A method for planning plate rolling considering the capacity limit of cooling bed

Abstract

This invention provides a method for compiling a rolling schedule for medium and heavy plates that considers the limitations of cooling bed capacity, relating to the field of medium and heavy plate rolling technology. The method involves selecting slabs that meet the roll cycle constraints as candidate slabs for the rolling schedule, matching and grouping these candidate slabs for cooling beds to obtain a centralized production arrangement of slabs; quantitatively describing the optimization target of the slab position in the rolling schedule; incorporating the slabs in the billet warehouse into the rolling schedule and optimizing them; if two slabs with the same steel grade and cooling bed parameters exist, and swapping their positions in the rolling schedule results in a specification jump penalty value lower than a preset threshold, and the swapping operation reduces the number of billet warehouse repacking operations, then the positions of the two slabs in the rolling schedule are swapped; adjusting the positions of all slabs in the rolling schedule to reduce the number of billet warehouse repacking operations forms the final medium and heavy plate rolling schedule; and issuing the final medium and heavy plate rolling schedule to the medium and heavy plate rolling production line for execution to complete the rolling of the medium and heavy plates.

Description

Technical Field

[0001] This invention relates to the field of medium and heavy plate rolling technology, and in particular to a method for compiling a medium and heavy plate rolling plan that takes into account the limitations of cooling bed capacity. Background Technology

[0002] Medium and heavy plates are a type of steel product widely used in industries such as construction and engineering machinery. Customer orders are typically for multiple specifications in small batches. In the rolling production of medium and heavy plates, slabs that have reached the required rolling temperature are first widened on a roughing mill, and then extended on a finishing mill. Under the rolling pressure of the mill rolls, the slabs deform, transforming into rolled steel plates. As production increases, roll wear becomes more severe, leading to a decline in the surface quality of the finished products. When the quality of the rolled products can no longer meet the requirements of any customer, new rolls must be replaced. However, roll replacement is not easy and consumes considerable time. Roll wear during production is closely related to the slab production sequence. To ensure product performance and quality, three factors related to roll wear are considered: First, variations in the steel grade of the slab; for medium and heavy plates, a significant difference in hardness between adjacent slabs can greatly affect roll condition. The other two main factors are variations in slab width and slab thickness.

[0003] Today, roller cooling beds are widely used in medium and heavy plate mills in the steel industry. Their main purpose is to allow the previously forged, high-temperature medium and heavy plates to air-cool naturally, playing a crucial role in medium and heavy plate rolling. The main components of a roller cooling bed include a roller conveyor on the input side, a steel transfer device on the input side, a steel transfer device at the output side, a roller conveyor on the output side, and the cooling bed body itself. The cooling bed body consists of numerous roller shafts, each individually operated by a motor, arranged in parallel. The motor drives the rollers, causing the roller discs on the shafts to rotate. Friction forces the steel plates to move laterally, allowing them to dissipate heat and cool. The capacity of the cooling bed significantly impacts the planning of medium and heavy plate rolling. Allocating too many slabs to a single cooling bed can lead to congestion, resulting in low rolling efficiency or even production stoppage. Conversely, allocating too few slabs will result in low utilization of the cooling bed, increasing rolling costs and time.

[0004] To meet the needs of large-scale production in steel enterprises, it is necessary to break down or combine the products required by users through steel production planning and scheduling methods, and to arrange on-site production considering resources and equipment conditions. Based on the characteristics of the products required by users, the production process of medium and heavy plates has its own operational characteristics. The main difficulties in preparing the rolling plan lie in two aspects: slab selection and the position of the slab in the rolling plan. The goal of rolling plan preparation is to minimize the specification jumps between adjacent slabs and the number of times the slab warehouse is repacked, while also maximizing the utilization rate of the cooling bed.

[0005] Regarding the issue of rolling schedule preparation, some domestic and international literature and patents have conducted relevant research on similar problems. Zheng et al. published a patent entitled "Optimization Method and Control System for Batch Planning of Multi-Hot Rolling Units to Maximize Roll Utilization", which accurately evaluates the impact of multi-hot rolling unit plans composed of different production order combinations on roll wear, effectively optimizes the batch plan of multi-hot rolling units, fully considers the wear of rolls caused by specification jumps between adjacent slabs in the rolling plan, and finally determines the optimization principles that need to be followed and considered when preparing rolling plans. Kosiba et al. published an article titled "Discrete eventsequencing as a traveling salesman problem," which described and analyzed the problem of planning strip rolling units in steel plants. To reduce roll wear and improve product quality and production efficiency, they proposed that the rolling planning problem can be viewed as a multi-objective, multi-constraint optimization problem. This problem involves at least three objectives: minimizing the hardness jump between adjacent slabs, minimizing the thickness jump between adjacent slabs, and minimizing the width jump between adjacent slabs. Ultimately, the problem is modeled and solved as a traveling salesman problem (TSP), with the objective of minimizing the comprehensive jump penalty of the rolling unit. The constraints mainly consider feasibility constraints related to the TSP problem. Finally, an exact algorithm is directly used to optimize and solve the problem.

[0006] The solutions mentioned above all aim to minimize the size jump between adjacent slabs in a rolling unit, arranging the slabs in the billet warehouse in a certain order to form a rolling production plan. None of them involve the constraints of the cooling bed capacity in the medium and heavy plate production process, nor do they consider the impact of the number of times the billet warehouse is re-stacked on the rolling production plan. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a method for compiling rolling plans for medium and heavy plates that considers the limitations of cooling bed capacity. This method integrates the constraints of cooling bed capacity during the production of medium and heavy plates with the impact of the number of times the billet is turned over on the rolling production plan, resulting in better global optimization.

[0008] The technical solution of the present invention is as follows:

[0009] On the one hand, the present invention provides a method for compiling a rolling schedule for medium and heavy plates that takes into account the limitations of cooling bed capacity, comprising the following steps:

[0010] Step 1: Select slabs that meet the roll cycle constraints as candidate slabs for the rolling plan;

[0011] The roll cycle constraint specifically involves: setting the rolling tonnage range of the initial rolls, and the corresponding range of slab width and thickness; setting the rolling tonnage range of the intermediate rolls, used to roll slabs of all specifications; setting the rolling tonnage range of the final rolls, and the corresponding range of slab width and thickness; and selecting slabs that meet the current roll cycle constraint as candidate slabs for the rolling plan based on the current rolling tonnage of the rolls.

[0012] Step 2: Match and group the candidate slabs on the cooling bed according to their thickness, waiting time, and steel grade to obtain the slab centralized production scheduling combination;

[0013] Step 2.1: Match the slabs in the rolling pre-plan to the cooling bed according to the thickness of the slab;

[0014] The rules for matching the cooling beds are as follows: if the slab thickness is less than the set value, the slab is cooled by cooling bed A and then sheared; if the slab thickness is greater than or equal to the set value, the slab is cooled by cooling bed B and then flame-cut; the rolling plan allocates the corresponding slabs to different cooling beds for cooling, and the cooling bed capacity cannot be exceeded.

