A steel hot rolling process task allocation method based on Ising model

Abstract

The application relates to a steel hot rolling process task allocation method based on an Ising model. The method is realized through the following steps: firstly, setting a hot rolling scheduling problem parameter, establishing a multi-traveling salesman problem model of the problem and further converting the model into a conventional traveling salesman problem model; secondly, combining the Ising model to transform the original steel hot rolling scheduling problem model, converting the problem into a form capable of being solved by using the Ising model; then, based on the transformed Ising model, an Ising machine based on a Hamilton Monte Carlo sampling simulated annealing algorithm is used for solving; finally, the solving result is converted into an understandable hot rolling scheduling scheme. Compared with the prior art, the application introduces a novel simulated annealing algorithm based on a Hamilton Monte Carlo sampling, which is used for solving a large-scale scheduling problem. The algorithm can improve the search solving efficiency, and enhance the accuracy and applicability of multi-task allocation planning. Therefore, the application has important practical engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of large-scale system planning, scheduling and optimization, and in particular relates to a task allocation method for hot rolling processes in steel based on the Ising model. Background Technology

[0002] Steel is one of the world's most important production materials, and the steel industry is the foundation for the development of many other industries. Therefore, optimizing production processes and improving task allocation efficiency are of great significance to steel production. Using effective production planning and scheduling methods can not only improve production efficiency but also enhance product quality and significantly reduce production costs.

[0003] In the steel industry, hot rolling, which involves pressing high-temperature steel into coils or plates of specific dimensions using rolls, is often considered the bottleneck in the entire production process. Therefore, developing an efficient hot rolling production scheduling method will greatly improve steel production efficiency. Hot rolling scheduling specifically refers to determining the hot rolling order units and sequence; see the appendix for details. Figure 1 The most traditional method for hot rolling scheduling relies on manual intervention. A feasible production plan can be found by sequentially arranging the data using a greedy algorithm, but it is difficult to achieve the optimal solution.

[0004] Besides manual methods, the hot rolling production scheduling problem can actually be modeled as a complex combinatorial optimization problem, and a scheduling scheme can be obtained by solving the combinatorial optimization. Currently, methods for solving combinatorial optimization problems can be broadly divided into two categories: exact solutions and heuristic methods. Exact solutions include branch and bound, relaxation methods, and dynamic programming, etc. Although they can find the global optimum, they take exponential time as the problem size increases, thus failing to solve large-scale system problems. Heuristic methods include simulated annealing, genetic algorithms, ant colony optimization, particle swarm optimization, etc. Although they are relatively faster, they often fall into local optima.

[0005] In summary, existing research still faces the challenge of rapidly and accurately scheduling hot rolling production in steel plants. In fact, some specific combinatorial optimization problems can be transformed into the Ising model. The Ising model was originally proposed to explain phase transitions in ferromagnetic materials. Due to its high degree of abstraction, it has been applied to many other fields, and Ising machines based on principles such as simulated annealing, quantum annealing, and coherent optics have been developed to solve the Ising problem. By solving the Ising model, hot rolling scheduling schemes can be obtained more quickly and accurately. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a task allocation method for hot rolling processes in steel based on the Ising model, and to conduct experimental verification.

[0007] The objective of this invention is achieved through the following technical solution: a task allocation method for hot rolling processes in steel based on the Ising model, comprising the following steps:

[0008] S1. Set the parameters for the hot rolling scheduling problem and establish a traveling salesman problem model for the hot rolling scheduling problem;

[0009] S2. Transform the traveling salesman problem model into a form that can be solved using the Ising model, so as to obtain the Hamiltonian in the Ising model;

[0010] S3. Solve the Hamiltonian H using the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm to obtain the system variables;

[0011] S4. Transform the system variables to obtain the cycle in which each hot rolling order is located and the order of each hot rolling order within each cycle, thereby realizing the allocation of tasks for the hot rolling process of steel.

[0012] Preferably, in S1, the functional form of the traveling salesman problem model is as follows:

[0013]

[0014] The functional form of the constraints in the traveling salesman problem model is as follows:

[0015]

[0016]

[0017] a ik ∈{0,1} (4)

[0018] Where f represents the objective function of the traveling salesman problem model; W kl This represents the switching penalty cost between hot-rolled order k and order l; the total number of hot-rolled orders K = {k, l} in the hot-rolled scheduling problem is M virtual hot-rolled orders and N real hot-rolled orders; the number of hot-rolling cycles in the hot-rolled scheduling problem is M.

