Intelligent two-dimensional plate grouping method and device for medium plate in steel plant based on two-stage optimization

Abstract

The application provides a two-stage optimization-based intelligent two-dimensional plate grouping method and device for a steel plant, which comprises the following steps: defining decision variables g kv , h ik , p lk , p wk , al ij and bl ij ; taking the minimum waste of the area difference between the mother plate and the total order sub-plate and the area difference between the plate blank section and the mother plate as the multi-optimization target, and constructing an optimization model; using an improved genetic algorithm to solve the first stage, and solving g kv , h ik , p k , p k ; converting the original problem into a two-dimensional packing problem in a certain mother plate area, and performing the second stage optimization to solve al ij and bl ij . The application can better realize the plate grouping scheme formulation of the medium plate.

Description

Technical Field

[0001] This invention relates to the field of metallurgical machinery and automatic combination optimization technology, and in particular to a two-stage optimization-based intelligent two-dimensional plate assembly method and device for medium and heavy plates in steel plants. Background Technology

[0002] In most cases, the design and production assembly methods for steel slabs in steel mills often rely on the experience and knowledge of operators rather than the high-quality, highly intelligent production plans and optimization schemes required by the enterprise. Therefore, the different properties of order sub-slabs, the randomness of processing parameters, and the issue of surplus materials present challenges for steel companies. Firstly, the era of large-scale personalized customization of steel materials is gradually arriving, and downstream users are increasingly demanding personalized services. For traditional medium and heavy plate assembly planning, some factories still rely heavily on manual experience to arrange assembly plans, resulting in low efficiency and unstable arrangement levels. Furthermore, traditional assembly optimization problems generally only involve one-dimensional permutations and combinations, leading to significant surplus materials on the parent slab, insufficient material utilization, and a lack of diverse assembly methods. Summary of the Invention

[0003] This invention provides a two-stage optimization-based intelligent two-dimensional plate assembly method and apparatus for medium and heavy plates in steel plants. The technical solution is as follows:

[0004] On the one hand, a two-stage optimization-based intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants is provided, including:

[0005] S1. Obtain the sub-board parameters of the user's order and the cross-sectional parameters of the slab in the warehouse area, and define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable g. kv The variable h represents the mutual selection relationship between the motherboard and the daughterboard. ik Motherboard length variable pl k Motherboard width variable pw k Sub-board spatial positional relationship variable al ij and BL ij ;

[0006] S2. Based on the defined decision variables and auxiliary intermediate variables, an optimization model is constructed with minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards and the area difference between the slab cross-section and the mother board as multiple optimization objectives.

[0007] S3. An improved genetic algorithm is used to solve the constructed optimization model in the first stage, and the optimal combination of the sub-plate, mother plate, and slab is obtained. kv h ik and pl k ,pw k ;

[0008] S4. Based on the solved g kv h ik and pl k ,pw k The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the algebraic equation representing the spatial positional relationship of the sub-boards on the selected motherboard. ij and BL ij .

[0009] Optionally, S1 specifically includes:

[0010] The parameters of the user order sub-board are obtained, including: the number of order sub-boards n, two distinct sub-boards i and j belonging to the same order set, and the length l of order sub-board i. i Width w i ;

[0011] Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs d, and the length and width sl corresponding to the cross-sectional specification v of the slabs. v ,sw v The width ratio of the slab in the width direction is M = 1.4;

[0012] Define the decision variables as:

[0013] Construct a transitional master board, and assemble the existing order sub-boards onto the master board first;

[0014] pl k ,pw k Let g represent the length and width of mother plate k, and there are m mother plates in total, all of which are real variables; if the k-th mother plate is selected with slab cross-section specification v, then g kv =1, otherwise g kv =0; if the i-th order sub-board selects motherboard k, then h ik =1, otherwise h ik =0;

[0015] Establish a Cartesian coordinate system, with the coordinate axes corresponding to the length and width of the motherboard k, and the origin corresponding to the lower left corner of a motherboard. The lower left corner coordinates of each order sub-board i are represented by (x, y). Then:

[0016]

[0017] (x i ,y i () represents the coordinates of the lower left corner of the order sub-board i in the motherboard to be assembled; (y) j ,y j Let x be the coordinate of the lower left corner of the order sub-board j, which is located under a certain motherboard k, along with i. i x j yi y j All are real number variables;

[0018] If the i-th order sub-board is located to the left of the j-th order sub-board in terms of spatial position, and both are located within the same motherboard, then al ij =1, otherwise al ij =0; If the i-th order sub-board is located below the j-th order sub-board in its spatial position, and both are located within the same motherboard, then bl ij =1, otherwise bl ij =0;

[0019] Define the auxiliary intermediate variable as:

[0020] If the k-th motherboard is used, then the auxiliary intermediate variable z k =1, otherwise z k =0; if the cross-section of the vth slab is used, then the auxiliary intermediate variable y v =1, otherwise y v =0.