[0015] Step 2.2: Group the slabs according to whether or not they have a waiting time;

[0016] The waiting time refers to the time that the slab needs to be heated in the heating furnace; among them, slabs with waiting time are produced in a concentrated manner and the waiting time is arranged in order from shortest to longest and then back to shortest.

[0017] Step 2.3: Group the slabs according to their steel grade;

[0018] Specifically, this involves the centralized production of slabs of the same steel grade.

[0019] Step 2.4: Obtain an initial rolling plan by centrally scheduling and combining slabs;

[0020] Specifically, the process is as follows: First, candidate slabs are divided into two categories based on cooling bed matching: slabs corresponding to cooling bed A and slabs corresponding to cooling bed B. Second, slabs in each cooling bed are further divided into two categories based on whether they have a waiting time, resulting in four categories of slabs: slabs with a waiting time in cooling bed A, slabs without a waiting time in cooling bed A, slabs with a waiting time in cooling bed B, and slabs without a waiting time in cooling bed B. Finally, these four categories of slabs are centrally scheduled for production based on their steel grade. Slabs with a larger quantity of steel grade are scheduled first, and the quantity cannot exceed the cooling bed capacity. Production is alternated between the two cooling beds until there are not enough candidate slabs or the rolling plan quantity meets the planner's requirements, resulting in an initial rolling plan.

[0021] Step 3: Quantitatively describe the optimization objective of the slab's position in the rolling schedule;

[0022] Step 3.1: Quantitatively describe the decision variable x of the slab's position in the rolling schedule. ijk ;

[0023] The position decision variable x of the slab in the rolling plan ijk The position decision variable x indicates whether slab j in cooling bed k is rolled after slab i. When slab j in cooling bed k is rolled after slab i, the position decision variable x... ijk The value is 1; otherwise, the location decision variable x ijk The value is 0;

[0024] Step 3.2: Quantitatively describe the optimization objective of the slab's position in the rolling schedule;

[0025] The specific optimization objectives for the position of the slab in the rolling plan include: minimizing the specification jump penalty between two adjacent slabs, minimizing the number of steel grade changes between two adjacent slabs, maximizing the utilization rate of the cooling bed and the slab rolling priority reward cost, and minimizing the number of times the billet warehouse is restacked.

[0026] The specification jump penalty for minimizing the specification jump penalty between two adjacent slabs specifically includes: the thickness jump penalty between two adjacent slabs in a rolling schedule; and the width jump penalty between two adjacent slabs in a rolling schedule.

[0027] The specification jump penalty between two adjacent slabs is quantitatively described mathematically, resulting in the minimized specification jump penalty between the two adjacent slabs:

[0028] (1);

[0029] Where N is the set of all slabs to be rolled, and K is the set of cooling beds. Penalty for specification jump between slab j and slab i:

[0030] (2);

[0031] in: These are the weighting coefficients for the thickness jump penalty between two adjacent slabs and the weighting coefficients for the width jump penalty between two adjacent slabs, respectively, with the weighting coefficient for the thickness jump penalty being greater than the weighting coefficient for the width jump penalty. The thickness jump penalty between slab i and slab j is calculated as follows: In a rolling plan, slab j is located after slab i. The absolute value of the difference in rolling thickness between slab i and slab j is used as the thickness jump penalty between slab i and slab j. The width jump penalty between slab i and slab j is calculated as follows: In a rolling plan, slab j is positioned after slab i. The absolute value of the difference in rolling width between slab i and slab j is used as the width jump penalty between slab i and slab j.

[0032] The specific measure of minimizing the number of steel grade changes between two adjacent slabs is: slabs with the same steel grade should be produced in a concentrated manner;

[0033] The process of minimizing the number of steel grade changes between two adjacent slabs is quantitatively described using mathematical expressions:

[0034] (3);

[0035] Among them, b ij It is a variable that can be either 0 or 1. When the steel grade of slab i and slab j changes, the value is 1; otherwise, it is 0.

[0036] The specific steps for maximizing the utilization rate of the cooling bed and the priority bonus cost for slab rolling are as follows: Select the corresponding cooling bed according to the thickness of the slab. Since the length and width of the slab are different, the utilization rate of the cooling bed is maximized by adjusting the position of the slab in the rolling plan. The rolling plan should allocate slabs with high priority bonus costs as much as possible. According to the capacity of the cooling bed and the different specifications of the corresponding slab, the slabs with high priority bonus costs are allocated to the corresponding positions of the corresponding cooling bed in the rolling plan. Under the premise of meeting the cooling bed capacity, as many slabs as possible are allocated to maximize the utilization rate of the cooling bed and the priority bonus cost for slab rolling.

[0037] The cost of maximizing cooling bed utilization and slab rolling priority incentives will be quantitatively described using mathematical expressions:

[0038] (4);

[0039] in, This indicates that slab i is allocated to cooling bed k. The rolling priority bonus for slab i is given by the following formula:

[0040] (5);

[0041] in, Priority bonus for delivery time of slab i. Bonus fee for heat treatment priority of slab i;

[0042] The specific number of stacking operations to minimize the blank warehouse is as follows:

[0043] The term "stack reversal" refers to the need to include a slab in the middle of a stack in the rolling plan due to factors such as waiting time, concentrated production of steel grades, and penalties for specification jumps between slabs. In this case, the slab above the selected slab needs to be moved to another stack. In the rolling process of medium and heavy plates, the number of stack reversals should be minimized as much as possible.

[0044] The minimum number of stacking operations in the blank storage is quantitatively described mathematically, resulting in the minimum number of stacking operations in the blank storage:

[0045] (6);

[0046] in, The number of times the slab to be rolled is moved out is expressed mathematically and quantitatively as follows:

[0047] (7);

[0048] in, D represents the number of slabs above slab i. i Let i be the position of slab i in the rolling schedule. This indicates the stack position where slab i is located. This represents the set of slabs that meet the following conditions: they are in the same stack position as slab i and their position in the rolling plan is within the slab stack. In front of. The value is 1 when the position of slab j in the rolling plan of the cooling bed k is d; otherwise, it is 0. The decision variable represents a value of 1 when slab j is assigned to the cooling bed k; otherwise, it is 0.

[0049] The objective function for the slab position allocation problem is as follows:

[0050] (8);

[0051] in, The weighting coefficients for the specification jump penalty between two adjacent slabs in the objective function. The weighting coefficients for the number of steel grade changes between two adjacent slabs in the objective function. The weighting coefficients for cooling bed utilization and slab rolling priority incentive costs in the objective function are: This represents the weighting coefficient of the number of times the blank warehouse is turned over in the objective function;

[0052] Step 3.3: Quantitatively describe the positional process constraints of the slab in the rolling schedule;

[0053] The process constraints at the location specifically include production process constraints and cooling bed capacity constraints;

[0054] The specific production process constraints are as follows: each slab can be assigned to a maximum of one cooling bed, and slabs of different thicknesses need to be assigned to corresponding cooling beds;

[0055] The production process constraints can be converted into a mathematical expression as follows:

[0056] (9);

[0057] (10);

[0058] (11);

[0059] in This refers to the set of slabs corresponding to cooling bed A. Let k=0 be the set of slabs corresponding to cooling bed B, and k=1 be the set of cooling bed A. Let $\frac{i}{k}$ be the decision variable representing the allocation of slab $i$ to cooling bed $k$. The value is $1$ when slab $i$ is allocated to cooling bed $k$, and $0$ otherwise.