[0019] For each hot-rolled order k∈{1,2,...,N,N+1,N+2,...,N+M}, where a ik Let a represent the allocation state in step i. ik Only take the value 0 or 1, when a ik A value of 1 indicates that hot-rolled order k is assigned in step i; when a ik A value of 0 indicates that no hot-rolled order k was assigned in step i.

[0020] For each hot-rolled order l∈{1,2,...,N,N+1,N+2,...,N+M}, where a (i+1)l Let a represent the allocation state of each hot-rolled order l∈{1, 2, ..., N} at step i+1. (i+1)l Only take the value 0 or 1, when a (i+1)l A value of 1 indicates that a hot-rolled order l is assigned in step i+1. (i+1)l A value of 0 indicates that no hot-rolled order l was assigned in step i+1; and satisfies

[0021] a (N+M+1 ) l =a 1l (5)

[0022] At the same time, using a ik a (i+1)l Construct the allocation result matrix A (N+M)×(N+M) .

[0023] Preferably, the method for transforming the traveling salesman problem model of the hot rolling scheduling problem in S2 is as follows:

[0024] S21. Construct the objective function f, which carries the constraints. The objective function has the following form:

[0025]

[0026] S22. Introducing the intermediate variable σ ik According to formula (7), a ik Replace ∈{0,1} with σ ik ∈{-1, 1}, intermediate matrix σ={σ ik}, the functional form of formula (7) is:

[0027]

[0028] S23. σ ik Substituting into formula (6), we obtain H by squaring and combining the results. A H B H C H A H B H C The function form is:

[0029]

[0030]

[0031]

[0032] S24. HA H B H C The summation yields the Hamiltonian H in the Ising model, and the functional form of Hamiltonian H is:

[0033]

[0034] S25. Expanding and combining like terms of the summation sign of the Hamiltonian H described in S24, the final functional form of the Hamiltonian H is obtained as follows:

[0035]

[0036] Among them, h ik The function form is:

[0037]

[0038] Among them, J ikjl The function form is:

[0039]

[0040] Where A, B, and C represent positive hyperparameters used to balance the relative strength of the objective function and the constraints; const represents a constant; H A It is the expansion result of the first term of the objective function; H B It is the expansion result of the second term of the objective function; H C It is the result of expanding the third term of the objective function.

[0041] Preferably, in step S3, the method for obtaining the system variable s* is as follows:

[0042] S31. First, set the constant and variable hyperparameters in the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm; among them, the constant hyperparameters include dimension, acceptance rate threshold, temperature iteration value, maximum number of iterations, cooling threshold, number of update steps per iteration, and simulation degree γ; the variable hyperparameters include the current temperature value T, learning rate ε, system displacement variable p, system velocity variable q, system variable s*, and system temperature T; and randomly initialize the system variable s* and system temperature T.

[0043] S32. After setting the constant hyperparameters and variable hyperparameters, the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm is used to solve the Hamiltonian quantity H. In each iteration, the gradient of the Hamiltonian change is updated using Hamiltonian Monte Carlo, the Hamiltonian Monte Carlo sampling acceptance rate is calculated and the temperature of the Ising machine is updated, and the spin state of the Ising machine is updated. The iteration process is repeated until T < the cooling threshold, at which point the iteration stops and the system variable s* is output. s* is a (N+M)×(N+M) one-dimensional array, thus completing the solution of the Hamiltonian quantity H.

[0044] Preferably, in step S4, the method for transforming the system variable s* to obtain the cycle in which each hot-rolled order belongs and the order of each hot-rolled order within each cycle is as follows:

[0045] Arrange the system variables s* in rows to form an intermediate matrix σ. For each element σ in the intermediate matrix σ... ik The allocation result matrix A is obtained by converting according to formula (7). Each row of the allocation result matrix has only one 1 value, and the rest of the elements of the allocation result matrix are all 0 values. In each row of the allocation result matrix, the order of each hot-rolled order in each round is determined by the position of the 1 value. The total hot-rolled orders are sorted to obtain the order of each hot-rolled order in each round. At the same time, the M virtual hot-rolled orders are removed from the sorted total hot-rolled orders, so that the N real hot-rolled orders can be divided into M rounds to complete the allocation of the hot-rolling process tasks of steel.

