{11}{11 - - η η} - - - - - - ((44))$

Q_O＝Q_E+Q_IV-Q_C-Q_L-Q_S (5)Q _O ＝Q _E +Q _IV -Q _C -Q _L -Q _S (5)

${Q Q}_{C C} = = {Σ Σ}_{i i = = 11}^{I I} {rq rq}_{i i} + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((m m i i n no (({τ τ}_{e e},, {x x}_{{ik ik}^{d d}} + + {τ τ}_{{ik ik}^{d d}})) - - {x x}_{{ik ik}^{d d}})) \cdot \cdot ρ ρ \cdot &Center Dot; {wa w}_{{ik ik}^{d d}} \cdot &Center Dot; {ws ws}_{{ik ik}^{d d}} - - - - - - ((66))$

${Q Q}_{L L} = = {Q Q}_{C C} \cdot \cdot \frac{η η}{11 - - η η} - - - - - - ((77))$

${Q Q}_{S S} = = \frac{{Q Q}_{C C} \cdot \cdot {τ τ}_{A A}}{(({τ τ}_{e e} - - {τ τ}_{s the s})) \cdot \cdot ((11 - - η η))} + + {Q Q}_{r r c c o o n no} - - - - - - ((88))$

(2)式表示被选炉次相互间钢种差异惩罚费用和交货期差异费用、未开浇的剩余炉次的惩罚费用、各炉次未准时开浇惩罚费用之和最小；The formula (2) indicates that the sum of the penalty fee for the steel type difference between the selected furnaces and the delivery time difference fee, the penalty fee for the remaining furnaces that have not started pouring, and the penalty fee for each furnace that is not poured on time is the smallest;

(3)式表示生产线积压金属量Q_o最小；The formula (3) indicates that the backlog of metal Q _o in the production line is the smallest;

(4)式表示优质铁水未有效利用量最小；The formula (4) indicates that the unutilized amount of high-quality molten iron is the smallest;

(8)式表示在生产线安全库存金属量，它需要在生产线平均在库存金属量基础上加一个随机波动需求金属量Q_rcon，其中，平均在生产线库存金属量可依据“平均库存＝平均单位时间产出×平均流程时间”计算。Equation (8) represents the safe stock of metal in the production line. It needs to add a random fluctuating metal demand Q _rcon on the basis of the average stock of metal in the production line. Among them, the average stock of metal in the production line can be based on "average stock = average unit time Output × average process time" calculation.

其中，针对被选择炉次的排序问题，将在编码解码过程中通过被选炉次序号与开浇时间的对应关系来间接体现。Among them, regarding the ordering of the selected furnaces, it will be indirectly reflected through the corresponding relationship between the sequence number of the selected furnaces and the pouring time during the encoding and decoding process.

S3，建立生产批量计划中预选池炉次与待开浇炉次关系的约束关系，金属资源平衡相关约束关系，连铸设备可用时间约束关系以及待开浇的炉次间的顺序及时间约束关系；S3. Establish the constraint relationship between the heats in the pre-selected pool and the heats to be poured in the production batch plan, the constraints related to the balance of metal resources, the available time constraints of continuous casting equipment, and the sequence and time constraints between the heats to be poured ;

进行求解时的约束条件为：The constraints when solving are:

①生产批量计划中预选池炉次与待开浇炉次关系的约束：① Constraints on the relationship between pre-selection pool furnaces and to-be-cast furnaces in production batch planning:

${Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k} = = {K K}_{i i}^{d d},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]] - - - - - - ((99))$

${K K}_{i i}^{d d} &GreaterEqual; &Greater Equal; {K K}_{i i}^{n no},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]] - - - - - - ((1111))$

(9)式表示计划期内预选池内各连铸机被选中的炉次数量与各铸机待开浇炉次的数量之间的关系。Equation (9) expresses the relationship between the number of furnaces selected for each continuous casting machine in the pre-selection pool and the number of furnaces to be started for each casting machine within the planning period.

(10)式是为适应资源限制条件而设置，表示各铸机的待开浇炉数不超过预选池批量计划总炉数与该铸机产能需求的最小值，其中，表示向上取整，mean()表示计算平均值。Equation (10) is set up to adapt to resource constraints, indicating that the number of furnaces to be started for each casting machine does not exceed the minimum value of the total number of furnaces planned in the pre-selection pool and the capacity demand of the casting machine, where, Indicates rounding up, and mean() indicates calculating the average value.

(11)式为提高中间包及连铸设备利用率而设置，表示若铸机开浇则必须大于预定的该铸机最低浇铸炉数。Formula (11) is set up to improve the utilization rate of tundish and continuous casting equipment, which means that if the casting machine starts pouring, it must be greater than the predetermined minimum number of casting furnaces of the casting machine.

②金属资源平衡相关约束：②Constraints related to the balance of metal resources:

Q_O≥0 (12)Q _O ≥ 0 (12)

Q_D≤Q_E·π^p+Q_IV·δ^p’ (13)Q _D ≤ Q _E · π ^p + Q _IV · δ ^p' (13)

${Q Q}_{D D.} = = (({δ δ}^{p p} \cdot &Center Dot; {Σ Σ}_{i i = = 11}^{I I} {rq rq}_{i i} + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} {v v}_{{ik ik}^{d d}} \cdot &Center Dot; ((m m i i n no (({τ τ}_{e e},, {x x}_{{ik ik}^{d d}} + + {τ τ}_{{ik ik}^{d d}})) - - {x x}_{{ik ik}^{d d}})) \cdot &Center Dot; ρ ρ \cdot &Center Dot; {wa w}_{{ik ik}^{d d}} \cdot &Center Dot; {ws ws}_{{ik ik}^{d d}})) \cdot &Center Dot; 11 / / ((11 - - η η)) - - - - - - ((1414))$

(12)式的生产线积压金属量非负是为了确保计划期之间的生产稳定而设置。The non-negative metal backlog of the production line in formula (12) is set to ensure stable production between planning periods.

(13)式表示浇铸的优质品种钢所需优质铁水量不应超出期初库存与计划期进铁的优质铁水量之和。Formula (13) indicates that the amount of high-quality molten iron required for casting high-quality steel should not exceed the sum of the initial inventory and the amount of high-quality molten iron that is fed into the iron during the planning period.

(14)式表示浇铸优质品种钢所需要的优质铁水量Q_D，分别由遗留任务与待开炉次所需两部分优质铁水量构成。Equation (14) expresses the quantity Q _D of high-quality molten iron required for casting high-quality steel, which is composed of two parts of high-quality molten iron required for the remaining tasks and the time to be opened.

③连铸设备可用时间约束，被选定炉次的开浇时间不早于该铸机的最早可用时间。③Constraints on the available time of continuous casting equipment, the pouring time of the selected furnace should not be earlier than the earliest available time of the casting machine.

${τ τ}_{i i}^{e e a a r r l l i i e e s the s t t} \leq \leq {x x}_{{ik ik}^{d d}},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] - - - - - - ((1515))$

④待开浇的炉次间的顺序及时间约束：④Sequence and time constraints between furnaces to be poured:

${y the y}_{{ik ik}^{d d}} \{\begin{matrix} = = 11,, {wa w}_{{ik ik}^{d d}} &NotEqual; &NotEqual; {wa w}_{i i (({k k}^{d d} - - 11))},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] \\ = = 00,, {wa w}_{{ik ik}^{d d}} = = {wa w}_{i i (({k k}^{d d} - - 11))},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] \end{matrix} - - - - - - ((1616))$

${τ τ}_{s the s} \leq \leq {x x}_{{ik ik}^{d d}} \leq \leq {τ τ}_{e e},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[22,, {K K}_{i i}^{d d}]] - - - - - - ((1717))$

${τ τ}^{' '} + + {τ τ}_{i i}^{g g a a p p} \cdot \cdot {y the y}_{{ik ik}^{d d}} \leq \leq {x x}_{{ik ik}^{d d}} \leq \leq {τ τ}^{' '} + + (({τ τ}_{e e} - - {τ τ}^{' '})) \cdot &Center Dot; {y the y}_{{ik ik}^{d d}},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] - - - - - - ((1818))$

(16)式表示炉次间断面规格不同时强制断。The formula (16) indicates that the furnace breaks are forced to break when the specification of the section is different.