[0060] The cooling bed capacity constraint is specifically defined as follows: the cooling bed capacity is regarded as a two-dimensional space capacity constraint, and the number of slabs allocated to a cooling bed cannot exceed the capacity of the cooling bed.

[0061] The cooling bed capacity constraint can be converted into a mathematical expression as follows:

[0062] (12);

[0063] (13);

[0064] in The x-coordinate of the vertex of slab i that is closest to the edge of the cooling bed; The vertical coordinate of slab i is the closest vertex to the edge of the cooling bed; W represents the width of the cooling bed; H represents the length of the cooling bed. As a decision variable, it takes the value 1 when slab j is arranged above slab i in the y-axis direction; otherwise, it takes the value 0. As a decision variable, it takes the value 1 when slab j is arranged on the positive side of slab i in the x-axis direction; otherwise, it takes the value 0. Indicates the exit length of the slab; Indicates the exit width of the slab;

[0065] In addition, there are constraints on the values ​​of the decision variables:

[0066] (14);

[0067] Step 4: For each slab in the billet warehouse, based on the roll cycle constraint in Step 1, the slab centralized production scheduling combination in Step 2, and the position of the slab in the rolling plan in Step 3, the slabs in the billet warehouse are incorporated into the rolling plan and optimized.

[0068] Step 4.1: Create an initial slab rolling plan;

[0069] The initial slab rolling plan is designed with the following objectives: minimizing the penalty for skipping adjacent slab specifications, minimizing the number of steel grade changes, and maximizing the utilization rate of each cooling bed. The initial rolling plan is constructed using a greedy heuristic based on these objectives.

[0070] Step 4.1.1: Determine whether the slab needs to be included in the rolling plan based on its steel grade and stack position number: Determine whether the slab is a special slab based on its steel grade. If it is a special slab, it needs to be rolled using a special process and cannot be rolled together with ordinary slabs. Determine whether the slab is allowed to be rolled based on its stack position number. Slabs with virtual stack positions and slabs not in stacks are not allowed to be included in the rolling plan. Starting from the first slab in the billet warehouse, select the slabs that need to be rolled and include them in the rolling plan to form rolling scheme 1.

[0071] Step 4.1.2: Determine whether the slab is assigned to cooling bed A or cooling bed B based on its thickness: slabs with a thickness less than the set value need to be cooled by cooling bed A, and slabs with a thickness greater than or equal to the set value need to be cooled by cooling bed B; starting from the first slab in rolling scheme 1, the slab is assigned to the corresponding cooling bed until the cooling bed reaches its capacity limit, at which point the cooling bed is switched to form rolling scheme 2;

[0072] Step 4.1.3: Determine whether the slab belongs to the controlled-rolled slab based on whether it has a waiting time; if the waiting time of the slab is 0, then the slab belongs to the ordinary-rolled slab; if the waiting time of the slab is greater than 0, then the slab belongs to the controlled-rolled slab; ordinary-rolled slabs and controlled-rolled slabs need to be centrally scheduled for production, and the rolling sequence of controlled-rolled slabs should be rolled in order of waiting time from shortest to longest and then back to shortest; starting from the first slab in rolling scheme 2, all slabs are divided into ordinary-rolled slabs or controlled-rolled slabs, among which the controlled-rolled slabs should be sorted in order of waiting time from shortest to longest and then back to shortest to form rolling scheme 3;

[0073] Step 4.1.4: Arrange the rolling plan by minimizing the number of steel grade changes between adjacent slabs; slabs of the same steel grade should be rolled together as much as possible to reduce the number of steel grade changes between adjacent slabs in the rolling plan. Cluster the slabs in rolling scheme 3 according to steel grade to form rolling scheme 4.

[0074] Step 4.1.5: Arrange the rolling schedule by minimizing the specification jump penalty between adjacent slabs, i.e., calculate the specification jump penalty between two slabs, where the specification jump penalty is equal to... × Absolute value of the thickness difference between adjacent slabs × The absolute value of the width difference between adjacent slabs These are the weighting coefficients for thickness jump penalties and width jump penalties, respectively. Starting with the first slab in rolling scheme 4, the slabs within each steel grade cluster are incorporated into the rolling plan in order of minimum specification jump, forming the initial rolling plan;

[0075] Step 4.2: Based on the rolling plan optimization objectives in Step 3, assign weights to each objective and perform neighborhood optimization on the initial rolling plan: Use a local search algorithm and a neighborhood exchange method to optimize the initial rolling plan, and exchange the positions of multiple slabs in the initial rolling plan to obtain a new rolling plan;

[0076] Step 4.3: Update the initial rolling plan: If the slab specification jump penalty and stacking number in the new rolling plan are both lower than those in the initial rolling plan, then update the initial rolling plan with this new rolling plan and proceed to step 4.2; otherwise, if no new rolling plan is generated, proceed to step 5.

[0077] Step 5: For the rolling plan, if there are two slabs with the same steel grade and cooling bed parameters, and the resulting specification jump penalty value is lower than the preset threshold after swapping the positions of these two slabs in the rolling plan, and the swapping operation can reduce the number of times the billet is re-stacked, then swap the positions of the two slabs in the rolling plan; adjust the positions of all slabs in the rolling plan to reduce the number of times the billet is re-stacked, and form the final medium and heavy plate rolling plan;

[0078] Step 6: Issue the final medium and heavy plate rolling plan to the medium and heavy plate rolling production line for execution, and complete the rolling of the medium and heavy plates.

[0079] On the other hand, this application proposes an electronic device comprising: one or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the method for compiling a medium-thick plate rolling schedule that takes into account the limitations of the cooling bed capacity.

[0080] The beneficial effects of adopting the above technical solution are as follows:

[0081] This invention provides a method for compiling rolling plans for medium and heavy plates that takes into account the limitations of cooling bed capacity. Addressing the problem of production planning for medium and heavy plate rolling considering cooling bed capacity, this invention improves the utilization rate of the cooling bed, reduces sizing jumps between adjacent slabs in the rolling plan, reduces roll wear, and improves rolling efficiency, thus saving enterprises significant production costs. Regarding the adjustment of slab positions in the rolling plan, this method optimizes the number of slab stacking operations while minimizing sizing jumps between adjacent slabs, effectively improving rolling efficiency and reducing production costs. Attached Figure Description

[0082] Figure 1 A flowchart of a method for compiling a rolling schedule for medium-thick plates considering the limitations of cooling bed capacity, according to an embodiment of the present invention;

[0083] Figure 2 This invention provides a flowchart for compiling medium and heavy plate rolling plans using slabs from a billet warehouse.