[0046] The beneficial effects of this invention are:

[0047] A novel Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm is introduced into the hot rolling scheduling problem of steel to solve large-scale scheduling problems. The Ising machine algorithm based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm can improve the search efficiency, enhance the accuracy and applicability of multi-task allocation planning, and ultimately obtain a hot rolling scheduling scheme more quickly and accurately. Attached Figure Description

[0048] Figure 1 This is a schematic diagram illustrating the meaning of hot rolling scheduling, specifically referring to determining the hot rolling order unit and the order sequence of hot rolling orders. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0050] This invention provides a method for task allocation in hot rolling processes of steel based on the Ising model. The specific technical solution adopted in this embodiment is as follows:

[0051] 1) Set the parameters for the hot rolling scheduling problem, establish a multiple traveling salesman problem (MTSP) model for the hot rolling scheduling problem, and further transform it into a regular traveling salesman problem (TSP) model for the hot rolling scheduling problem.

[0052] Since the hot-rolled material within each hot-rolling cycle only requires simple manual determination, it is not considered in the modeling. When building the model, specific information for each order needs to be set, including the required steel width w, thickness h, and hardness g. The penalty weight W for adjacent steels with different requirements also needs to be specified in advance. Table 1 shows the penalty structure for width changes before and after the hot-rolling unit. Table 2 shows the penalty structure for hardness changes before and after the hot rolling unit. Table 3 shows the penalty structure for thickness changes before and after the hot rolling unit.

[0053] Table 1

[0054]

[0055] Table 2

[0056]

[0057] Table 3

[0058]

[0059] Since the width, thickness, and hardness required for each order are different, the wear of the rolls will be caused, which will affect the hot rolling efficiency and product quality. Therefore, the hot rolling scheduling problem can be described as arranging the round in which each hot rolling order is located and its order in the corresponding round in order to achieve high hot rolling efficiency, low roll wear, and high product quality.

[0060] If we set up a virtual warehouse, the hot rolling scheduling problem becomes equivalent to the standard MTSP model of M traveling salesmen traversing N cities, the only difference being that the distance between the virtual warehouse and all other nodes is 0. If we set up M-1 more virtual nodes in the same location as the virtual warehouse, then the MTSP model of the hot rolling scheduling problem can be transformed into the standard TSP model of one traveling salesman traversing N+M cities, the only difference being that the distance between the M virtual nodes and all other normal nodes is 0, while the distance between the virtual nodes is infinite.

[0061] The functional form of the traveling salesman problem model is as follows:

[0062]

[0063] The functional form of the constraints in the traveling salesman problem model is as follows:

[0064]

[0065]

[0066] a ik ∈{0,1} (18)

[0067] Where f represents the objective function of the traveling salesman problem model; the total hot-rolled orders K = {k, l} of the hot-rolled scheduling problem have M virtual hot-rolled orders and N real hot-rolled orders; the number of hot-rolled rolls in the hot-rolled scheduling problem is M.

[0068] For each hot-rolled order k∈{1,2,...,N,N+1,N+2,...,N+M}, where a ik Let a represent the allocation state in step i. ik Only take the value 0 or 1, when a ik A value of 1 indicates that hot-rolled order k is assigned in step i; when a ik A value of 0 indicates that no hot-rolled order k was assigned in step i.

[0069] For each hot-rolled order l∈{1,2,...,N,N+1,N+2,...,N+M}, where a (i+1)l Let a represent the allocation state of each hot-rolled order l∈{1, 2, ..., N} at step i+1. (i+1)l Only take the value 0 or 1, when a (i+1)l A value of 1 indicates that a hot-rolled order l is assigned in step i+1. (i+1)l A value of 0 indicates that no hot-rolled order l was assigned in step i+1; and satisfies

[0070] a (N+M+1)l =a 1l (19)

[0071] At the same time, using a ik a (i+1)l Construct the allocation result matrix A (N+M)×(N+M) W kl Let W represent the switching penalty cost between hot-rolled order k and order l, and W kl satisfy

[0072]

[0073] in, It can be determined by looking up a table; for specific table lookup methods, please refer to Table 1-3.