(17)式表示被选定的各待开浇炉次开浇时间处于计划期内。Equation (17) indicates that the pouring time of the selected heats to be poured is within the planning period.

(18)式表示当待开浇炉次与遗留任务连浇时，开浇时间点取遗留任务结束时刻，τ'＝rq_i/ρ·ra_i·rs_i，非连浇时，取遗留任务结束时刻加炉次间隔至计划期末间的某时刻，当各待开炉次相互间连浇时，该开浇时间点取前炉次结束时刻，非连浇时，取前炉次结束时刻加炉次间隔至计划期末间的某时刻， Equation (18) indicates that when the batch of furnaces to be poured is continuously poured with the leftover task, the time of the pouring start is taken as the end time of the leftover task, τ'=rq _i /ρ·ra _i ·rs _i , and when the continuous pouring is not performed, the leftover task is taken A certain time between the end time and the interval between furnace times and the end of the planning period, When the batches to be started are continuously poured, the time of starting the pouring is taken as the end time of the previous batch, In the case of non-continuous pouring, take the end time of the previous furnace and add the furnace interval to a certain time at the end of the planning period,

S4，基于炉次序号选择进行编码并进行种群初始化。S4, select and encode based on the furnace order number and perform population initialization.

S5，解码并计算适应度值，获得初始解集。由于金属资源约束(12)、(13)式同时受全体决策变量的影响，较难准确表达其与每个决策变量取值范围间的量化关系，为防止因取值等因素导致部分取值上限可能超出计划期上限τ_e，将与τ_e的关系也纳入惩罚函数构造中，适应度函数构造如下，利用适应度函数进行求解：S5, decode and calculate the fitness value, and obtain the initial solution set. Since metal resource constraints (12) and (13) are affected by all decision variables at the same time, it is difficult to accurately express the quantitative relationship between them and the value range of each decision variable. Values and other factors lead to some The upper limit of the value may exceed the upper limit of the planning period τ _e , and the The relationship with τ _e is also included in the construction of the penalty function. The fitness function is constructed as follows, and the fitness function is used to solve it:

$\begin{matrix} min min & F f = = {{{f f}_{{eval eval}_{11}},, {f f}_{{eval eval}_{22}},, {f f}_{{eval eval}_{33}}}} \end{matrix} - - - - - - ((1919))$

${f f}_{{eval eval}_{11}} = = {f f}_{11} - - - - - - ((2020))$

${f f}_{{eval eval}_{33}} = = {f f}_{33} + + M m \cdot &Center Dot; m m a a x x {{{Q Q}_{D D.},, {Q Q}_{E E.} \cdot &Center Dot; {π π}^{p p} + + {Q Q}_{I I V V} \cdot \cdot {δ δ}^{p p}}} - - - - - - ((22 twenty two))$

(19)式表示整个计算过程以求适应度函数的最小值为目标；Equation (19) expresses the whole calculation process to find the fitness function The minimum value of is the target;

(20)式表示适应度函数值等于目标函数值f₁；Equation (20) represents the fitness function value equal to the objective function value f ₁ ;

(21)式表示适应度函数值等于目标函数值f₂加上违反积压金属量关系约束的惩罚与开浇时间超越计划期的惩罚之和；Equation (21) represents the fitness function value It is equal to the sum of the objective function value f ₂ plus the penalty for violating the relationship constraints of the backlog metal quantity and the penalty for the pouring time exceeding the planned period;

(22)式表示适应度函数值等于目标函数值f₃与计划用优质铁水超出所能供应优质铁水所受惩罚之和；Equation (22) represents the fitness function value It is equal to the sum of the objective function value f ₃ and the penalty for planning to use high-quality molten iron beyond the supply of high-quality molten iron;

M为惩罚因子，通过设置惩罚因子将非法解去除，M为足够大的正数(需要根据具体问题具体确定，本文选取的是100000)，以确保解不满足约束时受到足够大的适应度值的惩罚(无具体规定，只要通过设置惩罚能将非法解去除即可，一般受到惩罚的适应度值应该至少高于未受到惩罚的适应度值一个数量级，否则，难于通过惩罚排除非法解)；M is the penalty factor, by setting the penalty factor to remove illegal solutions, M is a sufficiently large positive number (it needs to be determined according to the specific problem, this paper chooses 100000), to ensure that the solution does not meet the constraints and receives a large enough fitness value (There is no specific regulation, as long as the illegal solution can be removed by setting the penalty, the fitness value that is generally punished should be at least an order of magnitude higher than the fitness value that is not punished, otherwise, it is difficult to eliminate illegal solutions through punishment);

:为量纲统一系数； : is the dimensional unity coefficient;

获得有效的z_ik、及适应度函数后，依据z_ik与炉次序号对照表获得各待开炉次的批量计划信息，进而计算出包括等系数后即可计算个体的适应度值。get effective z _ik , and the fitness function, according to z _ik and furnace sequence number comparison table to obtain the batch planning information of each furnace to be opened, and then calculate the After equalizing the coefficients, the fitness value of the individual can be calculated.

S6，对初始解集中的解进行非支配排序与拥挤距离排序。S6, performing non-dominated sorting and crowding distance sorting on the solutions in the initial solution set.

S7，选择步骤S6中种群中的一部分规模的个体作为父代，在本发明的优选实施方式中，可以选择种群中的2/3，1/2，1/3或者1/4规模的个体作为父代，更优选选择1/2规模的个体作为父代，保证了计算的准确和快速。S7, select individuals of a part of the scale in the population in step S6 as parents, in a preferred embodiment of the present invention, individuals of 2/3, 1/2, 1/3 or 1/4 scale in the population can be selected as For the parent generation, it is more preferable to select individuals with a scale of 1/2 as the parent generation to ensure the accuracy and speed of calculation.

S8，对步骤S7选出的父代按铸机分段的双亲双子多点交叉，以及按铸机分段取点随机变异，确保染色体特征与真实生产炉次序号特征的一致性。S8, the multi-point crossover of parents and sons of the parent generation selected in step S7 according to the casting machine segment, and random mutation of points selected according to the casting machine segment, to ensure the consistency of the chromosome characteristics and the real production furnace sequence number characteristics.

S9，对步骤S8计算后的结果解码并计算适应度，所述适应度函数为步骤S5中的适应度函数。S9. Decode the result calculated in step S8 and calculate fitness, where the fitness function is the fitness function in step S5.

S10，确定精英解集，限制计算拥挤距离个体数量，计算拥挤距离与排序。S10, determine the elite solution set, limit the number of individuals for calculating the crowding distance, calculate the crowding distance and sort.

S11，判断是否达到最大迭代次数，如果是，执行步骤S12，否则，执行步骤S7。S11, judging whether the maximum number of iterations is reached, if yes, execute step S12, otherwise, execute step S7.

S12，输出精英解集，用模糊选优法选出最大满意度方案作为连铸开浇炉次时间决策方法。S12, output the elite solution set, and use the fuzzy optimization method to select the most satisfactory solution as the decision-making method for the continuous casting furnace time.

S13，将最大满意度方案传输给炼钢-连铸生产运行控制系统，该系统按照所述最大满意度方案实现对各台连铸机上的待开浇炉次选择、排序和开浇时间决策的有效生产运行控制。S13, transmit the maximum satisfaction plan to the steelmaking-continuous casting production operation control system, and the system realizes the selection, sorting and decision-making of the furnaces to be poured on each continuous casting machine according to the maximum satisfaction plan Effective production operation control.

本发明的方法求解以预选池内选择的炉次序号为基因进行编码，在精英解集策略中采取了调整传统计算顺序、限定计算拥挤距离个体数目的改进措施，最后利用对pareto解进行模糊选优的方法来确定最终优化解。The method of the present invention uses the sequence number of furnace selected in the pre-selection pool as the gene to code, adopts the improvement measures of adjusting the traditional calculation sequence and limiting the number of individuals in the calculation of crowding distance in the elite solution set strategy, and finally uses fuzzy selection of the Pareto solution method to determine the final optimal solution.