[0084] Figure 3 This is a schematic diagram of the search neighborhood in a specific embodiment of the present invention;

[0085] Where (a) represents the search neighborhood for 1-to-1 exchanges, and (b) represents the search neighborhood for m-to-m exchanges. Detailed Implementation

[0086] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0087] On the one hand, the present invention provides a method for compiling a rolling schedule for medium and heavy plates that takes into account the limitations of cooling bed capacity, such as... Figure 1 As shown, it includes the following steps:

[0088] Step 1: Select slabs that meet the roll cycle constraints as candidate slabs for the rolling plan;

[0089] The roll cycle constraint specifically involves: setting the rolling tonnage range of the initial rolls, and the corresponding range of slab width and thickness; setting the rolling tonnage range of the intermediate rolls, used to roll slabs of all specifications; setting the rolling tonnage range of the final rolls, and the corresponding range of slab width and thickness; and selecting slabs that meet the current roll cycle constraint as candidate slabs for the rolling plan based on the current rolling tonnage of the rolls.

[0090] In this embodiment: the initial rolling tonnage ranges from 0 to 1000 tons, used to roll slabs with a thickness greater than 20 mm and a width greater than 2500 mm; the intermediate rolling tonnage ranges from 1000 to 7000 tons, used to roll slabs of all specifications; the final rolling tonnage ranges from 7000 to 8500 tons, used to roll slabs with a thickness greater than 12 mm and a width less than 2500 mm; based on the current rolling tonnage of the rolling rolls, slabs that meet the current rolling cycle constraints are selected as candidate slabs for the rolling plan;

[0091] Step 2: Match and group the candidate slabs on the cooling bed according to their thickness, waiting time, and steel grade to obtain the slab centralized production scheduling combination;

[0092] Step 2.1: Match the slabs in the rolling pre-plan to the cooling bed according to the thickness of the slab;

[0093] The rules for matching the cooling beds are as follows: if the slab thickness is less than the set value, the slab is cooled by cooling bed A and then sheared; if the slab thickness is greater than or equal to the set value, the slab is cooled by cooling bed B and then flame-cut; the rolling plan allocates the corresponding slabs to different cooling beds for cooling, and the cooling bed capacity cannot be exceeded.

[0094] Step 2.2: Group the slabs according to whether or not they have a waiting time;

[0095] The waiting time refers to the time that the slab needs to be heated in the heating furnace; among them, slabs with waiting time are produced in a concentrated manner and the waiting time is arranged in order from shortest to longest and then back to shortest.

[0096] Step 2.3: Group the slabs according to their steel grade (i.e., steel type);

[0097] Specifically, slabs of the same steel grade are produced in a concentrated manner; this reduces the hardness jump between adjacent slabs in the rolling schedule, thereby reducing roll wear and improving rolling efficiency.

[0098] Step 2.4: Obtain an initial rolling plan by centrally scheduling and combining slabs;

[0099] Specifically, the process is as follows: First, candidate slabs are divided into two categories based on cooling bed matching: slabs corresponding to cooling bed A and slabs corresponding to cooling bed B. Second, slabs from each cooling bed are further divided into two categories based on whether they require a waiting time, resulting in four categories of slabs: slabs with a waiting time on cooling bed A, slabs without a waiting time on cooling bed A, slabs with a waiting time on cooling bed B, and slabs without a waiting time on cooling bed B. Finally, these four categories of slabs are scheduled for production based on their steel grades. For example, if cooling bed A has slabs with steel grades C, D, and E, with quantities of 20, 30, and 40 pieces respectively, and cooling bed B has slabs with steel grades F and G, with quantities of 20 and 30 pieces respectively, then the slabs with the larger quantity of steel grades will be scheduled first, and the production quantity cannot exceed the cooling bed capacity.

[0100] Assume that the maximum capacity of cooling bed A is 30 slabs and the maximum capacity of cooling bed B is 15 slabs. First, 30 slabs of steel grade E from cooling bed A (without waiting time) are included in the rolling schedule. Then, 15 slabs of steel grade G from cooling bed B (without waiting time) are included in the rolling schedule. Next, 30 slabs of steel grade D from cooling bed A (without waiting time) are included in the rolling schedule, followed by 15 slabs of steel grade F from cooling bed B (without waiting time). This process continues. The same principle applies to slabs with waiting time. The two cooling beds alternate in scheduling until there are insufficient candidate slabs or the required number of slabs for the rolling schedule is reached, resulting in an initial rolling schedule.

[0101] Step 3: Quantitatively describe the optimization objective of the slab's position in the rolling schedule;

[0102] Step 3.1: Quantitatively describe the decision variable x of the slab's position in the rolling schedule. ijk ;

[0103] The position decision variable x of the slab in the rolling plan ijk The position decision variable x indicates whether slab j in cooling bed k is rolled after slab i. When slab j in cooling bed k is rolled after slab i, the position decision variable x... ijk The value is 1; otherwise, the location decision variable x ijk The value is 0;

[0104] Step 3.2: Quantitatively describe the optimization objective of the slab's position in the rolling schedule;

[0105] The specific optimization objectives for the position of the slab in the rolling plan include: minimizing the specification jump penalty between two adjacent slabs, minimizing the number of steel grade changes between two adjacent slabs, maximizing the utilization rate of the cooling bed and the slab rolling priority reward cost, and minimizing the number of times the billet warehouse is restacked.

[0106] The specification jump penalty for minimizing the specification jump penalty between two adjacent slabs specifically includes: the thickness jump penalty between two adjacent slabs in a rolling schedule; and the width jump penalty between two adjacent slabs in a rolling schedule.

[0107] In this embodiment, the specification jump penalty between two adjacent slabs is quantitatively described mathematically, resulting in a minimized specification jump penalty between the two adjacent slabs:

[0108] (1);

[0109] Where N is the set of all slabs to be rolled, and K is the set of cooling beds. Penalty for specification jump between slab j and slab i:

[0110] (2);

[0111] in: These are the weighting coefficients for the thickness jump penalty between two adjacent slabs and the weighting coefficients for the width jump penalty between two adjacent slabs, respectively, with the weighting coefficient for the thickness jump penalty being greater than the weighting coefficient for the width jump penalty. The thickness jump penalty between slab i and slab j is calculated as follows: In a rolling schedule, slab j is positioned after slab i. The absolute value of the difference between the rolling thickness (entry thickness) of slab i and slab j is used as the thickness jump penalty between slab i and slab j. The smaller the thickness jump penalty between two adjacent slabs, the lower the rolling cost of medium and heavy plates and the higher the rolling efficiency. The width jump penalty between slab i and slab j is calculated when slab j is positioned after slab i in a rolling schedule. The absolute value of the difference in the rolling width (entry width) between slab i and slab j is used as the width jump penalty. A smaller width jump penalty between two adjacent slabs results in lower rolling costs and higher rolling efficiency for medium and heavy plates.