[0021] Optionally, minimizing the excess material between the motherboard and the sub-board is taken as the first optimization objective function of the optimization model, and its expression is as follows:

[0022]

[0023] The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area;

[0024] Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows:

[0025]

[0026] The second optimization objective function represents minimizing the difference between the cross-sectional area of ​​the slab multiplied by the width ratio and the corresponding mother slab area.

[0027] Optionally, S3 specifically includes:

[0028] Set the initial parameters for the algorithm;

[0029] Set g kv h ik Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population.

[0030] Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized.

[0031] Setting constraints for the first phase includes:

[0032] 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.4, then pl k ,pw k All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula:

[0033]

[0034] 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula:

[0035]

[0036] 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula:

[0037] (pw k ·pl k -1.4sw v ·sl v )·g kv =0,k=1,...,m,v=1,...,d

[0038] 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula:

[0039]

[0040] h ik ≤z k , i∈n,k∈m

[0041] By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected as the next generation until convergence, finding the optimal solution. The optimal solution includes g... kv h ik and pl k ,pw k .

[0042] Optionally, S4 specifically includes:

[0043] The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board.

[0044]

[0045] The constraints for the second phase include:

[0046] 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula:

[0047]

[0048] 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set so that different sub-plates i and j belonging to the same set will not intersect or overlap in space, thus ensuring spatial feasibility. This constraint is expressed as the following formula:

[0049]

[0050] 3) To ensure that there can only be one spatial relationship between the two sub-boards, it is necessary to adjust the decision variable al that determines the spatial relationship. ij and BL ij To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula:

[0051] al ij +al ji +bl ij +bl ji ≥h ik +h jk -1, i, j ∈ n, k ∈ m, i ≠ j

[0052] The second stage of optimization is performed using a large-scale integer programming solver to obtain the equation representing the spatial relationship between the sub-board and the selected parent board. ij and BL ij .

[0053] On the other hand, a two-stage optimization-based intelligent two-dimensional plate assembly device for medium and heavy plates in steel plants is provided, the device comprising:

[0054] The definition acquisition module is used to acquire user order sub-board parameters and warehouse slab cross-sectional parameters, and to define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable g. kv The variable h represents the mutual selection relationship between the motherboard and the daughterboard. ik Motherboard length variable pl k Motherboard width variable pw k Sub-board spatial positional relationship variable al ij and BL ij ;

[0055] The module is used to construct an optimization model based on the defined decision variables and auxiliary intermediate variables, with the goal of minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards, and the area difference between the slab cross-section and the mother board.

[0056] The first solution module is used to perform the first-stage solution of the constructed optimization model using an improved genetic algorithm, and to solve for g under the optimal combination of the sub-plate, the mother plate, and the slab. kv h ik and pl k ,pw k ;

[0057] The second solution module is used to solve for the g. kv h ik and pl k ,pw k The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the algebraic equation representing the spatial positional relationship of the sub-boards on the selected motherboard. ij and BL ij .

[0058] Optionally, the definition acquisition module is specifically used for:

[0059] The parameters of the user order sub-board are obtained, including: the number of order sub-boards n, two distinct sub-boards i and j belonging to the same order set, and the length l of order sub-board i. i Width w i ;

[0060] Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs d, and the length and width sl corresponding to the cross-sectional specification v of the slabs. v ,sw v The width ratio of the slab in the width direction is M = 1.4;

[0061] Define the decision variables as:

[0062] Construct a transitional master board, and assemble the existing order sub-boards onto the master board first;

[0063] pl k ,pw k Let g represent the length and width of mother plate k, and there are m mother plates in total, all of which are real variables; if the k-th mother plate is selected with slab cross-section specification v, then g kv =1, otherwise g kv =0; if the i-th order sub-board selects motherboard k, then h ik =1, otherwise h ik =0;

[0064] Establish a Cartesian coordinate system, with the coordinate axes corresponding to the length and width of the motherboard k, and the origin corresponding to the lower left corner of a motherboard. The lower left corner coordinates of each order sub-board i are represented by (x, y). Then:

[0065]

[0066] (x i ,y i (x) represents the coordinates of the lower left corner of the order sub-board i in the motherboard to be assembled; (x) j ,y j Let x be the coordinate of the lower left corner of the order sub-board j, which is located under a certain motherboard k, along with i. i x j y i y j All are real number variables;

[0067] If the i-th order sub-board is located to the left of the j-th order sub-board in terms of spatial position, and both are located within the same motherboard, then al ij =1, otherwise al ij =0; If the i-th order sub-board is located below the j-th order sub-board in its spatial position, and both are located within the same motherboard, then bl ij =1, otherwise bl ij =0;

[0068] Define the auxiliary intermediate variable as:

[0069] If the k-th motherboard is used, then the auxiliary intermediate variable z k =1, otherwise z k =0; if the cross-section of the vth slab is used, then the auxiliary intermediate variable y v =1, otherwise y v =0.