[0074] 2) Transform the traveling salesman problem model into a form that can be solved using the Ising model, so as to obtain the Hamiltonian in the Ising model;

[0075] Step 21. Construct the objective function f, which carries the constraints. The objective function has the following form:

[0076]

[0077] Step 22. Introduce the intermediate variable σ ik According to formula (22), a ik Replace ∈{0,1} with σ ik ∈{-1, 1}, intermediate matrix σ={σ ik}, the functional form of formula (22) is:

[0078]

[0079] Step 23. σ ik Substituting into formula (21), we obtain H by squaring and combining the results. A H B H C H A H B H C The function form is:

[0080]

[0081]

[0082]

[0083] Step 24. Transfer H A H B H C The summation yields the Hamiltonian H in the Ising model, and the functional form of Hamiltonian H is:

[0084]

[0085] Step 25. Expand the summation sign of the Hamiltonian H described in S24 and combine like terms to obtain the final functional form of the Hamiltonian H as follows:

[0086]

[0087] Among them, h ik The function form is:

[0088]

[0089] Among them, Jikjl The function form is:

[0090]

[0091] Where A, B, and C represent positive hyperparameters used to balance the relative strength of the objective function and the constraints; const represents a constant; H A It is the expansion result of the first term of the objective function; H B It is the expansion result of the second term of the objective function; H C It is the result of expanding the third term of the objective function.

[0092] 3) The Hamiltonian H is solved using the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm to obtain the system variable s*; the method for obtaining the system variable s* is as follows:

[0093] Step 31. First, set the constant and variable hyperparameters in the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm; among them, the constant hyperparameters include dimension, acceptance rate threshold, temperature iteration value, maximum number of iterations, cooling threshold, number of update steps per iteration, and simulation degree γ; the variable hyperparameters include the current temperature value T, learning rate ε, system displacement variable p, system velocity variable q, system variable s*, and system temperature T; and randomly initialize the system variable s* and system temperature T.

[0094] The specific hyperparameter settings for the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm are as follows:

[0095] Dimension: dim = N + M

[0096] Acceptance rate threshold: accept_rate = 0.98

[0097] Temperature iteration value: delta_step = 1.2

[0098] Maximum number of iterations: stop_time = 2**dim

[0099] Cooling threshold (final temperature): temp_threshold = 0.1

[0100] Number of update steps per iteration: step_num = 30

[0101] Simulation degree: γ = 100

[0102] Current temperature: T = 100

[0103] Learning rate: ε: = 0.01

[0104] System displacement variable: p := uniform[-1, 1]N

[0105] System velocity variable: q := uniform[-1, 1]N

[0106] The system variable s* is randomly initialized with a value of ±1;

[0107] Step 32. After setting the constant and variable hyperparameters, the Hamiltonian H is solved using the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm. In each iteration, the gradient of the Hamiltonian change is updated using Hamiltonian Monte Carlo, the Hamiltonian Monte Carlo sampling acceptance rate is calculated and the temperature of the Ising machine is updated, and the spin state of the Ising machine is updated. The iteration process is repeated until T < the cooling threshold, at which point the iteration stops and the system variable s* is output. s* is a (N+M)×(N+M) one-dimensional array, thus completing the solution for the Hamiltonian H.

[0108] 4) Transform the system variable s* to obtain the round in which each hot rolling order is located and the order of each hot rolling order in each round, so as to realize the allocation of tasks for the hot rolling process of steel.

[0109] The method for transforming the system variable s* to obtain the cycle number of each hot-rolled order and the order of each hot-rolled order within each cycle is as follows:

[0110] Arrange the system variables s* in rows to form an intermediate matrix σ. For each element σ in the intermediate matrix σ... ik The allocation result matrix A is obtained by converting according to formula (7). Each row of the allocation result matrix has only one 1 value, and the rest of the elements of the allocation result matrix are all 0 values. In each row of the allocation result matrix, the order of each hot-rolled order in each round is determined by the position of the 1 value. The total hot-rolled orders are sorted to obtain the order of each hot-rolled order in each round. At the same time, the M virtual hot-rolled orders are removed from the sorted total hot-rolled orders, so that the N real hot-rolled orders can be divided into M rounds to complete the allocation of the hot-rolling process tasks of steel.