[0112] The specific method for minimizing the number of steel grade changes between two adjacent slabs is as follows: slabs with the same steel grade should be produced in a concentrated manner to reduce the number of steel grade changes between adjacent slabs, thereby reducing the wear of the rolls and improving rolling efficiency.

[0113] In this embodiment, minimizing the number of steel grade changes between two adjacent slabs is quantitatively described using mathematical expressions:

[0114] (3);

[0115] Among them, b ijIt is a variable that can be either 0 or 1. When the steel grade of slab i and slab j changes, the value is 1; otherwise, it is 0.

[0116] The specific steps for maximizing cooling bed utilization and slab rolling priority bonus fees are as follows: Select the appropriate cooling bed based on the slab thickness. For example, slabs less than 40mm thick require cooling on cooling bed A, while slabs thicker than 40mm require cooling on cooling bed B. Since slab lengths and widths differ, the slab's position in the rolling schedule is adjusted to maximize cooling bed utilization. During the rolling schedule arrangement, slabs have different priorities, such as slabs for urgent orders or those requiring heat treatment. The rolling schedule should allocate slabs with higher priority bonus fees to meet customer needs and shorten contract production cycles. Based on the cooling bed capacity and corresponding slab specifications, slabs with higher priority bonus fees are assigned to their corresponding positions in the rolling schedule. While ensuring sufficient cooling bed capacity, the maximum number of slabs is allocated to maximize cooling bed utilization and slab rolling priority bonus fees.

[0117] The cost of maximizing cooling bed utilization and slab rolling priority incentives will be quantitatively described using mathematical expressions:

[0118] (4);

[0119] in, This indicates that slab i is allocated to cooling bed k. The rolling priority bonus for slab i is mainly determined by considering the slab delivery time and whether heat treatment is required. As shown in the following formula:

[0120] (5);

[0121] in, The delivery time priority bonus cost for slab i is determined by the order delivery time of the slab, which affects the rolling priority of the slab. In order to ensure that the order is delivered on time, the rolling priority of the slab is defined to be proportional to the order delivery time. That is, the rolling priority bonus cost of the slab that is closer to the order delivery time is higher. Bonus fee for heat treatment priority of slab i; In order to meet customer needs, some slabs need to undergo heat treatment after rolling. In order to improve the efficiency of heat treatment, if the slab needs subsequent heat treatment operation, the slab is given a higher rolling priority.

[0122] The specific number of stacking operations to minimize the blank warehouse is as follows:

[0123] The term "stack repositioning" refers to the need to include slabs in the middle of a stack in the rolling schedule due to factors such as waiting time, concentrated production of steel grades, and penalties for size jumps between slabs. This necessitates moving the slabs above the selected slabs to other stacks, inevitably resulting in stack repositioning in actual production. Small-scale stack repositioning is feasible, but large-scale repositioning will affect rolling efficiency. Therefore, the number of stack repositioning operations should be minimized during the rolling of medium and heavy plates.

[0124] In this embodiment, the minimum number of stacking operations in the blank warehouse is quantitatively described using mathematical expressions, resulting in the minimum number of stacking operations in the blank warehouse:

[0125] (6);

[0126] in, The number of times the slab to be rolled is moved out is expressed mathematically and quantitatively as follows:

[0127] (7);

[0128] in, D represents the number of slabs above slab i. i Let be the position of slab i in the rolling plan. For example, if the rolling plan is for 100 slabs, then... If slab i is the 12th rolled slab, then . This indicates the stack position where slab i is located. This represents the set of slabs that meet the following conditions: they are in the same stack position as slab i and their position in the rolling plan is within the slab stack. In front of. The value is 1 when the position of slab j in the rolling plan of the cooling bed k is d; otherwise, it is 0. The decision variable represents a value of 1 when slab j is assigned to the cooling bed k; otherwise, it is 0.

[0129] The objective function for the slab position allocation problem is as follows:

[0130] (8);

[0131] in, The weighting coefficients for the specification jump penalty between two adjacent slabs in the objective function. The weighting coefficients for the number of steel grade changes between two adjacent slabs in the objective function. The weighting coefficients for cooling bed utilization and slab rolling priority incentive costs in the objective function are: This represents the weighting coefficient of the number of times the blank warehouse is turned over in the objective function;

[0132] Step 3.3: Quantitatively describe the positional process constraints of the slab in the rolling schedule;

[0133] The process constraints at the location specifically include production process constraints and cooling bed capacity constraints;

[0134] The specific production process constraints are as follows: each slab can be assigned to a maximum of one cooling bed, and slabs of different thicknesses need to be assigned to corresponding cooling beds;

[0135] The production process constraints can be converted into a mathematical expression as follows:

[0136] (9);

[0137] (10);

[0138] (11);

[0139] in This refers to the set of slabs corresponding to cooling bed A, i.e., slabs with a thickness of less than 40mm; For cooling bed B, there is a set of slabs, i.e. slabs with a thickness greater than or equal to 40mm. k=0 represents cooling bed A, and k=1 represents cooling bed B. Let $\frac{i}{k}$ be the decision variable representing the allocation of slab $i$ to cooling bed $k$. The value is $1$ when slab $i$ is allocated to cooling bed $k$, and $0$ otherwise.

[0140] The cooling bed capacity constraint is specifically defined as follows: the cooling bed capacity is regarded as a two-dimensional space capacity constraint, and the number of slabs allocated to a cooling bed cannot exceed the capacity of the cooling bed.

[0141] The cooling bed capacity constraint can be converted into a mathematical expression as follows:

[0142] (12);

[0143] (13);

[0144] in The x-coordinate of the vertex of slab i that is closest to the edge of the cooling bed; The vertical coordinate of slab i is the closest vertex to the edge of the cooling bed; W represents the width of the cooling bed; H represents the length of the cooling bed. As a decision variable, it takes the value 1 when slab j is arranged above slab i in the y-axis direction; otherwise, it takes the value 0. As a decision variable, it takes the value 1 when slab j is arranged on the positive side of slab i in the x-axis direction; otherwise, it takes the value 0. Indicates the exit length (post-rolling length) of the slab. This indicates the exit width of the slab (post-rolling width).

[0145] In addition, there are constraints on the values ​​of the decision variables:

[0146] (14);

[0147] Step 4: For each slab in the billet warehouse, based on the roll cycle constraint in Step 1, the slab centralized production scheduling combination in Step 2, and the position of the slab in the rolling plan in Step 3, the slabs in the billet warehouse are incorporated into the rolling plan and optimized.

[0148] Step 4.1: Create an initial slab rolling plan;

[0149] The initial slab rolling plan is designed with the following objectives: minimizing the penalty for skipping adjacent slab specifications, minimizing the number of steel grade changes, and maximizing the utilization rate of each cooling bed. The initial rolling plan is constructed using a greedy heuristic based on these objectives.