[0070] Optionally, minimizing the excess material between the motherboard and the sub-board is taken as the first optimization objective function of the optimization model, and its expression is as follows:

[0071]

[0072] The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area;

[0073] Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows:

[0074]

[0075] The second optimization objective function represents minimizing the difference between the cross-sectional area of ​​the slab multiplied by the width ratio and the corresponding mother slab area.

[0076] Optionally, the first solution module is specifically used for:

[0077] Set the initial parameters for the algorithm;

[0078] Set g kv h ik Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population.

[0079] Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized.

[0080] Setting constraints for the first phase includes:

[0081] 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.4, then pl k ,pw k All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula:

[0082]

[0083] 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula:

[0084]

[0085] 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula:

[0086] (pw k ·pl k -1.4sw v ·sl v )·g kv =0,k=1,...,m,v=1,...,d

[0087] 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula:

[0088]

[0089] h ik ≤z k , i∈n,k∈m

[0090] By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected as the next generation until convergence, finding the optimal solution. The optimal solution includes g... kv h ik and pl k ,pw k .

[0091] Optionally, the second solution module is specifically used for:

[0092] The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board.

[0093]

[0094] The constraints for the second phase include:

[0095] 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula:

[0096]

[0097] 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set so that different sub-plates i and j belonging to the same set will not intersect or overlap in space, thus ensuring spatial feasibility. This constraint is expressed as the following formula:

[0098]

[0099] 3) To ensure that there can only be one spatial relationship between the two sub-boards, it is necessary to adjust the decision variable al that determines the spatial relationship. ij and BL ij To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula:

[0100] al ij +al ji +bl ij +bl ji ≥h ik +h jk -1, i, j ∈ n, k ∈ m, i ≠ j

[0101] The second stage of optimization is performed using a large-scale integer programming solver to obtain the equation representing the spatial relationship between the sub-board and the selected parent board. ij and BL ij .

[0102] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants based on two-stage optimization.

[0103] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, the at least one instruction being loaded and executed by a processor to implement the above-described intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants based on two-stage optimization.

[0104] The beneficial effects of the technical solution provided by this invention include at least the following:

[0105] This invention proposes a two-stage optimization-based intelligent two-dimensional plate assembly method for medium and heavy plates in steel mills. On the one hand, this invention comprehensively considers multiple optimization objectives in the intelligent plate assembly process of medium and heavy plates, taking the different surplus material utilization rates between sub-plates and mother plates, and between mother plates and slabs, as optimization objectives, thereby enhancing the practicality of the model. Furthermore, it statistically analyzes and identifies the types and numbers of slabs and sub-plates in user orders, automatically analyzes and identifies their positional relationships, and displays them using coordinates, thus realizing the design of steel billet materials. On the other hand, this invention selects a genetic algorithm suitable for multi-objective optimization problems for the first stage of solution, improving the efficiency of the algorithm. A large-scale linear solver is used to solve the slab assembly problem in two-dimensional space in the second stage. By using spatial mathematical relationships to calculate the optimal combination between different sub-plates, the plate assembly scheme of medium and heavy plates can be better formulated, improving the slab utilization rate and saving more production costs for the production plant. Attached Figure Description

[0106] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0107] Figure 1 This is a flowchart of a two-stage optimization-based intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants, provided by an embodiment of the present invention.

[0108] Figure 2 This is a schematic diagram of the space allocation result provided in an embodiment of the present invention;

[0109] Figure 3 This is a schematic diagram illustrating the change of the fitness function value from its initial state to finding the optimal state during 50 iterations of the improved genetic algorithm provided in this embodiment of the invention.

[0110] Figure 4 This is a block diagram of a two-stage optimization-based intelligent two-dimensional plate assembly device for medium and heavy plates in steel plants, provided by an embodiment of the present invention.