如图1所示，算法在初始化阶段，设计了一种批量计划与待开浇炉次关系约束足下、以炉次序号选择(即z_ik)为基因、通过解码求解炉次间是否连浇(即)、以及开浇时间(即)的分步处理法来减小解的无效搜索空间；在主循环的遗传操作阶段，采用按铸机分段的双亲双子多点交叉，与按铸机分段取点随机变异的办法以确保染色体特征与真实生产炉次序号特征的一致性；在主循环的非支配排序阶段，以不影响解的性能为前提，设计了以限制计算拥挤距离个体数量为核心的新方法，该方法通过只计算排序与纳入精英解集直接相关的个体的限制性措施，以减轻NSGAII在保留精英解环节的计算负荷，而在非支配排序、精英解集填充环节仍然采用NSGAII中的规则；在最终解形成阶段采用模糊选优技术从pareto解集中选出最终决策方案，以利于调度人员直接使用。As shown in Figure 1, in the initialization stage of the algorithm, a constraint on the relationship between the batch plan and the furnaces to be poured is designed, and the selection of the furnace sequence number (ie z _ik ) is used as the gene to solve whether continuous pouring between furnaces is performed by decoding ( which is ), and the pouring time (i.e. ) to reduce the invalid search space of the solution; in the genetic operation stage of the main cycle, the multi-point crossover of parents and children according to the casting machine segment, and the random mutation method of taking points according to the casting machine segment are used to ensure The consistency between the chromosome characteristics and the real production furnace sequence number characteristics; in the non-dominated sorting stage of the main cycle, on the premise that the performance of the solution is not affected, a new method is designed with the core of limiting the number of individuals to calculate the crowding distance. Computational sorting is directly related to the restrictive measures of individuals included in the elite solution set, so as to reduce the calculation load of NSGAII in the link of retaining elite solutions, while the rules in NSGAII are still used in the links of non-dominated sorting and elite solution set filling; in the final solution formation In the stage, fuzzy optimization technology is used to select the final decision-making scheme from the pareto solution set, so as to facilitate the direct use of dispatchers.

在本实施方式中，提高搜索效率，编码方法为：In this embodiment, to improve the search efficiency, the encoding method is:

S31，统计预选池内各铸机i的总炉次数K_i，对各炉次按批量计划预定的开浇时间先后排序，并依次给排序后的各炉赋予炉次序号，建立各铸机炉次序号参考表，在本实施方式中，要保证炉次序号的顺序与批量计划预定开浇时间顺序保持一致性，以保证后续运算的顺利进行。S31, count the total number of furnaces K _i of each casting machine i in the pre-selection pool, and start pouring time for each furnace according to the batch plan Sequentially sort, and sequentially assign furnace sequence numbers to each furnace after sorting, and establish a furnace sequence number reference table for each casting machine. In this embodiment, it is necessary to ensure that the sequence of furnace sequence numbers is consistent with the scheduled pouring time sequence of the batch plan , to ensure the smooth progress of subsequent operations.

S32，按约束(9-11)式中被选炉次数量范围，随机生成长度为K_i的各铸机二进制序列，与炉次序号参考表一一对应。例如，染色体(0,1,1,0,1)表示K_i＝5，对应参考表，第2、3、5炉次序号被选作待开浇炉次，第1、4炉次未被选中，同铸机基因段内的0-1比例可在满足约束要求的范围内变化。S32, according to the range of the number of furnaces selected in constraint (9-11), randomly generate a binary sequence of length K _i for each casting machine, corresponding to the reference table of furnace order numbers one by one. For example, chromosome (0,1,1,0,1) means K _i =5, Corresponding to the reference table, the serial numbers of furnaces 2, 3, and 5 are selected as furnaces to be poured, and furnaces 1 and 4 are not selected. The ratio of 0-1 in the gene segment of the same casting machine can be within the range that meets the constraint requirements internal changes.

S33，各铸机的染色体基因段相连接形成一条完整染色体，并随机产生设定规模的初始种群，基于炉次序号选择的编码如图2所示。S33, the chromosome gene segments of each casting machine are connected to form a complete chromosome, and an initial population of a set size is randomly generated, and the code selected based on the furnace sequence number is shown in Figure 2.

在本实施方式中，以炉次序号选择z_ik为基因的染色体在交叉变异过程中可能会出现非法解，为便于优化，在获得以炉次序号选择(即z_ik)为基因的编码串后，除了需要修复非法染色体z_ik，还需要依据约束条件先通过解码求解另外两类决策变量：炉次间是否连浇(即)、以及开浇时间(即)，并结合约束条件构建合适的适应度函数。解码过程如下:In this embodiment, the chromosome whose gene is selected by furnace order number z _ik may have an illegal solution during the crossover mutation process _. , in addition to repairing the illegal chromosome z _ik , it is also necessary to solve the other two types of decision variables by decoding according to the constraint conditions: whether continuous pouring between furnaces (ie ), and the pouring time (i.e. ), and construct a suitable fitness function in combination with constraints. The decoding process is as follows:

S41，处理非法染色体的：经交叉变异后的非法染色体可分为两类：被选待开浇炉次总数大于约束(10)使计算的炉次数量范围上限及小于约束(11)式计算的炉次数量范围下限，对于前者随机将多出约束上限个数的1变为0，对于后者随机将低于约束下限个数的0变为1，未违反约束的染色体不变；S41, dealing with illegal chromosomes: the illegal chromosomes after cross-mutation can be divided into two categories: the total number of furnaces selected to be poured is greater than the upper limit of the number of furnaces calculated by constraint (10) and less than the upper limit of the range of furnaces calculated by constraint (11) The lower limit of the number of furnaces, for the former, randomly change the number of 1s that exceed the upper limit of the constraint to 0, and for the latter, randomly change the number of 0s that are lower than the lower limit of the constraint to 1, and the chromosomes that do not violate the constraint remain unchanged;

S42，根据各铸机的染色体中从左到右出现1的炉次顺序产生待开浇炉次序列，对照参考表及批量计划中的炉次特征，结合约束(16)式产生 S42, according to the sequence of furnaces that appear 1 from left to right in the chromosomes of each casting machine, generate the sequence of furnaces to be poured, compare the reference table and the characteristics of the furnaces in the batch plan, and combine the constraint (16) to generate

Step3若待开炉次序列内的某炉次与前炉次断浇且有最早可用时间，按约束(15)、(17)式确定否则，按照约束(17-18)式确定 Step3 If a furnace in the sequence to be fired is interrupted from the previous furnace and has the earliest available time, it is determined according to the constraints (15) and (17) Otherwise, according to constraint (17-18) to determine

在本实施方式中，在获得适应度函数与z_ik、后，依据z_ik与炉次序号对照表获得各待开炉次的批量计划信息，进而计算出包括等系数后即可计算每条染色体的适应度值。In this embodiment, after obtaining the fitness function with z _ik , Finally, according to the comparison table of z _ik and furnace order number, the batch planning information of each batch to be opened is obtained, and then calculated including After equal coefficients, the fitness value of each chromosome can be calculated.

在本实施方式中，确定精英解集方法为：In this embodiment, the method for determining the elite solution set is:

S51，合并父代与子代染色体，定义个体间支配关系，按照支配关系给每个个体赋予序号等级并排序，产生不同序号等级的非支配个体集合，记录各序号等级内非支配个体数目。在本实施方式中，个体间支配关系是这样确定的：S51. Merge parent and offspring chromosomes, define dominance relationship among individuals, assign serial numbers and ranks to each individual according to the dominance relationship, generate non-dominated individual sets of different serial number levels, and record the number of non-dominated individuals in each serial number level. In this embodiment, the dominance relationship among individuals is determined as follows:

假设任何二解S1及S2对所有目标而言，S1均小于S2，则我们称S1支配S2，若S1的解没有被其他解所支配，则S1称为非支配解；若S1及S2对所有目标f1，f2，f3而言，f1(s1)<f1(s2),f2(s2)<f2(s2),f3(s1)>f3(s2)，也就是说，目标函数值之间难分大小，有相互支配的关系，称此时的S1，S2为非支配解；所有非支配解构成的集合即为pareto解集。Assume that any two solutions S1 and S2 are smaller than S2 for all targets, then we say that S1 dominates S2, and if the solution of S1 is not dominated by other solutions, then S1 is called a non-dominated solution; For the objectives f1, f2, and f3, f1(s1)<f1(s2), f2(s2)<f2(s2), f3(s1)>f3(s2), that is to say, the objective function values are indistinguishable There is a relationship of dominance between them, so S1 and S2 at this time are called non-dominated solutions; the set of all non-dominated solutions is the pareto solution set.