[0150] Step 4.1.1: Determine whether the slab needs to be included in the rolling plan based on its steel grade and stack position number: Determine whether the slab is a special slab based on its steel grade. If it is a special slab, it needs to be rolled using a special process and cannot be rolled together with ordinary slabs. Determine whether the slab is allowed to be rolled based on its stack position number. Slabs with virtual stack positions and slabs not in stacks are not allowed to be included in the rolling plan. Starting from the first slab in the billet warehouse, select the slabs that need to be rolled and include them in the rolling plan to form rolling scheme 1.

[0151] Step 4.1.2: Determine whether the slab is assigned to cooling bed A or cooling bed B based on its thickness: slabs with a thickness less than the set value of 40mm need to be cooled by cooling bed A, and slabs with a thickness greater than or equal to the set value of 40mm need to be cooled by cooling bed B; starting from the first slab in rolling scheme 1, the slabs are assigned to the corresponding cooling bed until the cooling bed reaches its capacity limit, at which point the cooling bed is switched to form rolling scheme 2;

[0152] Step 4.1.3: Determine whether the slab belongs to the controlled-rolled slab based on whether it has a waiting time; if the waiting time of the slab is 0, then the slab belongs to the ordinary-rolled slab; if the waiting time of the slab is greater than 0, then the slab belongs to the controlled-rolled slab; ordinary-rolled slabs and controlled-rolled slabs need to be centrally scheduled for production, and the rolling sequence of controlled-rolled slabs should be rolled in order of waiting time from shortest to longest and then back to shortest; starting from the first slab in rolling scheme 2, all slabs are divided into ordinary-rolled slabs or controlled-rolled slabs, among which the controlled-rolled slabs should be sorted in order of waiting time from shortest to longest and then back to shortest to form rolling scheme 3;

[0153] Step 4.1.4: Arrange the rolling schedule by minimizing the number of steel grade changes between adjacent slabs; slabs of the same steel grade should be rolled together as much as possible to reduce the number of steel grade changes between adjacent slabs in the rolling schedule, thereby reducing roll wear. Cluster the slabs in rolling scheme 3 according to steel grade to form rolling scheme 4;

[0154] Step 4.1.5: Arrange the rolling schedule by minimizing the specification jump penalty between adjacent slabs, i.e., calculate the specification jump penalty between two slabs, where the specification jump penalty is equal to... × Absolute value of the thickness difference between adjacent slabs × The absolute value of the width difference between adjacent slabs These are the weighting coefficients for thickness jump penalties and width jump penalties, respectively. Starting with the first slab in rolling scheme 4, the slabs within each steel grade cluster are incorporated into the rolling plan in order of minimum specification jump, forming the initial rolling plan;

[0155] Step 4.2: Based on the rolling plan optimization objectives in Step 3, assign weights to each objective and perform neighborhood optimization on the initial rolling plan: Use a local search algorithm and a neighborhood exchange method to optimize the initial rolling plan, and exchange the positions of multiple slabs in the initial rolling plan to obtain a new rolling plan;

[0156] Step 4.3: Update the initial rolling plan: If the slab specification jump penalty and stacking number in the new rolling plan are both lower than those in the initial rolling plan, then update the initial rolling plan with this new rolling plan and proceed to step 4.2; otherwise, if no new rolling plan is generated, proceed to step 5.

[0157] Step 5: For the rolling plan, if there are two slabs with the same steel grade and cooling bed parameters, and the resulting specification jump penalty value is lower than the preset threshold after swapping the positions of these two slabs in the rolling plan, and the swapping operation can reduce the number of times the billet is re-stacked, then swap the positions of the two slabs in the rolling plan; adjust the positions of all slabs in the rolling plan to reduce the number of times the billet is re-stacked, and form the final medium and heavy plate rolling plan;

[0158] Step 6: Issue the final medium and heavy plate rolling plan to the medium and heavy plate rolling production line for execution, and complete the rolling of the medium and heavy plates.

[0159] This implementation requires the following hardware system: at least one PC; at least one fiber optic or cable interface; and at least one router. These devices form a small local area network (LAN) and connect to the enterprise ERP system (an ERP system is a management platform built on information technology, using a systematic management approach to provide decision-making and operational tools for enterprise decision-makers and employees). An Oracle database system is installed on the PC, and the server address, server port, database name, username, and password are configured.

[0160] Download slab data: The downloaded slab information fields include: steel grade, delivery date, exit thickness, exit width, exit length, slab entry thickness, slab entry width, slab entry length, slab fire-cutting mark, slab shearing mark, slab cooling bed mark, slab controlled rolling mark, slab stack number, slab layer number, slab flaw detection mark, slab heat treatment mark, slab cutting time, slab waiting time, slab delivery status, slab entry material number, slab warehousing time, slab contract number, slab manufacturing order number, slab entry material type, slab controlled rolling temperature, slab trimming mark, and slab weight. Use SQL statements to read information from the Oracle database. Existing slab data can be managed through data query and management functions, including adding, deleting, modifying, querying, and exporting data. Parameters can be set according to actual production needs, including data source selection (slab conditions that need to be included in the rolling plan, slab conditions that do not need to be included in the rolling plan), and maximum specification jump penalty settings (including width jump penalty and thickness jump penalty).

[0161] For each slab in the billet warehouse, the slab to be rolled is selected based on the roll cycle constraint in step 1. An initial rolling plan is created through the centralized scheduling and combination of slabs in step 2. The initial rolling plan is optimized by addressing the position of the slabs in the rolling plan in step 3. Finally, the optimized rolling plan is adjusted to reduce the number of stacking operations to obtain the final plan. Figure 2 As shown;

[0162] When optimizing rolling schedules, due to the complexity and large scale of the problem, traditional neighborhood methods cannot quickly improve the quality of the allocation scheme. Therefore, a new neighborhood method is proposed, such as... Figure 3 As shown, traditional swap neighborhoods mainly involve one-to-one swaps, adjusting the rolling sequence before a single slab, such as... Figure 3 As shown in (a); unlike the traditional neighborhood, the neighborhood proposed in this invention adopts an m-to-m exchange method, that is, the rolling positions of multiple slab combinations in the rolling plan are exchanged to obtain a new rolling plan, where m is the number of slabs exchanged, as shown in (a). Figure 3As shown in (b). This approach can improve the quality of the allocation scheme on a larger scale and effectively avoid getting trapped in local optima.