[0111] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0112] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0113] To address the technical problems of low efficiency and unsatisfactory optimization results in existing one-dimensional plate assembly optimization methods, this invention comprehensively considers multi-objective optimization of the medium-thick plate assembly process and uses intelligent optimization algorithms to solve the assembly optimization problem. Therefore, it proposes a two-stage optimization-based intelligent two-dimensional plate assembly method for steel plants' medium-thick plates. This multi-objective optimization of the plate assembly problem can be achieved using a genetic algorithm combined with a large-scale integer programming solver. The execution flow of this method is as follows: Figure 1 As shown, it includes the following steps:

[0114] S1. Obtain the sub-board parameters of the user's order and the cross-sectional parameters of the slab in the warehouse area, and define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable g. kv The variable h represents the mutual selection relationship between the motherboard and the daughterboard. ik Motherboard length variable pl k Motherboard width variable pw k Sub-board spatial positional relationship variable al ij and BL ij ;

[0115] S2. Based on the defined decision variables and auxiliary intermediate variables, an optimization model is constructed with minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards and the area difference between the slab cross-section and the mother board as multiple optimization objectives.

[0116] S3. An improved genetic algorithm is used to solve the constructed optimization model in the first stage, and the optimal combination of the sub-plate, mother plate, and slab is obtained. kv h ik and pl k ,pw k ;

[0117] S4. Based on the solved g kv h ik and pl k ,pw kThe original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the algebraic equation representing the spatial positional relationship of the sub-boards on the selected motherboard. ij and BL ij .

[0118] The following is combined with Figure 2-3 This invention provides a detailed description of a two-stage optimization-based intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants, comprising:

[0119] S1. Obtain the sub-board parameters of the user's order and the cross-sectional parameters of the slab in the warehouse area, and define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable g. kv The variable h represents the mutual selection relationship between the motherboard and the daughterboard. ik Motherboard length variable pl k Motherboard width variable pw k Sub-board spatial positional relationship variable al ij and BL ij ;

[0120] Optionally, S1 specifically includes:

[0121] The parameters of the user order sub-board are obtained, including: the number of order sub-boards n, two distinct sub-boards i and j belonging to the same order set, and the length l of order sub-board i. i Width w i ;

[0122] Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs d, and the length and width sl corresponding to the cross-sectional specification v of the slabs. v ,sw v The width ratio of the slab in the width direction is M = 1.4;

[0123] Define the decision variables as:

[0124] Construct a transitional master board, and assemble the existing order sub-boards onto the master board first;

[0125] pl k ,pw k Let g represent the length and width of mother plate k, and there are m mother plates in total, all of which are real variables; if the k-th mother plate is selected with slab cross-section specification v, then g kv =1, otherwise g kv =0; if the i-th order sub-board selects motherboard k, then h ik =1, otherwise h ik =0;

[0126] To visually represent the two-dimensional assembly of panels, a Cartesian coordinate system is established. The coordinate axes of the coordinate system correspond to the length and width of the mother panel k, respectively, and the origin of the coordinate system corresponds to the lower left corner of a certain mother panel. The lower left corner coordinates of each order sub-panel i are represented by (x, y). Then:

[0127]

[0128] (x i ,y i (x) represents the coordinates of the lower left corner of the order sub-board i in the motherboard to be assembled; (x) j ,y j Let x be the coordinate of the lower left corner of the order sub-board j, which is located under a certain motherboard k, along with i. i x j y i y j All are real number variables;

[0129] If the i-th order sub-board is located to the left of the j-th order sub-board in terms of spatial position, and both are located within the same motherboard, then al ij =1, otherwise al ij =0; If the i-th order sub-board is located below the j-th order sub-board in its spatial position, and both are located within the same motherboard, then bl ij =1, otherwise bl ij =0;

[0130] Define the auxiliary intermediate variable as:

[0131] If the k-th motherboard is used, then the auxiliary intermediate variable z k =1, otherwise z k =0; if the cross-section of the vth slab is used, then the auxiliary intermediate variable y v =1, otherwise y v =0.

[0132] The order sub-board and slab size parameters of this invention embodiment are shown in Tables 1 and 2 below (thickness is uniformly 10mm by default), including 10 different size models of sub-boards and 3 different slab sizes, which can be imported into the model settings set Orders and Sections and stored in the table below.

[0133] Table 1. Dimensions of hot-rolled subplates at the site

[0134]

[0135]

[0136] Table 2 Hot-rolled slab dimensions

[0137]

[0138] S2. Based on the defined decision variables and auxiliary intermediate variables, an optimization model is constructed with minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards and the area difference between the slab cross-section and the mother board as multiple optimization objectives.

[0139] Optionally, minimizing the excess material between the motherboard and the sub-board is taken as the first optimization objective function of the optimization model, and its expression is as follows:

[0140]

[0141] The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area;

[0142] Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows:

[0143]

[0144] The second optimization objective function represents minimizing the difference between the cross-sectional area of ​​the slab multiplied by the width ratio and the corresponding mother slab area.