S52，依据精英解集容量、各序号等级内非支配个体数目、序号等级的从小到大顺序，确定精英解集所能容纳的最大序号，依据人为设定的精英解集容量大小，确定其所能容纳的最大序号，小于等于该序号值的个体需要计算拥挤距离，超出该序号范围内的个体不计算拥挤距离也不排序，直接被抛弃；S52, according to the capacity of the elite solution set, the number of non-dominated individuals in each sequence number level, and the order of the sequence number levels from small to large, determine the maximum sequence number that the elite solution set can accommodate, and determine the size of the elite solution set according to the artificially set capacity of the elite solution set The maximum serial number that can be accommodated. Individuals that are less than or equal to the value of the serial number need to calculate the crowding distance. Individuals that exceed the range of the serial number will not calculate the crowding distance and will not be sorted, and will be discarded directly;

S53，计算精英解集内与当前非支配等级下解的个数总和，并判断所述解的个数总和是否大于精英解集规模，如果是，执行步骤S54，如果不是，执行步骤S55；S53, calculate the sum of the number of solutions in the elite solution set and the current non-dominated level, and judge whether the sum of the numbers of the solutions is greater than the size of the elite solution set, if yes, execute step S54, if not, execute step S55;

S54，计算当前非支配等级个体的拥挤距离并降序排列，将精英解按拥挤距离从大到小顺序依次加入精英解集；S54, calculate the crowding distance of the current non-dominated individuals and arrange them in descending order, and add the elite solutions to the elite solution set in order of crowding distance from large to small;

S55，计算当前非支配等级下的拥挤距离并将精英解加入精英解集；S55, calculating the crowding distance under the current non-dominated level and adding the elite solution to the elite solution set;

S56，判断是否达到精英解集规模，如果达到，则执行如说明书中步骤S11，如果没达到，则令非支配等级加1，执行步骤S53。S56, judging whether the scale of the elite solution set has been reached, if so, execute step S11 in the description, if not, increase the non-dominated level by 1, and execute step S53.

在本实施方式中，精英解加入精英解集的规则为：设定精英解集大小，在其中按等级排序号从小到大顺序添加个体，直到精英解集被填满，同一序号等级内，当遇上排序号相同的两个体时，优先添加拥挤距离大的个体，超出精英解集大小的个体被抛弃。In this embodiment, the rules for adding elite solutions to the elite solution set are as follows: set the size of the elite solution set, and add individuals in ascending order according to the ranking number until the elite solution set is filled. When encountering two individuals with the same sort number, the individual with the largest crowding distance is added first, and the individual that exceeds the size of the elite solution set is discarded.

精英解策略的目的是确保优良的父代炉次能顺利进入子代。如图3所示，传统NSGAII的精英解集策略的步骤为:The purpose of the elite solution strategy is to ensure that the good heat of the parent generation can enter the offspring smoothly. As shown in Figure 3, the steps of the elite solution set strategy of traditional NSGAII are:

①定义个体间支配关系，按照支配关系给每个个体赋予序号等级并排序，产生不同序号等级的非支配个体集合；①Define the dominance relationship among individuals, assign serial numbers to each individual according to the dominance relationship and sort them, and generate non-dominated individual sets with different serial numbers;

②根据相邻个体适应度值计算该集合中所有序号的个体间的拥挤距离；②Calculate the crowding distance between individuals of all serial numbers in the set according to the fitness value of adjacent individuals;

③设定精英解集大小，在其中按等级排序号从小到大顺序添加个体，直到精英解集被填满，同一序号等级内，当遇上排序号相同的两个体时，优先添加拥挤距离大的个体，超出精英解集大小的个体被抛弃，该过程又称为精英解集截断，精英解集截断原理如图3所示。③Set the size of the elite solution set, and add individuals in ascending order according to the ranking number until the elite solution set is filled. In the same serial number level, when two individuals with the same sorting number are encountered, the priority is to add individuals with the largest crowding distance. Individuals exceeding the size of the elite solution set are discarded. This process is also called elite solution set truncation. The principle of elite solution set truncation is shown in Figure 3.

NSGAII在计算拥挤距离过程中，计算且排序了大量超出精英解集容量的、序号等级较高且会被抛弃的非支配个体的拥挤距离，当问题规模较大且迭代次数较多时，时间浪费将较突出。为此，INSGAII的改进或调整如下：In the process of calculating the crowding distance, NSGAII calculates and sorts the crowding distances of a large number of non-dominated individuals that exceed the capacity of the elite solution set, have higher serial numbers and will be discarded. When the problem scale is large and the number of iterations is large, the time wasted will be more prominent. To this end, the improvements or adjustments of INSGAII are as follows:

Step1，除NSGAII步骤①内容外，记录各序号等级内非支配个体数目；Step1, except for the content of NSGAII step ①, record the number of non-dominated individuals in each serial number level;

Step2，依据精英解集容量、各序号等级内非支配个体数目、序号等级的从小到大顺序，确定精英解集所能容纳的最大序号；Step2, according to the capacity of the elite solution set, the number of non-dominated individuals in each sequence number level, and the order of the sequence number levels from small to large, determine the maximum sequence number that the elite solution set can hold;

Step3，依据Step2确定的序号计算各等级内的拥挤距离并排序，并按NSGAII步骤③的规则填充精英解集。Step3, calculate and sort the crowding distances in each level according to the serial numbers determined in Step2, and fill the elite solution set according to the rules of NSGAII step ③.

INSGAII改变了NSGAII中拥挤距离与精英解集填充顺序，只计算了与纳入精英解集相关的部分非支配个体的拥挤距离(如图3中方括号范围内个体)，不计算与排序会被抛弃且序号大于精英解集将被填满时所含最大序号的非支配个体(图3集合B中带#号的个体)的拥挤距离，为节约计算时间创造了条件。INSGAII changed the crowding distance and filling order of the elite solution set in NSGAII, and only calculated the crowding distance of some non-dominated individuals related to the inclusion of the elite solution set (individuals within the square brackets in Figure 3), and the calculation and sorting would be discarded and The crowding distance of the non-dominated individual whose serial number is greater than the maximum serial number contained when the elite solution set will be filled (individual with # in Figure 3 set B) creates conditions for saving calculation time.

在本实施方案中，遗传操作包括交叉和变异，其中，交叉为:由于各铸机编码段直接对应于生产批量计划的特征，若对整条染色体随机选点交叉，可能大量出现炉次序号选择特征与铸机真实参数不一致的现象。为此，采用按铸机分段的双亲双子多点交叉办法:①先取两条不同的完整的染色体，②将其按各铸机染色体长度分成i段，③在每个铸机染色体段内随机选取交叉点交叉。In this embodiment, the genetic operation includes crossover and mutation, wherein, the crossover is: because each casting machine coding segment directly corresponds to the characteristics of the production batch plan, if the entire chromosome is randomly selected for crossover, a large number of furnace sequence number selections may occur The phenomenon that the characteristics are inconsistent with the real parameters of the casting machine. For this reason, the method of multi-point crossover of parents and sons divided by casting machine is adopted: ① take two different complete chromosomes first, and ② divide them according to the chromosome length of each casting machine Divide into i segments, ③randomly select intersection points in each caster chromosome segment to intersect.

变异:将各铸机染色体长度分成i段，在每个铸机染色体段内随机选取变异点：若变异点的值为0则变为1，否则由1变为0。Variation: change the chromosome length of each casting machine Divide into i segments, and randomly select mutation points in each caster chromosome segment: if the value of the mutation point is 0, it becomes 1, otherwise it changes from 1 to 0.