[0111] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A task allocation method for hot rolling processes in steel based on the Ising model, characterized in that, Includes the following steps: S1. Set the parameters for the hot rolling scheduling problem and establish a traveling salesman problem model for the hot rolling scheduling problem; S2. Transform the traveling salesman problem model into a form that can be solved using the Ising model, so as to obtain the Hamiltonian in the Ising model; S3. Solve the Hamiltonian using the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm to obtain the system variables; S4. Transform the system variables to obtain the cycle in which each hot rolling order is located and the order of each hot rolling order within each cycle, so as to allocate the tasks of the hot rolling process of steel. In S3, the system variables are obtained. The method is as follows: S31. First, set the constant and variable hyperparameters in the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm; among them, the constant hyperparameters include dimension, acceptance rate threshold, temperature iteration value, maximum number of iterations, cooling threshold, number of update steps per iteration, and simulation degree. The hyperparameters include the current temperature value T and the learning rate. System displacement variables System velocity variables System variables System temperature ; and for system variables Randomly initialize with system temperature φ; S32. After setting the constant hyperparameters and variable hyperparameters, the Ising machine based on the Hamiltonian Monte Carlo sampling simulated annealing algorithm is used to solve the Hamiltonian. In each iteration, the Hamiltonian gradient is updated using Hamiltonian Monte Carlo algorithm, the Hamiltonian Monte Carlo sampling acceptance rate is calculated, and the temperature and spin state of the Ising machine are updated. This iterative process is repeated until φ < the cooling threshold, at which point the iteration stops and the system variables are output. , for A one-dimensional array is used to complete the calculation of the Hamiltonian. The solution; where This represents the actual number of hot-rolled orders. This represents the number of virtual hot-rolled orders; In S4, the system variables The method for converting and obtaining the cycle number of each hot-rolled order and the chronological order of each hot-rolled order within each cycle is as follows: System variables Arranged in rows to form an intermediate matrix For the intermediate matrix Each element in According to the formula Perform the conversion. Indicates the first Step-by-step allocation of states to obtain the allocation result matrix. Each row of the allocation result matrix contains only one 1 value, while the remaining elements are all 0 values. Within each row of the allocation result matrix, the order of each hot-rolled order within each round is determined by the position of the 1 value. The total hot-rolled orders are then sorted to obtain the chronological order of each hot-rolled order within each round. Simultaneously, from the sorted total hot-rolled orders, orders that are not 1 are removed. A virtual hot-rolled order can be used to... Each real hot-rolled order is divided into Each round completes the allocation of tasks for the hot rolling process of steel.

2. The task allocation method for hot rolling steel processes based on the Ising model as described in claim 1, characterized in that, The functional form of the traveling salesman problem model is as follows: The functional form of the constraints in the traveling salesman problem model is as follows: in, This represents the objective function of the traveling salesman problem model. Indicates hot-rolled orders Orders Switching penalty costs between; total hot-rolled orders for hot-rolled scheduling issues. have Virtual hot rolling orders and hot rolling scheduling problems The actual hot-rolled orders in the hot-rolling scheduling problem; the number of hot-rolling rolls in the hot-rolling scheduling problem. Second-rate; For each hot-rolled order ,in, Only take the value 0 or 1, when A value of 1 indicates that the number of times ... Step-by-step allocation to hot-rolled orders ;when A value of 0 indicates the first time. Step not assigned to hot rolling orders ; For each hot-rolled order ,in, Indicates the first Each hot-rolled order The allocation status, Only take the value 0 or 1, when A value of 1 represents the first time. Step-by-step allocation to hot-rolled orders ,when A value of 0 indicates the first time. Step not assigned to hot rolling orders ; and satisfy At the same time, utilizing Construct the allocation result matrix .

3. The task allocation method for hot rolling steel processes based on the Ising model as described in claim 2, characterized in that, In S2, the method for transforming the traveling salesman problem model of the hot rolling scheduling problem is as follows: S21. Construct the objective function. , With the aforementioned constraints, the objective function has the following form: S22. Introducing intermediate variables According to formula (7) for intermediate matrix The functional form of formula (7) is: S23. Will Substituting into formula (6), we obtain the result by squaring and combining the results. The function form is: S24. Will The Hamiltonian in the Ising model is obtained by summing. Hamiltonian The function form is: S25. The Hamiltonian described in S24 Expand and combine like terms to obtain the final Hamiltonian. The function form is: in, The function form is: in, The function form is: in, A, B, and C represent positive hyperparameters used to balance the relative strength of the objective function and the constraints. Represents a constant; It is the result of expanding the first term of the objective function; It is the result of expanding the second term of the objective function; It is the result of expanding the third term of the objective function.

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