[0145] S3. The improved genetic algorithm (GA) is used to solve the constructed optimization model in the first stage, and the g-values ​​are obtained under the optimal combination of the sub-plate, the mother plate, and the slab. kv h ik and pl k ,pw k ;

[0146] Optionally, S3 specifically includes:

[0147] Set the initial parameters for the algorithm;

[0148] Initial parameters may include the population size (Population) and the maximum number of iterations (Iter).

[0149] Set g kv h ik Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population.

[0150] Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized.

[0151] The fitness function can be set to calculate the sum of the first and second optimization objective functions (Min1 + Min2), and the selection is based on the principle of maximizing the utilization of the mother plate and the slab.

[0152] Setting constraints for the first phase includes:

[0153] 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.4, then pl k ,pw k All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula:

[0154]

[0155] 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula:

[0156]

[0157] 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula:

[0158] (pw k ·pl k -1.4sw v ·sl v )·g kv =0,k=1,...,m,v=1,...,d

[0159] 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula:

[0160]

[0161] h ik ≤z k , i∈n,k∈m

[0162] By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected as the next generation until convergence, finding the optimal solution. The optimal solution includes g... kv h ik and pl k ,pw k .

[0163] Figure 3 This is a schematic diagram illustrating the change of the fitness function value from its initial state to finding the optimal state during 50 iterations of the improved genetic algorithm provided in this embodiment of the invention.

[0164] S4. Based on the solved g kv h ik and pl k ,pwk The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the algebraic equation representing the spatial positional relationship of the sub-boards on the selected motherboard. ij and BL ij .

[0165] Optionally, S4 specifically includes:

[0166] The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board.

[0167]

[0168] The constraints for the second phase include:

[0169] 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula:

[0170]

[0171] 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set so that different sub-plates i and j belonging to the same set will not intersect or overlap in space, thus ensuring spatial feasibility. This constraint is expressed as the following formula:

[0172]

[0173] 3) To ensure that there can only be one spatial relationship between the two sub-boards, it is necessary to adjust the decision variable al that determines the spatial relationship. ij and BL ij To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula:

[0174] al ij +al ji +bl ij +bl ji ≥h ik +h jk -1, i, j ∈ n, k ∈ m, i ≠ j

[0175] The second stage of optimization is performed using a large-scale integer programming solver to obtain the equation representing the spatial relationship between the sub-board and the selected parent board. ij and BL ij .

[0176] Based on the input sub-plate and slab size parameters, this invention can obtain the optimal or near-optimal solution under the objective function of minimizing space waste, thus determining the specifications of the mother plate to be assembled, the selected slab cross-section, and the spatial positional relationship of the sub-plate on the selected mother plate. The spatial solution set of the model solution is shown in Table 3 below, which gives the spatial position of the sub-plate, the mutual selection relationship between the sub-plate and the slab, and the slab usage status.

[0177] Table 3 Spatial coordinate distribution of each type of sub-board (bottom left vertex)

[0178]

[0179]

[0180] like Figure 4 As shown, this embodiment of the invention also provides an intelligent two-dimensional plate assembly device for medium and heavy plates in steel plants based on two-stage optimization. The device includes:

[0181] The definition acquisition module 410 is used to acquire user order sub-board parameters and warehouse slab cross-sectional parameters, and to define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable g. kv The variable h represents the mutual selection relationship between the motherboard and the daughterboard. ik Motherboard length variable pl k Motherboard width variable pw k Sub-board spatial positional relationship variable al ij and BL ij ;

[0182] Module 420 is used to construct an optimization model based on the defined decision variables and auxiliary intermediate variables, with minimizing the waste of surplus material formed by the area difference between the mother board and the total order sub-boards and the area difference between the slab cross-section and the mother board as multiple optimization objectives;

[0183] The first solution module 430 is used to perform the first-stage solution of the constructed optimization model using an improved genetic algorithm, and to solve for g under the optimal combination of the sub-plate, the mother plate, and the slab. kv h ik and pl k ,pw k ;

[0184] The second solving module 440 is used to solve for the g... kv h ik and pl k ,pw k The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the algebraic equation representing the spatial positional relationship of the sub-boards on the selected motherboard. ij and BLij .