在本实施方式中，求解的结果是以适应度值表示的精英解集合，为便于调度人员直接应用，先用(19-21)式将其转换为目标函数值集合，再通过模糊选优法从中确定最优折中解。模糊选优方法如下:In this embodiment, the result of the solution is an elite solution set represented by the fitness value. In order to facilitate the direct application of the dispatcher, it is first converted into a set of objective function values using formula (19-21), and then through the fuzzy optimization method Determine the optimal compromise solution from it. The fuzzy selection method is as follows:

S71，计算目标函数值集合中每个个体的比重ω_(r,m)，ω_(r,m)表示个体r中第m个目标函数值所占比重，分别表示目标函数值集合中的第m个目标函数值的最小、最大值:S71, calculate the proportion ω _{(r, m)} of each individual in the objective function value set, ω _{(r, m)} represents the proportion of the mth objective function value in the individual r, respectively represent the minimum and maximum value of the mth objective function value in the objective function value set:

${ω ω}_{((r r,, m m))} = = \{\begin{matrix} 11,, & {f f}_{((r r,, m m))} \leq \leq {f f}_{((m m))}^{min min} \\ \frac{{f f}_{((m m))}^{max max} - - {f f}_{((r r,, m m))}}{{f f}_{((m m))}^{max max} - - {f f}_{((m m))}^{min min}},, & {f f}_{((m m))}^{min min} < < {f f}_{{eval eval}_{((r r,, m m))}} < < {f f}_{((m m))}^{max max} \\ 00,, & {f f}_{((r r,, m m))} &GreaterEqual; &Greater Equal; {f f}_{((m m))}^{max max} \end{matrix} - - - - - - ((23 twenty three))$

S72，标准化所有个体的满意度ω_r，其中N为精英解集的种群规模；S72, standardize the satisfaction ω _r of all individuals, where N is the population size of the elite solution set;

${ω ω}_{r r} = = \frac{{Σ Σ}_{m m = = 11}^{44} {ω ω}_{((r r,, m m))}}{{Σ Σ}_{r r = = 11}^{N N} {Σ Σ}_{m m = = 11}^{44} {ω ω}_{((r r,, m m))}} - - - - - - ((24 twenty four))$

S73，取标准化满意度最大的个体为最终开浇炉次与时间决策方案z_ik、 S73, take the individual with the greatest standardization satisfaction z _ik ,

以国内某钢厂连铸机开浇炉次与时间决策的实际生产数据为基础，进行模型实例验证，模型适应性及算法性能测试，来检验模型及算法的有效性。Based on the actual production data of the continuous casting machine casting furnace and time decision in a domestic steel plant, the model instance verification, model adaptability and algorithm performance testing are carried out to verify the effectiveness of the model and algorithm.

模型验证实例：该厂有5台连铸机，生产中的开浇炉次与时间决策由人工经验的方式完成，简称人工决策。以日作业时间为计划期，取生产实绩数据作为人工决策结果，并以此作为模型决策实例验证比较的基础。生产输入数据分别见表1-3，限于篇幅，表1只给出批量计划浇次第一炉预定开始时间同浇次内其余各炉预定开始时间在此基础上依次加τ_ik。Example of model verification: There are 5 continuous casting machines in the factory, and the decision-making of casting furnaces and time in production is completed by manual experience, referred to as manual decision-making. Taking the daily operation time as the planning period, the actual production performance data is taken as the result of manual decision-making, and it is used as the basis for verification and comparison of model decision-making examples. The production input data are shown in Table 1-3 respectively. Due to space limitations, Table 1 only shows the scheduled start time of the batch plan pouring times and the first furnace Add τ _ik sequentially to the scheduled start time of other furnaces within the same pouring time on this basis.

为测试模型适应性及算法性能，首先，以表1-3数据为依据，通过改变参数I、∑K_i、Q_E、τ_A的取值形成4种不同规模的问题，其中，参数I＝2表示仅第1、2号铸机浇铸，I＝3表示仅第1、2、3号铸机浇铸，以此类推；其次，另外构造三种对比算例，通过用不同算例分别求解4种不同规模问题的结果比较来测试模型的适应性与算法的性能。对比算例的构造目的及特征描述如下：In order to test the adaptability of the model and the performance of the algorithm, firstly, based on the data in Table 1-3, four kinds of problems of different scales are formed by changing the values of the parameters I, ∑K _i , Q _E , and τ _A , where the parameter I= 2 means only No. 1 and No. 2 casting machines are casting, I=3 means only No. 1, 2 and No. 3 casting machines are casting, and so on; secondly, construct three comparison examples, and solve 4 by using different examples The results of different scale problems are compared to test the adaptability of the model and the performance of the algorithm. The construction purpose and characteristics of the comparison example are described as follows:

(1)为验证所选多目标算法的有效性，设计一种基于强度Pareto进化算法(Strength Pareto Evolutionary Algorithm,SPEAII),其编码与解码同本文。(1) In order to verify the effectiveness of the selected multi-objective algorithm, a strength-based Pareto evolutionary algorithm (Strength Pareto Evolutionary Algorithm, SPEAII) is designed, and its encoding and decoding are the same as in this paper.

(2)为同时效验所选编码方式与改进的精英解策略的有效性，以NSGAII为基础，以炉次序号为基因进行编码，遗传操作与精英解策略同文献(DEB K,PRATAP A,AGARWAL S,etal.A fast and elitist multi-objective genetic algorithm:NSGA-II[J].IEEETransactions on Evolutionary Computation,2002,6(2):182-197)，记为NSGAII①；(2) In order to verify the effectiveness of the selected coding method and the improved elite solution strategy at the same time, based on NSGAII, the furnace sequence number is used as the gene to encode, and the genetic operation and elite solution strategy are the same as the literature (DEB K, PRATAP A, AGARWAL S, etal. A fast and elitist multi-objective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197), denoted as NSGAII①;

(3)为效验精英解集改进策略的效果，采用本文编码方式，遗传操作与精英解策略同第(2)点中的文献，记为NSGAII②；(3) In order to verify the effect of the elite solution set improvement strategy, the coding method in this article is adopted, and the genetic operation and elite solution strategy are the same as those in point (2), denoted as NSGAII②;

各对比算例的最终Pareto解集选优方式与本文相同，性能测试均取10次运行的平均值。The optimal selection method of the final Pareto solution set of each comparative example is the same as that of this paper, and the performance test takes the average value of 10 runs.

以matlab7.0a为平台编程，各算例在Intel(R)Core(TM)i3-4010U/1.70GHz/4.00GB/WIN7环境中独立运行，其中算例参数设置为:种群大小40，迭代次数100，交叉概率0.8，变异概率0.2，此外，SPEAII的外部种群大小为40。Using matlab7.0a as the platform programming, each calculation example runs independently in the Intel(R) Core(TM) i3-4010U/1.70GHz/4.00GB/WIN7 environment, and the calculation example parameters are set as: population size 40, iteration number 100 , the crossover probability is 0.8, and the mutation probability is 0.2. In addition, the external population size of SPEAII is 40.

表1批量计划主要参数Table 1 Main parameters of batch planning

表2铸机主要参数Table 2 Main parameters of casting machine

表3辅助参数Table 3 Auxiliary parameters

图4是本发明的最小适应度值进化过程；表4是两种决策方式的目标函数值比较情况，其中本发明决策的结果为pareto解集，序号14对应目标函数值为pareto解集的模糊选优结果，人工与模型决策的目标函数值计算方式相同；图5是表4中第14号方案对应的本发明决策方案甘特图；图6是人工决策甘特图。Fig. 4 is the minimum fitness value evolution process of the present invention; Table 4 is the objective function value comparison situation of two kinds of decision-making modes, wherein the result of the decision-making of the present invention is the Pareto solution set, and the corresponding objective function value of sequence number 14 is fuzzy of the Pareto solution set As a result of the selection, the calculation method of the objective function value of manual and model decision-making is the same; Fig. 5 is a Gantt diagram of the decision-making scheme of the present invention corresponding to No. 14 scheme in Table 4; Fig. 6 is a Gantt diagram of manual decision-making.

表4两种决策方式目标函数值比较Table 4 Comparison of objective function values of two decision-making methods

由图4-图6以及表4可见，本发明的方法有利于炉次浇铸周期的稳定控制。在相同金属资源量情况下，因可在工艺要求范围内提前设定铸机拉速、安排各铸机各炉次的开浇时刻及浇铸炉数，有效避免了浇铸周期波动现象。人工决策由于缺乏对多铸机下开浇炉次与时间优化决策的手段，一旦人为决定铸机开浇后，只能通过频繁调整铸机拉速以维持铸机连续浇铸，导致至少15炉次出现浇铸周期剧烈波动。炉次浇铸周期的频繁波动可严重制约铸坯质量的提高。It can be seen from Fig. 4-Fig. 6 and Table 4 that the method of the present invention is beneficial to the stable control of the casting cycle of the heat. In the case of the same amount of metal resources, the caster casting speed can be set in advance within the range of process requirements, and the pouring time and number of casting furnaces of each caster can be arranged in advance, effectively avoiding the phenomenon of casting cycle fluctuations. Manual decision-making due to the lack of means to optimize decision-making on the number of furnaces and time for multiple casting machines, once the casting machine is artificially decided to start casting, the casting machine can only be adjusted frequently to maintain the continuous casting of the casting machine, resulting in at least 15 furnaces There are drastic fluctuations in the casting cycle. Frequent fluctuations in the casting cycle of heats can seriously restrict the improvement of billet quality.