[0163] Taking the rolling data of a large domestic steel mill for seven consecutive cycles as an example, and using one round of alternating production of cooling beds A and B as a rolling plan, the allocation and adjustment schemes of the above data obtained by the method of this invention are compared with the scheme obtained manually as follows:

[0164] Table 1. Comparison of statistical indicators related to artificial (M) and the method (A) proposed in this invention (each time):

[0165] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0166] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of the methods disclosed herein and their equivalents, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A method for compiling a rolling schedule for medium-thick plates considering the limitations of cooling bed capacity, characterized in that, Includes the following steps: Step 1: Select slabs that meet the roll cycle constraints as candidate slabs for the rolling plan; Step 2: Match and group the candidate slabs on the cooling bed according to their thickness, waiting time, and steel grade to obtain the slab centralized production scheduling combination; Step 2 includes the following steps: Step 2.1: Match the slabs in the rolling pre-plan to the cooling bed according to the thickness of the slab; The rules for matching the cooling beds are as follows: if the slab thickness is less than the set value, the slab is cooled by cooling bed A and then sheared; if the slab thickness is greater than or equal to the set value, the slab is cooled by cooling bed B and then flame-cut; the rolling plan allocates the corresponding slabs to different cooling beds for cooling, and the cooling bed capacity cannot be exceeded. Step 2.2: Group the slabs according to whether or not they have a waiting time; The waiting time refers to the time that the slab needs to be heated in the heating furnace; Among them, the slabs with waiting time are produced in a concentrated manner, and the waiting time is arranged in order from shortest to longest and then back to shortest. Step 2.3: Group the slabs according to their steel grade; Specifically, this involves the centralized production of slabs of the same steel grade. Step 2.4: Obtain an initial rolling plan by centrally scheduling and combining slabs; Specifically, the process is as follows: First, candidate slabs are divided into two categories based on cooling bed matching: slabs corresponding to cooling bed A and slabs corresponding to cooling bed B. Second, slabs in each cooling bed are further divided into two categories based on whether they have a waiting time, resulting in four categories of slabs: slabs with a waiting time in cooling bed A, slabs without a waiting time in cooling bed A, slabs with a waiting time in cooling bed B, and slabs without a waiting time in cooling bed B. Finally, these four categories of slabs are centrally scheduled for production based on their steel grade. Slabs with a larger quantity of steel grade are scheduled first, and the quantity cannot exceed the cooling bed capacity. Production is alternated between the two cooling beds until there are not enough candidate slabs or the rolling plan quantity meets the planner's requirements, resulting in an initial rolling plan. Step 3: Quantitatively describe the optimization objective of the slab's position in the rolling schedule; Step 4: For each slab in the billet warehouse, based on the roll cycle constraint in Step 1, the slab centralized production scheduling combination in Step 2, and the slab position optimization target in the rolling plan in Step 3, the slabs in the billet warehouse are incorporated into the rolling plan and optimized. Step 5: For the rolling plan, if there are two slabs with the same steel grade and cooling bed parameters, and the resulting specification jump penalty value is lower than the preset threshold after swapping the positions of these two slabs in the rolling plan, and the swapping operation can reduce the number of times the billet is re-stacked, then swap the positions of the two slabs in the rolling plan; adjust the positions of all slabs in the rolling plan to reduce the number of times the billet is re-stacked, and form the final medium and heavy plate rolling plan; Step 6: Issue the final medium and heavy plate rolling plan to the medium and heavy plate rolling production line for execution, and complete the rolling of the medium and heavy plates.

2. The method for compiling a medium-thick plate rolling schedule considering cooling bed capacity limitations according to claim 1, characterized in that, The roll cycle constraint mentioned in step 1 is specifically as follows: setting the rolling tonnage range of the initial roll, and the corresponding range of slab width and thickness; setting the rolling tonnage range of the intermediate roll, used to roll slabs of all specifications; setting the rolling tonnage range of the final roll, and the corresponding range of slab width and thickness; and selecting slabs that meet the current roll cycle constraint as candidate slabs for the rolling plan based on the current rolling tonnage of the roll.