[0185] Optionally, the definition acquisition module is specifically used for:

[0186] The parameters of the user order sub-board are obtained, including: the number of order sub-boards n, two distinct sub-boards i and j belonging to the same order set, and the length l of order sub-board i. i Width w i ;

[0187] Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs d, and the length and width sl corresponding to the cross-sectional specification v of the slabs. v ,sw v The width ratio of the slab in the width direction is M = 1.4;

[0188] Define the decision variables as:

[0189] Construct a transitional master board, and assemble the existing order sub-boards onto the master board first;

[0190] pl k ,pw k Let g represent the length and width of mother plate k, and there are m mother plates in total, all of which are real variables; if the k-th mother plate is selected with slab cross-section specification v, then g kv =1, otherwise g kv =0; if the i-th order sub-board selects motherboard k, then h ik =1, otherwise h ik =0;

[0191] Establish a Cartesian coordinate system, with the coordinate axes corresponding to the length and width of the motherboard k, and the origin corresponding to the lower left corner of a motherboard. The lower left corner coordinates of each order sub-board i are represented by (x, y). Then:

[0192]

[0193] (x i ,y i (x) represents the coordinates of the lower left corner of the order sub-board i in the motherboard to be assembled; (x) j ,y j Let x be the coordinate of the lower left corner of the order sub-board j, which is located under a certain motherboard k, along with i. i x j y i y j All are real number variables;

[0194] If the i-th order sub-board is located to the left of the j-th order sub-board in terms of spatial position, and both are located within the same motherboard, then al ij =1, otherwise al ij=0; If the i-th order sub-board is located below the j-th order sub-board in its spatial position, and both are located within the same motherboard, then bl ij =1, otherwise bl ij =0;

[0195] Define the auxiliary intermediate variable as:

[0196] If the k-th motherboard is used, then the auxiliary intermediate variable z k =1, otherwise z k =0; if the cross-section of the vth slab is used, then the auxiliary intermediate variable y v =1, otherwise y v =0.

[0197] Optionally, minimizing the excess material between the motherboard and the sub-board is taken as the first optimization objective function of the optimization model, and its expression is as follows:

[0198]

[0199] The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area;

[0200] Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows:

[0201]

[0202] The second optimization objective function represents minimizing the difference between the cross-sectional area of ​​the slab multiplied by the width ratio and the corresponding mother slab area.

[0203] Optionally, the first solution module is specifically used for:

[0204] Set the initial parameters for the algorithm;

[0205] Set g kv h ik Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population.

[0206] Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized.

[0207] Setting constraints for the first phase includes:

[0208] 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.4, then pl k ,pw k All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula:

[0209]

[0210] 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula:

[0211]

[0212] 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula:

[0213] (pw k ·pl k -1.4sw v ·sl v )·g kv =0,k=1,...,m,v=1,...,d

[0214] 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula:

[0215]

[0216] h ik ≤z k , i∈n,k∈m

[0217] By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected as the next generation until convergence, finding the optimal solution. The optimal solution includes g... kv h ik and pl k ,pw k .

[0218] Optionally, the second solution module is specifically used for:

[0219] The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board.

[0220]

[0221] The constraints for the second phase include:

[0222] 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula:

[0223]

[0224] 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set so that different sub-plates i and j belonging to the same set will not intersect or overlap in space, thus ensuring spatial feasibility. This constraint is expressed as the following formula:

[0225]

[0226] 3) To ensure that there can only be one spatial relationship between the two sub-boards, it is necessary to adjust the decision variable al that determines the spatial relationship. ij and BL ij To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula:

[0227] al ij +al ji +bl ij +bl ji ≥h ik +h jk -1, i, j ∈ n, k ∈ m, i ≠ j

[0228] The second stage of optimization is performed using a large-scale integer programming solver to obtain the equation representing the spatial relationship between the sub-board and the selected parent board. ij and BL ij .

[0229] The present invention provides an intelligent two-dimensional plate assembly device for medium and heavy plates in steel plants based on two-stage optimization. Its functional structure corresponds to the intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants based on two-stage optimization provided in the present invention, and will not be described again here.

[0230] Figure 5 This is a schematic diagram of the structure of an electronic device 500 provided in an embodiment of the present invention. The electronic device 500 may vary considerably due to different configurations or performance. It may include one or more central processing units (CPUs) 501 and one or more memories 502. The memory 502 stores at least one instruction, which is loaded and executed by the processor 501 to implement the steps of the above-mentioned intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants based on two-stage optimization.

[0231] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to complete the above-described intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants based on two-stage optimization. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device, etc.