本发明的方法有助于炼钢连铸推行计划管理。本发明方法的第1、第2个目标函数值较人工决策优，而第三个目标函数值稍差，原因是模型决策可在全局范围内寻优；而人工决策虽能通过调换1#、2#铸机上待开浇炉次浇铸顺序、甚至任意添加非本计划期的品种钢(图6中炉次号NaN)来优化第三个目标，但因不能准确确定各待开浇炉次的类别、数量、顺序以及开浇时间，导致了第1、第2个目标函数值恶化。从甘特图特征可见，模型决策有助于其使用者将上层批量计划与钢厂作业计划相连接，以便在炼钢连铸推行计划管理。The method of the invention is helpful to the implementation plan management of steelmaking and continuous casting. The 1st, the 2nd objective function value of the inventive method are better than manual decision-making, and the 3rd objective function value is slightly poorer, and reason is that model decision-making can be optimized in the global scope; The casting sequence of the heats to be poured on the 2# casting machine, or even arbitrarily adding steels that are not in the planned period (heat number NaN in Figure 6) to optimize the third goal, but the category of each heat to be poured cannot be accurately determined , quantity, sequence and pouring time lead to the deterioration of the first and second objective function values. It can be seen from the characteristics of the Gantt chart that model decision-making helps its users connect the upper-level batch planning with the steel plant operation plan, so as to implement plan management in steelmaking and continuous casting.

针对现实生产环境中的连铸机开浇炉次与时间决策问题涉及影响因素多，人工决策随意性大的现象，本发明在综合考虑批量计划预选池炉次与待开浇炉次关系、金属资源平衡、连铸设备可用时间、待开浇炉次间时间顺序等约束基础上，建立了以批量计划违反总惩罚、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、生产工艺及生产组织要求为约束的连铸机开浇炉次与时间决策多目标优化模型。Aiming at the fact that in the real production environment, the decision-making problem of casting furnaces and time of continuous casting machine involves many influencing factors and the phenomenon that manual decision-making is arbitrarily large, the present invention comprehensively considers the relationship between the batch planning preselection pool furnaces and the furnaces to be poured, metal On the basis of constraints such as resource balance, continuous casting equipment availability time, and time sequence between furnaces to be poured, an objective function was established with the total penalty for violation of the batch plan, the amount of backlog metal in the production line, and the minimum non-effective utilization of high-quality molten iron as the objective function, and the production process and The production organization requires a multi-objective optimization model for constrained continuous casting machine casting heats and time decision-making.

设计了适合该模型特点的改进非支配排序遗传算法INSGAII。该算法以炉次序号选择为基因，通过解码产生另外两个决策变量的分步处理法来减小解的无效搜索空间，采取调整传统精英解集计算顺序、限定计算排序非支配个拥挤距离的新措施以减轻保留精英解环节的计算负荷，对最终精英解集进行模糊选优来生成便于直观理解的模型优化解，以便于模型使用人员参考。An improved non-dominated sorting genetic algorithm INSGAII suitable for the characteristics of the model is designed. The algorithm takes the selection of furnace sequence number as the gene, and reduces the invalid search space of the solution through the step-by-step processing method of decoding and generating the other two decision variables. New measures are taken to reduce the calculation load of the elite solution link, and fuzzy optimization is performed on the final elite solution set to generate a model optimization solution that is easy to understand intuitively, so that model users can refer to it.

实验测试结果表明:模型有利于对连铸生产各炉次浇铸周期的稳定控制，并有利于炼钢－连铸生产切实推行计划管理；同时算法性能试验表明：本发明的改进非支配排序遗传算法INSGAII较传统非支配排序遗传算法NSGAII及强度pareto进化算法SPEAII，在求解连铸开浇炉次时间决策多目标问题中有更高效率。Experimental test results show that: the model is beneficial to the stable control of the casting cycle of each furnace in continuous casting production, and is conducive to the practical implementation of plan management in steelmaking-continuous casting production; at the same time, the algorithm performance test shows that: the improved non-dominated sorting genetic algorithm of the present invention Compared with the traditional non-dominated sorting genetic algorithm NSGAII and the intensity pareto evolutionary algorithm SPEAII, INSGAII has higher efficiency in solving the multi-objective problem of continuous casting furnace time decision-making.

在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

尽管已经示出和描述了本发明的实施例，本领域的普通技术人员可以理解：在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and modifications can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims

1. A multi-objective optimization method for continuous casting unit pouring time selection, sorting and pouring time decision-making, characterized in that it comprises the following steps:

S1, the controller is connected to the MES database of the steel plant to obtain the production batch plan in the pre-selected pool of the steel plant MES plan, the batch plan includes the number of pouring times allocated to each casting machine, the steel of each furnace in the pouring time Types, section specifications and scheduled pouring time;

S2, establishing an objective function that minimizes the total penalty for the implementation of the production batch plan of the steelworks, the amount of backlogged metal in the production line, and the non-effective utilization of high-quality molten iron. The objective function is:

min F＝{f ₁ ,f ₂ ,f ₃ } (1)

in,

{f f}_{11} = = {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} (({ξ ξ}_{i i k k ((k k + + 11))}^{11} + + {ξ ξ}_{i i k k ((k k + + 11))}^{22})) \cdot &Center Dot; {z z}_{i i k k} \cdot \cdot {z z}_{i i ((k k + + 11))} + + {Σ Σ}_{i i = = 11}^{I I} {d d}_{i i} \cdot \cdot (({K K}_{i i} - - {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k})) + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((| | {x x}_{{ik ik}^{d d}} - - {τ τ}_{{ik ik}^{d d}}^{d d a a t t e e} | | \cdot \cdot {ψ ψ}_{i i} + + {y the y}_{{ik ik}^{d d}} \cdot &Center Dot; {e e}_{i i})) - - - - - - ((22))

f ₂ =Q _O (3)

{f f}_{33} = = {Q Q}_{E E.} \cdot &Center Dot; {π π}^{p p} + + {Q Q}_{I I} \cdot &Center Dot; {δ δ}^{p p} - - {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k} \cdot \cdot {v v}_{i i k k} \cdot \cdot {q q}_{i i} \cdot \cdot \frac{11}{11 - - η η} - - - - - - ((44))

Q _O ＝Q _E +Q _IV -Q _C -Q _L -Q _S (5)

{Q Q}_{C C} = = {Σ Σ}_{i i = = 11}^{I I} {rq rq}_{i i} + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} ((min min (({τ τ}_{e e},, {x x}_{{ik ik}^{d d}} + + {τ τ}_{{ik ik}^{d d}})) - - {x x}_{{ik ik}^{d d}})) \cdot \cdot ρ ρ \cdot \cdot {wa w}_{{ik ik}^{d d}} \cdot \cdot {ws ws}_{{ik ik}^{d d}} - - - - - - ((66))

{Q Q}_{L L} = = {Q Q}_{C C} \cdot &Center Dot; \frac{η η}{11 - - η η} - - - - - - ((77))

{Q Q}_{S S} = = \frac{{Q Q}_{C C} \cdot &Center Dot; {τ τ}_{A A}}{(({τ τ}_{e e} - - {τ τ}_{s the s})) \cdot \cdot ((11 - - η η))} + + {Q Q}_{r r c c o o n no} - - - - - - ((88))

The formula (2) represents the sum of the penalty fee for the steel type difference among the selected furnaces and the difference fee for the delivery date, the penalty fee for the remaining furnaces that have not started pouring, and the penalty fee for each furnace not being poured on time;

The formula (3) represents the backlog of metal quantity Q _o in the production line;

The formula (4) represents the unutilized amount of high-quality molten iron;