3. The method for compiling a medium-thick plate rolling schedule considering cooling bed capacity limitations according to claim 1, characterized in that, Step 3 includes the following steps: Step 3.1: Quantitatively describe the decision variable x of the slab's position in the rolling schedule. ijk ; The position decision variable x of the slab in the rolling plan ijk The position decision variable x indicates whether slab j in cooling bed k is rolled after slab i. When slab j in cooling bed k is rolled after slab i, the position decision variable x... ijk The value is 1; otherwise, the location decision variable x ijk The value is 0; Step 3.2: Quantitatively describe the optimization objective of the slab's position in the rolling schedule; The specific optimization objectives for the position of the slab in the rolling plan include: minimizing the specification jump penalty between two adjacent slabs, minimizing the number of steel grade changes between two adjacent slabs, maximizing the utilization rate of the cooling bed and the slab rolling priority reward cost, and minimizing the number of times the billet warehouse is restacked. The specification jump penalty for minimizing the size jump penalty between two adjacent slabs specifically includes: the thickness jump penalty between two adjacent slabs in a rolling schedule; and the width jump penalty between two adjacent slabs in a rolling schedule. The specification jump penalty between two adjacent slabs is quantitatively described mathematically, resulting in the minimized specification jump penalty between the two adjacent slabs: (1)； Where N is the set of all slabs to be rolled, and K is the set of cooling beds. Penalty for specification jump between slab j and slab i: (2)； in: These are the weighting coefficients for the thickness jump penalty between two adjacent slabs and the weighting coefficients for the width jump penalty between two adjacent slabs, respectively, with the weighting coefficient for the thickness jump penalty being greater than the weighting coefficient for the width jump penalty. The thickness jump penalty between slab i and slab j is calculated as follows: In a rolling plan, slab j is located after slab i. The absolute value of the difference in rolling thickness between slab i and slab j is used as the thickness jump penalty between slab i and slab j. The width jump penalty between slab i and slab j is calculated as follows: In a rolling plan, slab j is positioned after slab i. The absolute value of the difference in rolling width between slab i and slab j is used as the width jump penalty between slab i and slab j. The specific measure of minimizing the number of steel grade changes between two adjacent slabs is: slabs with the same steel grade should be produced in a concentrated manner; The process of minimizing the number of steel grade changes between two adjacent slabs is quantitatively described using mathematical expressions: (3)； Among them, b ij It is a variable that can be either 0 or 1. When the steel grade of slab i and slab j changes, the value is 1; otherwise, it is 0. The specific steps for maximizing the utilization rate of the cooling bed and the priority bonus cost for slab rolling are as follows: Select the corresponding cooling bed according to the thickness of the slab. Since the length and width of the slab are different, the utilization rate of the cooling bed is maximized by adjusting the position of the slab in the rolling plan. The rolling plan should allocate slabs with high priority bonus costs as much as possible. According to the capacity of the cooling bed and the different specifications of the corresponding slab, the slabs with high priority bonus costs are allocated to the corresponding positions of the corresponding cooling bed in the rolling plan. Under the premise of meeting the cooling bed capacity, as many slabs as possible are allocated to maximize the utilization rate of the cooling bed and the priority bonus cost for slab rolling. The cost of maximizing cooling bed utilization and slab rolling priority incentives will be quantitatively described using mathematical expressions: (4)； in, This indicates that slab i is allocated to cooling bed k. The rolling priority bonus for slab i is given by the following formula: (5)； in, Priority bonus for delivery time of slab i. Bonus fee for heat treatment priority of slab i; The specific number of stacking operations to minimize the blank warehouse is as follows: The term "stack reversal" refers to the need to include a slab in the middle of a stack in the rolling plan due to factors such as waiting time, concentrated production of steel grades, and penalties for specification jumps between slabs. In this case, the slab above the selected slab needs to be moved to another stack. In the rolling process of medium and heavy plates, the number of stack reversals should be minimized as much as possible. The minimum number of stacking operations in the blank storage is quantitatively described mathematically, resulting in the minimum number of stacking operations in the blank storage: (6)； in, The number of times the slab to be rolled is moved out is expressed mathematically and quantitatively as follows: (7)； in, D represents the number of slabs above slab i. i Let i be the position of slab i in the rolling schedule. This indicates the stack position of slab i. This represents the set of slabs that meet the following conditions: they are located in the same stack as slab i and their position in the rolling plan is within the slab stack. In front of, The value is 1 when the position of slab j in the rolling plan of the cooling bed k is d; otherwise, it is 0. The decision variable represents a value of 1 when slab j is assigned to the cooling bed k; otherwise, it is 0. The objective function for the slab position allocation problem is as follows: (8)； in, The weighting coefficients for the specification jump penalty between two adjacent slabs in the objective function. The weighting coefficients for the number of steel grade changes between two adjacent slabs in the objective function. The weighting coefficients for cooling bed utilization and slab rolling priority incentive costs in the objective function are: This represents the weighting coefficient of the number of times the blank warehouse is turned over in the objective function; Step 3.3: Quantitatively describe the positional process constraints of the slab in the rolling schedule; The process constraints at the location specifically include production process constraints and cooling bed capacity constraints; The specific production process constraints are as follows: each slab can be assigned to a maximum of one cooling bed, and slabs of different thicknesses need to be assigned to corresponding cooling beds; The production process constraints can be converted into a mathematical expression as follows: (9)； (10)； (11)； in This refers to the set of slabs corresponding to cooling bed A. Let k=0 be the set of slabs corresponding to cooling bed B, and k=1 be the set of cooling bed A. Let $\frac{i}{k}$ be the decision variable representing the allocation of slab $i$ to cooling bed $k$. The value of $\frac{i}{k}$ is 1 when slab $i$ is allocated to cooling bed $k$, and 0 otherwise. The cooling bed capacity constraint is specifically defined as follows: the cooling bed capacity is regarded as a two-dimensional space capacity constraint, and the number of slabs allocated to a cooling bed cannot exceed the capacity of the cooling bed. The cooling bed capacity constraint can be converted into a mathematical expression as follows: (12)； (13)； in The x-coordinate of the vertex of slab i that is closest to the edge of the cooling bed; The vertical coordinate of slab i is the closest vertex to the edge of the cooling bed; W represents the width of the cooling bed; H represents the length of the cooling bed. As a decision variable, it takes the value 1 when slab j is arranged above slab i in the y-axis direction; otherwise, it takes the value 0. As a decision variable, it takes the value 1 when slab j is arranged on the positive side of slab i in the x-axis direction; otherwise, it takes the value 0. Indicates the exit length of the slab; Indicates the exit width of the slab; In addition, there are constraints on the values ​​of the decision variables: (14)。 4. The method for compiling a medium-thick plate rolling schedule considering cooling bed capacity limitations according to claim 1, characterized in that, Step 4 includes the following steps: Step 4.1: Create an initial slab rolling plan; Step 4.2: Based on the rolling plan optimization objectives in Step 3, assign weights to each objective and perform neighborhood optimization on the initial rolling plan: Use a local search algorithm and a neighborhood exchange method to optimize the initial rolling plan, and exchange the positions of multiple slabs in the initial rolling plan to obtain a new rolling plan; Step 4.3: Update the initial rolling plan: If the slab specification jump penalty and stacking number in the new rolling plan are both lower than those in the initial rolling plan, then update the initial rolling plan with this new rolling plan and proceed to step 4.2; otherwise, if no new rolling plan is generated, proceed to step 5.

5. The method for compiling a medium-thick plate rolling schedule considering cooling bed capacity limitations according to claim 4, characterized in that, The scheduling objectives of the initial slab rolling plan in step 4.1 include minimizing the penalty for skipping adjacent slab specifications, minimizing the number of steel grade changes, and maximizing the utilization rate of each cooling bed. The initial rolling plan is constructed using a greedy heuristic based on the scheduling objectives.

6. The method for compiling a medium-thick plate rolling schedule considering cooling bed capacity limitations according to claim 5, characterized in that, Step 4.1 includes the following steps: Step 4.1.1: Determine whether the slab needs to be included in the rolling plan based on its steel grade and stack position number: Determine whether the slab is a special slab based on its steel grade. If it is a special slab, it needs to be rolled using a special process and cannot be rolled together with ordinary slabs. Determine whether the slab is allowed to be rolled based on its stack position number. Slabs with virtual stack positions and slabs not in stacks are not allowed to be included in the rolling plan. Starting from the first slab in the billet warehouse, select the slabs that need to be rolled and include them in the rolling plan to form rolling scheme 1. Step 4.1.2: Determine whether the slab is assigned to cooling bed A or cooling bed B based on its thickness: slabs with a thickness less than the set value need to be cooled by cooling bed A, and slabs with a thickness greater than or equal to the set value need to be cooled by cooling bed B; starting from the first slab in rolling scheme 1, the slab is assigned to the corresponding cooling bed until the cooling bed reaches its capacity limit, at which point the cooling bed is switched to form rolling scheme 2; Step 4.1.3: Determine whether the slab belongs to the controlled-rolled slab based on whether it has a waiting time; if the waiting time of the slab is 0, then the slab belongs to the ordinary-rolled slab; if the waiting time of the slab is greater than 0, then the slab belongs to the controlled-rolled slab; ordinary-rolled slabs and controlled-rolled slabs need to be centrally scheduled for production, and the rolling sequence of controlled-rolled slabs should be rolled in order of waiting time from shortest to longest and then back to shortest; starting from the first slab in rolling scheme 2, all slabs are divided into ordinary-rolled slabs or controlled-rolled slabs, among which the controlled-rolled slabs should be sorted in order of waiting time from shortest to longest and then back to shortest to form rolling scheme 3; Step 4.1.4: Arrange the rolling plan by minimizing the number of steel grade changes between adjacent slabs; slabs of the same steel grade should be rolled together as much as possible to reduce the number of steel grade changes between adjacent slabs in the rolling plan. Cluster the slabs in rolling scheme 3 according to steel grade to form rolling scheme 4. Step 4.1.5: Arrange the rolling schedule by minimizing the specification jump penalty between adjacent slabs, i.e., calculate the specification jump penalty between two slabs, where the specification jump penalty is equal to... × Absolute value of the thickness difference between adjacent slabs × The absolute value of the width difference between adjacent slabs These are the weighting coefficients for thickness jump penalties and width jump penalties, respectively. Starting with the first slab in rolling scheme 4, the slabs within each steel grade cluster are incorporated into the rolling plan in the order of minimum specification jumps to form the initial rolling plan.

Images