[0232] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0233] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-stage optimization-based intelligent two-dimensional plate assembly method for medium and heavy plates in steel plants, characterized in that, The method includes: S1. Obtain the sub-board parameters of the user's order and the cross-sectional parameters of the slab in the warehouse area, and define decision variables and auxiliary intermediate variables. The decision variables include the mutual selection relationship variables between the parent board and the slab. Variables representing the mutual selection relationship between motherboard and daughterboard Motherboard length variable Motherboard width variable Sub-board spatial positional relationship variables and ; S1 specifically includes: The parameters of the user order sub-board are obtained, including: the number of order sub-boards. Two distinct sub-boards belonging to the same order set Order subboard length 、 width ; Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs. Slab cross-sectional specifications The corresponding length and width are , The width ratio of the slab is =1.4; Define the decision variables as: Construct a transitional master board, and assemble the existing order sub-boards onto the master board first; Representative motherboard The length and width, total The motherboards are all real variables; if the first motherboard is... Selecting the cross-sectional specifications of the mother plate ,but =1, otherwise =0; if the first Block order daughterboard selection motherboard ,but =1, otherwise =0; Establish a Cartesian coordinate system, with the coordinate axes corresponding to the parent plate. The length and width, the origin of the coordinate system corresponds to the lower left corner of a certain master board, and each order's sub-board The coordinates of the lower left corner are used If we express this, then we have: ， Indicates order subboard The coordinates of the lower left corner of the motherboard to be assembled; For and Both are located on the same motherboard Orders placed by the sub-board The coordinates of the lower left corner, , , , All are real number variables; If the first Block order sub-board is located in the first If the block order sub-board is located to the left of the space, and both are within the same motherboard, then... =1, otherwise =0; if the first Block order sub-board is located in the first If the order sub-board is located below the space of the block order sub-board, and both are located within the same motherboard, then =1, otherwise =0; Define the auxiliary intermediate variable as: If the first If the master block is used, then auxiliary intermediate variables are used. =1, otherwise =0; if the first If the cross-section of the slab is used, then =1, otherwise =0; S2. Based on the defined decision variables and auxiliary intermediate variables, an optimization model is constructed with minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards and the area difference between the slab cross-section and the mother board as multiple optimization objectives. Minimizing the excess material between the motherboard and the sub-board is the first optimization objective function of the optimization model, expressed as follows: ； The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area; Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows: ； The second optimization objective function represents minimizing the difference between the slab cross-sectional area multiplied by the width ratio and the corresponding mother slab area; S3. An improved genetic algorithm is used to solve the constructed optimization model in the first stage, obtaining the optimal combination of sub-plates, mother plates, and slabs. , and , ; S4. Based on the solution obtained... , and , The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the spatial positional relationship of the child boards on the selected motherboard. and .

2. The method according to claim 1, characterized in that, S3 specifically includes: Set the initial parameters for the algorithm; set up Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population. Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized; Setting constraints for the first phase includes: 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.

4. , All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula: ； 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula: ； 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula: ； 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula: ； ； By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected for the next generation until convergence, finding the optimal solution. The optimal solution includes... , and , .

3. The method according to claim 1, characterized in that, S4 specifically includes: The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board. ； The constraints for the second phase include: 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula: ； 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set to ensure that different sub-plates belonging to the same set do not conflict. The constraints ensure that the elements do not intersect or overlap in space, guaranteeing spatial feasibility. This can be expressed as a constraint using the following formula: ； 3) To ensure that there can only be one spatial relationship between two sub-boards, it is necessary to adjust the decision variables that determine the spatial relationship. and To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula: ； The second stage of optimization is performed using a large-scale integer programming solver to determine the spatial relationship between the sub-board and the selected parent board. and .