Equation (5) represents the amount of backlog metal, which is set based on the balance of metal resources in the production line. It consists of iron intake Q _E in the planning period, metal inventory on the production line at the beginning of the period Q _IV , continuous casting steel pouring Q _C , and metal loss Q _L , which is conducive to stable production and constitutes the metal quantity Q _S of the production line safety stock at the end of the period;

Formula (6) indicates that the steel pouring amount of each continuous casting machine is composed of the steel pouring amount of the remaining tasks in the previous planning period and the steel pouring amount of each furnace in the pouring time to be started;

Formula (7) represents the amount of metal loss corresponding to the amount of poured steel;

Equation (8) represents the safe stock metal quantity in the production line, which needs to add a random fluctuating demand metal quantity Q _rcon on the basis of the average stock metal quantity of the production line;

Among them, the specific meaning of the symbol is:

①. Defined symbols and sets:

i: serial number of the casting machine, i∈I, I is the set of continuous casting machines;

k: Furnace sequence number of each casting machine in the pre-selection pool, k∈K _i , K _ij is the set of casting times j of casting machine i in the pre-selection pool, K _i is the set of all heats of continuous casting machine i in the pre-selection pool, and k is generated successively according to the scheduled start-up time of each casting machine;

k ^d : the sequence number of the furnace to be poured, is the set of furnaces to be poured for continuous casting machine i, is the scheduled minimum number of pouring furnaces for casting machine i;

②. Known parameters:

q _ik : weight of molten steel in caster i furnace k;

v _ik : whether heat k of pre-selected pool casting machine is high-quality steel;

wa _ik : cross-sectional specification of furnace i heat k of pre-selection pool casting machine;

Cross-sectional specification of casting machine i to be poured k ^d ;

ws _ik : Casting speed of furnace k of pre-selection pool casting machine i;

The casting speed of casting machine i to be poured k ^d ;

rq _i : the molten steel weight of the remaining tasks on casting machine i;

ρ: molten steel density;

η: metal loss coefficient;

τ _s , τ _e : the start time and end time of the planning period;

τ _A : the average logistics time of the whole process;

Casting cycle of casting machine i to be poured k ^d ;

Scheduled pouring time of heat number k of casting machine i;

e _i : cost coefficient of intermittent pouring loss of heat of casting machine i;

Q _rcon : random fluctuation demand metal quantity;

δ ^p , π ^p , δ ^p' : the proportion of high-quality steel for the remaining tasks, the proportion of high-quality molten iron between incoming iron and the amount of metal in stock at the beginning of the period;

ψ _i : difference cost coefficient for on-time pouring;

The additional cost caused by the steel type difference between adjacent heats, if the steel type codes are the same 0, only belong to the same steel type category a ₁ , and belong to different steel type category a ₂ ;

Surcharges for scheduled pouring time differences, β ₁ is the cost coefficient of the difference in the delivery time of adjacent batches;

d _i : the heat of casting machine i is not selected as the delay loss cost coefficient of the heat to be poured;

M: penalty factor, by setting the penalty factor to remove illegal solutions, M is a positive number large enough to ensure that the solution is punished with a sufficiently large fitness value when it does not meet the constraints;

is the dimensional unity coefficient;

③. Decision variable to be solved:

Casting machine i is selected as the pouring time of furnace k ^d to be poured;

Binary variable, 1 means caster i to be started pouring heat k ^d and its immediate preceding heat interrupted pouring, 0 means continuous pouring with the immediately preceding heat;

z _ik : binary variable, 1 means that a furnace k in the casting machine i in the pre-selection pool is selected as the furnace to be poured, and 0 means that a furnace k is not selected;

S3. Establish the constraint relationship between the heats in the pre-selected pool and the heats to be poured in the production batch plan, the constraints related to the balance of metal resources, the available time constraints of continuous casting equipment, and the sequence and time constraints between the heats to be poured ;

S4, select and encode based on the furnace order number and perform population initialization;

S5, decode and calculate the fitness value to obtain the initial solution set, the fitness function is:

\begin{matrix} min min & F f = = {{{f f}_{{eval eval}_{11}},, {f f}_{{eval eval}_{22}},, {f f}_{{eval eval}_{33}}}} \end{matrix} - - - - - - ((99))

in,

{f f}_{{eval eval}_{11}} = = {f f}_{11} - - - - - - ((1010))

{f f}_{{eval eval}_{33}} = = {f f}_{33} + + M m \cdot \cdot m m a a x x {{{Q Q}_{D D.},, {Q Q}_{E E.} \cdot \cdot {π π}^{p p} + + {Q Q}_{I I V V} \cdot &Center Dot; {δ δ}^{p p}}} - - - - - - ((1212))

Equation (9) expresses the whole calculation process to find the fitness function The minimum value of is the target;

Equation (10) represents the fitness function value equal to the objective function value f ₁ ;

Equation (11) represents the fitness function value It is equal to the sum of the objective function value f ₂ plus the penalty for violating the relationship constraints of the backlog metal quantity and the penalty for the pouring time exceeding the planned period;

Equation (12) represents the fitness function value It is equal to the sum of the objective function value f ₃ and the penalty for planning to use high-quality molten iron beyond the supply of high-quality molten iron;

S6, performing non-dominated sorting and crowding distance sorting on the solutions in the initial solution set;

S7, selecting a part of individuals in the population in step S6 as the parent generation;

S8, for the parent generation selected in step S7 according to the multi-point crossover of the parent and child of the casting machine segment, and the random variation of the points selected according to the casting machine segment, to ensure the consistency of the chromosome characteristics and the real production furnace sequence number characteristics;

S9, decoding the result calculated in step S8 and calculating fitness, the fitness function being the fitness function in step S5;

S10, determine the elite solution set, limit the number of individuals for calculating the crowding distance, calculate the crowding distance and sort;

S11, judging whether the maximum number of iterations is reached, if yes, execute step S12, otherwise, execute step S7;

S12, output the elite solution set, and use the fuzzy optimal selection method to select the maximum satisfaction scheme as the decision-making method for the continuous casting furnace time;

S13, transmit the maximum satisfaction plan to the steelmaking-continuous casting production operation control system, and the system realizes the selection, sorting and casting time decision of the heats to be started on each continuous casting machine according to the maximum satisfaction plan Effective production operation control.

2. The multi-objective optimization method for selection, sorting and pouring time decision-making of continuous casting unit pouring times as claimed in claim 1, characterized in that, in the production batch plan in step S3, the preselected pool furnaces and the furnaces to be started are The constraints of the relationship are:

{Σ Σ}_{k k = = 11}^{{K K}_{i i}} {z z}_{i i k k} = = {K K}_{i i}^{d d},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]] - - - - - - ((1313))

{K K}_{i i}^{d d} &GreaterEqual; &Greater Equal; {K K}_{i i}^{n no},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]] - - - - - - ((1515))

Equation (13) expresses the relationship between the number of furnaces selected by each continuous casting machine in the pre-selection pool and the number of furnaces to be cast by each casting machine during the planning period,

Equation (14) is set up to adapt to resource constraints, indicating that the number of furnaces to be started for each casting machine does not exceed the minimum value of the total number of furnaces planned in the pre-selected pool and the capacity demand of the casting machine, where, Indicates rounding up, mean() means calculating the average value,

Formula (15) is set up to improve the utilization rate of tundish and continuous casting equipment, which means that if the casting machine starts pouring, it must be greater than the predetermined minimum number of casting furnaces of the casting machine;

The related constraint relationship of metal resource balance is:

Q _O ≥ 0 (16)

Q _D ≤ Q _E · π ^p + Q _IV · δ ^p' (17)

{Q Q}_{D D.} = = (({δ δ}^{p p} \cdot &Center Dot; {Σ Σ}_{i i = = 11}^{I I} {rq rq}_{i i} + + {Σ Σ}_{i i = = 11}^{I I} {Σ Σ}_{{k k}^{d d} = = 11}^{{K K}_{i i}^{d d}} {v v}_{{ik ik}^{d d}} \cdot \cdot ((min min (({τ τ}_{e e},, {x x}_{{ik ik}^{d d}} + + {τ τ}_{{ik ik}^{d d}})) - - {x x}_{{ik ik}^{d d}})) \cdot \cdot ρ ρ \cdot \cdot {wa w}_{{ik ik}^{d d}} \cdot \cdot {ws ws}_{{ik ik}^{d d}})) \cdot \cdot 11 / / ((11 - - η η)) - - - - - - ((1818))