4. A two-stage optimization-based intelligent two-dimensional plate assembly device for medium and heavy plates in steel plants, characterized in that, The device includes: The definition acquisition module is used to acquire user order sub-board parameters and warehouse slab cross-sectional parameters, and to define decision variables and auxiliary intermediate variables. The decision variables include the parent board slab mutual selection relationship variable. Variables representing the mutual selection relationship between motherboard and daughterboard Motherboard length variable Motherboard width variable Sub-board spatial positional relationship variables and ; The definition acquisition module is specifically used for: The parameters of the user order sub-board are obtained, including: the number of order sub-boards. Two distinct sub-boards belonging to the same order set Order subboard length 、 width ; Obtain the cross-sectional parameters of the slabs in the storage area, including: the number of slabs. Slab cross-sectional specifications The corresponding length and width are , The width ratio of the slab is =1.4; Define the decision variables as: Construct a transitional master board, and assemble the existing order sub-boards onto the master board first; Representative motherboard The length and width, total The motherboards are all real variables; if the first motherboard is... Selecting the cross-sectional specifications of the mother plate ,but =1, otherwise =0; if the first Block order daughterboard selection motherboard ,but =1, otherwise =0; Establish a Cartesian coordinate system, with the coordinate axes corresponding to the parent plate. The length and width, the origin of the coordinate system corresponds to the lower left corner of a certain master board, and each order's sub-board The coordinates of the lower left corner are used If we express this, then we have: ， Indicates order subboard The coordinates of the lower left corner of the motherboard to be assembled; For and Both are located on the same motherboard Orders placed by the sub-board The coordinates of the lower left corner, , , , All are real number variables; If the first Block order sub-board is located in the first If the block order sub-board is located to the left of the space, and both are within the same motherboard, then... =1, otherwise =0; if the first Block order sub-board is located in the first If the order sub-board is located below the space of the block order sub-board, and both are located within the same motherboard, then =1, otherwise =0; Define the auxiliary intermediate variable as: If the first If the master block is used, then auxiliary intermediate variables are used. =1, otherwise =0; if the first If the cross-section of the slab is used, then =1, otherwise =0; The module is used to construct an optimization model based on the defined decision variables and auxiliary intermediate variables, with the goal of minimizing the waste of surplus material caused by the area difference between the mother board and the total order sub-boards, and the area difference between the slab cross-section and the mother board. Minimizing the excess material between the motherboard and the sub-board is the first optimization objective function of the optimization model, expressed as follows: ； The first optimization objective function represents minimizing the difference between the motherboard area and the total ordered sub-board area; Minimizing the excess material between the cross sections of the mother slab blank is taken as the second optimization objective function of the optimization model, and its expression is as follows: ； The second optimization objective function represents minimizing the difference between the slab cross-sectional area multiplied by the width ratio and the corresponding mother slab area; The first solution module is used to perform the first stage of solving the constructed optimization model using an improved genetic algorithm, and to find the optimal combination of the sub-plate, mother plate, and slab. , and , ; The second solution module is used to solve the problem based on the solution obtained from the solution. , and , The original problem is transformed into a two-dimensional bin packing problem within a certain motherboard region. A large-scale integer programming solver is used for the second stage of optimization to solve for the spatial positional relationship of the child boards on the selected motherboard. and .

5. The apparatus according to claim 4, characterized in that, The first solution module is specifically used for: Set the initial parameters for the algorithm; set up Different combinations form the initial population set. The population is encoded using 0-1 encoding, and then the population is initialized to obtain the offspring population. The offspring population and the parent population are merged to generate a population that is twice the size of the original population. Set a fitness function to evaluate the population so that the space utilization of the daughter board on the mother board is maximized; Setting constraints for the first phase includes: 1) Define the upper limit of the mother plate dimensions, and set the width ratio of the slab cross-section as 1.

4. , All must be less than the length of the selected cross-section multiplied by the width ratio, as expressed by the following constraint formula: ； 2) The constraint stipulates that each type of motherboard can only select one slab cross-sectional specification, expressed as the following formula: ； 3) The cross-section of the expanded slab is equal in volume to the designed base plate. Assuming both have the same thickness, the volume relationship is converted into an area relationship, expressed as the constraint of the following formula: ； 4) It is necessary to determine that each sub-plate has exactly one slab blank for loading to meet the actual design requirements, expressed as the constraint described in the following formula: ； ； By implementing crossover and mutation mechanisms in the population, more combination possibilities are created between the daughter plate, mother plate, and slab. Then, the fitness functions of the new population and the previous generation are compared. Chromosomes with higher fitness functions are selected for the next generation until convergence, finding the optimal solution. The optimal solution includes... , and , .

6. The apparatus according to claim 4, characterized in that, The second solution module is specifically used for: The objective function for the second stage is to subtract the sum of the areas of all selected sub-boards from each mother board. ； The constraints for the second phase include: 1) To ensure that the two sub-boards do not overlap, a penalty value M with a maximum value is introduced to constrain the spatial relationship, so that each sub-board does not conflict with the others in space. This constraint is expressed by the following formula: ； 2) To ensure that the spatial relationships between sub-plates installed in the same slab do not conflict, a penalty function is set to ensure that different sub-plates belonging to the same set do not conflict. The constraints ensure that the elements do not intersect or overlap in space, guaranteeing spatial feasibility. This can be expressed as a constraint using the following formula: ； 3) To ensure that there can only be one spatial relationship between two sub-boards, it is necessary to adjust the decision variables that determine the spatial relationship. and To impose constraints, if two sub-plates belong to the same slab, their spatial relationship can only be one of two options: up, down, left, or right. This constraint is expressed by the following formula: ； The second stage of optimization is performed using a large-scale integer programming solver to determine the spatial relationship between the sub-board and the selected parent board. and .

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