Formula (16) indicates that the backlog of metal in the production line is non-negative;

Formula (17) indicates that the amount of high-quality molten iron required for casting high-quality steel does not exceed the sum of the initial inventory and the amount of high-quality molten iron that is fed into iron during the planning period;

Equation (18) represents the high-quality molten iron quantity Q _D required for casting high-quality steel, which is composed of two parts of high-quality molten iron required for the remaining tasks and the furnace to be opened;

The available time constraints of continuous casting equipment are:

{τ τ}_{i i}^{e e a a r r l l i i e e s the s t t} \leq \leq {x x}_{{ik ik}^{d d}},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] - - - - - - ((1919))

That is, the pouring time of the selected heat is not earlier than the earliest available time of the casting machine;

The sequence and time constraints between the heats to be poured are:

{y the y}_{{ik ik}^{d d}} \{\begin{matrix} = = 11,, {wa w}_{{ik ik}^{d d}} &NotEqual; &NotEqual; {wa w}_{i i (({k k}^{d d} - - 11))},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] \\ = = 00,, {wa w}_{{ik ik}^{d d}} = = {wa w}_{i i (({k k}^{d d} - - 11))},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] \end{matrix} - - - - - - ((2020))

{τ τ}_{s the s} \leq \leq {x x}_{{ik ik}^{d d}} \leq \leq {τ τ}_{e e},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[22,, {K K}_{i i}^{d d}]] - - - - - - ((21 twenty one))

{τ τ}^{' '} + + {τ τ}_{i i}^{g g a a p p} \cdot &Center Dot; {y the y}_{{ik ik}^{d d}} \leq \leq {x x}_{{ik ik}^{d d}} \leq \leq {τ τ}^{' '} + + (({τ τ}_{e e} - - {τ τ}^{' '})) \cdot &Center Dot; {y the y}_{{ik ik}^{d d}},, &ForAll; &ForAll; i i &Element; &Element; [[11,, I I]],, &ForAll; &ForAll; {k k}^{d d} &Element; &Element; [[11,, {K K}_{i i}^{d d}]] - - - - - - ((22 twenty two))

The formula (20) indicates that the specification of the section of the furnace is different, and the pouring is forced to be interrupted.

Equation (21) indicates that the pouring time of the selected heats to be poured is within the planned period,

Equation (22) indicates that when the furnaces to be poured are poured continuously with the legacy tasks, the time of the pouring start is taken as the end time of the legacy tasks, τ′=rq _i /ρ·ra _i ·rs _i , and when the pouring is not continuous, the legacy tasks are taken A certain time between the end time and the interval between furnace times and the end of the planning period, When the batches to be started are continuously poured, the time of starting the pouring is taken as the end time of the previous batch, In the case of non-continuous pouring, take the end time of the previous furnace and a certain time between the furnace interval and the end of the planning period,

3. The multi-objective optimization method for selection, sorting and pouring time decision-making of continuous casting unit pouring times as claimed in claim 1, characterized in that, the encoding method described in step S4 of claim 1 is:

S31, count the total number of furnaces K _i of each casting machine i in the pre-selection pool, and start pouring time for each furnace according to the batch plan Sequentially sort, and assign furnace sequence numbers to each furnace after sorting in turn, establish a furnace sequence number reference table for each casting machine, and ensure that the sequence of furnace sequence numbers is consistent with the scheduled pouring time sequence of the batch plan;

S32, determine the number range of the number of selected furnaces, randomly generate the binary sequence of each casting machine with a length of K _i , and correspond to the reference table of the furnace sequence number one by one, according to the relationship between the furnace number of the pre-selected pool and the number of furnaces to be poured in the production batch plan The constraint relationship determines the range of the number of selected heats;

S33, the chromosome gene segments of each casting machine are connected to form a complete chromosome, and an initial population of a set size is randomly generated.

4. The multi-objective optimization method for selection, sorting and pouring time decision-making of continuous casting unit pouring times as claimed in claim 1, characterized in that, the decoding method is:

S41, dealing with illegal chromosomes: the illegal chromosomes after cross-mutation can be divided into two categories: the total number of heats to be poured is greater than the upper limit of the number of heats calculated in claim 3 and less than the number of heats calculated in claim 3 The lower limit, for the former, randomly change the number of 1s that exceed the upper limit of the constraint to 0, and for the latter, randomly change the number of 0s that are lower than the lower limit of the constraint to 1, and the chromosomes that do not violate the constraint remain unchanged;

S42, according to the sequence of furnaces that appear 1 from left to right in the chromosomes of each casting machine, generate the sequence of furnaces to be poured, compare the reference table of furnace sequence numbers and the characteristics of furnaces in the batch plan, and combine constraint (20) to generate

S43, if a furnace in the sequence to be fired is interrupted from the previous furnace and has the earliest available time, it is determined according to constraints (19) and (21) Otherwise, according to constraint (21-22) to determine

5. The multi-objective optimization method for continuous casting unit pouring time selection, sorting and pouring time decision-making as claimed in claim 1, characterized in that the method for determining the elite solution set is:

S51, merging parent and offspring chromosomes, defining the dominance relationship among individuals, assigning serial numbers and ranks to each individual according to the dominance relationship, generating sets of non-dominated individuals of different serial number levels, and recording the number of non-dominated individuals in each serial number level;

S52, according to the capacity of the elite solution set, the number of non-dominated individuals in each serial number level, and the order of the serial number levels from small to large, determine the maximum serial number that the elite solution set can accommodate;

S53, calculate the sum of the number of solutions in the elite solution set and the current non-dominated level, and judge whether the sum of the numbers of the solutions is greater than the size of the elite solution set, if yes, execute step S54, if not, execute step S55;

S54, calculate the crowding distance of the current non-dominated individuals and arrange them in descending order, and add the elite solutions to the elite solution set in order of crowding distance from large to small;

S55, calculating the crowding distance under the current non-dominated level and adding the elite solution to the elite solution set;

S56, judging whether the scale of the elite solution set has been reached, if so, execute step S11 according to claim 1, if not, add 1 to the serial number level of the non-dominated solution, and execute step S53.

6. The multi-objective optimization method for continuous casting unit pouring times selection, sorting and casting time decision-making as claimed in claim 1. The multi-objective optimization method for continuous casting machine casting times and time decision-making, characterized in that the elite solution The rules for joining the elite solution set are as follows: set the size of the elite solution set, add individuals in ascending order according to the ranking number until the elite solution set is filled. When , the individuals with a large crowding distance are added first, and the individuals exceeding the size of the elite solution set are discarded.

7. The multi-objective optimization method of continuous casting unit pouring time selection, sorting and pouring time decision-making as claimed in claim 1, characterized in that, the maximum satisfaction scheme is selected as the continuous casting pouring time decision-making method, The fuzzy optimization method is as follows:

S71, calculate the proportion ω _{(r, m)} of each individual in the objective function value set, ω _{(r, m)} represents the proportion of the mth objective function value in the individual r, respectively represent the minimum and maximum value of the mth objective function value in the objective function value set:

{ω ω}_{((r r,, m m))} = = \{\begin{matrix} 11,, & {f f}_{((r r,, m m))} \leq \leq {f f}_{m m}^{min min} \\ \frac{{f f}_{((m m))}^{max max} - - {f f}_{((r r,, m m))}}{{f f}_{((m m))}^{max max} - - {f f}_{((m m))}^{min min}},, & {f f}_{((m m))}^{min min} < < {f f}_{{eval eval}_{((r r,, m m))}} < < {f f}_{((m m))}^{max max} \\ 00,, & {f f}_{((r r,, m m))} &GreaterEqual; &Greater Equal; {f f}_{((m m))}^{max max} \end{matrix} - - - - - - ((23 twenty three))

S72, standardize the satisfaction ω _r of all individuals, where N is the population size of the elite solution set;

{ω ω}_{r r} = = \frac{{Σ Σ}_{m m = = 11}^{44} {ω ω}_{((r r,, m m))}}{{Σ Σ}_{r r = = 11}^{N N} {Σ Σ}_{m m = = 11}^{44} {ω ω}_{((r r,, m m))}} - - - - - - ((24 twenty four))

S73, take the individual with the greatest standardization satisfaction z _ik ,