A hot rolling scheduling method and system considering uncertain rolling time

Abstract

A hot rolling scheduling method and system considering uncertain rolling time, relating to the field of automatic control technology, comprising the following steps: S1, constructing an objective function based on the total penalty for the differences in width, thickness and hardness between adjacent slabs; S2, constructing constraints of the objective function based on the uncertainty of the rolling time distribution of the slabs; S3, solving the objective function based on the constraints, and determining a scheduling scheme based on the solution results; by considering the uncertainty of the slab rolling time, the rolling sequence of the slabs and the rolling time of each slab are determined using limited probability distribution information. In the case of large fluctuations in rolling time, the limited probability distribution information can be used to provide a feasible scheduling scheme with good robustness, avoiding the impact of uncertain delays in the previous production process that is not considered, improving scheduling efficiency, and reducing cost losses caused by differences in width, thickness and hardness between slabs.

Description

Technical Field

[0001] The present application relates to the field of automatic control technology, and in particular to a hot rolling scheduling method and system considering uncertain rolling time. Background Art

[0002] In the hot rolling process of steel production, slabs from the continuous caster, slab storage, or holding pit are first fed into a walking or pusher furnace. The slabs heated in the furnace are then processed through a roughing mill, which is mainly used to reduce the thickness of the slabs (initially 20-30 cm). The roughed slabs are then fed into a finishing mill, where 6-7 rollers can further reduce the thickness of the slabs to the required value. However, during the rolling process, differences in width, thickness, and hardness between the slabs can occur, resulting in cost losses. How to reduce the cost losses caused by differences in width, thickness, and hardness between the slabs is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0003] (1) Purpose of application

[0004] In view of this, the purpose of this application is to provide a hot rolling scheduling method and system that takes into account uncertain rolling time, so as to solve the technical problem of how to reduce the cost loss caused by the differences in width, thickness and hardness between slabs.

[0005] (2) Technical solution

[0006] The present application discloses a hot rolling scheduling method considering uncertain rolling time, comprising the following steps:

[0007] S1, constructing an objective function based on the total penalty of the width, thickness and hardness differences between rolling adjacent slabs;

[0008] S2. constructing the constraint condition of the objective function based on the uncertainty of the rolling time distribution of the slab;

[0009] S3. Solve the objective function based on the constraint conditions, and determine a scheduling plan according to the solution result.

[0010] In a possible implementation, the constraint conditions for constructing the objective function based on the uncertainty of the rolling time distribution of the slab include:

[0011] S21. Construct a linear representation of the rolling start time of each slab based on the multi-commodity flow decision;

[0012] S22. constructing an uncertain set of rolling time distribution based on the support set, mean and covariance of the rolling time of the slab;

[0013] S23. Based on the linear representation and the set, construct an opportunity constraint on the latest rolling start time of each slab using conditional value at risk;

[0014] S24. Constructing a time constraint for slab rolling based on the directed arc;

[0015] S25, establishing hot rolling process constraints based on differences in width, thickness, and hardness of adjacent slabs during an actual hot rolling process;

[0016] S26. Construct the constraint condition based on the linear representation, chance constraint, slab rolling time constraint and hot rolling process constraint.

[0017] In a possible implementation, solving the objective function based on the constraint condition includes: estimating and solving a lower bound of the objective function based on a scenario and estimating and solving an upper bound of the objective function based on semi-definite programming.

[0018] In a possible embodiment, the multi-commodity flow decision-making is based on the construction of a linear representation of the rolling start time of each slab: including the construction of auxiliary variables Among them, the variable Indicates whether the slab i passes through the directed arc a when it starts to process. It means that when the slab i is processed, it passes through the directed arc a. Indicates that the slab i does not pass through the directed arc a when it starts to be processed; R + represents a positive real number, A is a set of directed arcs, |A| represents the number of elements in the set, The superscript |A| indicates s i The dimension of this vector is |A|, where the elements in A are arcs. The rolling time of slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i. The time of starting rolling of slab i is expressed as the linear form t i (x) = q T s i , where t i (x) is the starting rolling time of slab i, x is x i,j The decision matrix, x i,j is the decision variable, x i,j is whether slab j is rolled immediately after slab i; q is the rolling time of the slab.

[0019] In one possible embodiment, the time constraint includes: limiting the flow balance of slab rolling, using a virtual slab as the first slab to start rolling, and if the directed arc a is not passed in the rolling sequence, then when rolling slab i, the directed arc a must not be passed.

[0020] As a second aspect of the present application, a hot rolling scheduling system taking into account uncertain rolling time is also provided, including an objective function construction module, a constraint condition construction module and a solution module; wherein the objective function construction module is used to construct an objective function based on the total penalty for the width, thickness and hardness differences between adjacent slabs; the constraint condition construction module is used to construct the constraint conditions of the objective function based on the uncertainty of the rolling time distribution of the slab; the solution module is used to solve the objective function based on the constraint conditions, and determine the scheduling plan according to the solution result.

[0021] In one possible embodiment, the constraint condition construction module includes a linear representation construction unit, an uncertain set construction unit, an opportunity constraint construction unit, a time constraint construction unit, a hot rolling process constraint construction unit and a constraint condition construction unit; wherein, the linear representation construction unit is used to construct a linear representation of the start rolling time of each slab based on the multi-commodity flow decision; the uncertain set construction unit is used to construct an uncertain set of rolling time distribution based on the support set, mean and covariance of the rolling time of the slab; the opportunity constraint construction unit is used to construct the opportunity constraint of the latest start rolling time of each slab based on the linear representation and the set using conditional risk value; the time constraint construction unit is used to construct the time constraint of slab rolling based on directed arcs; the hot rolling process constraint construction unit is used to construct a penalty constraint based on the difference in width and thickness of adjacent slabs; the constraint condition construction unit is used to construct the constraint condition based on the linear representation, opportunity constraint, arc constraint and penalty constraint.

[0022] In one possible implementation, the solution module includes a lower bound estimation solution unit and an upper bound estimation solution unit; the lower bound estimation solution unit is used to estimate and solve the lower bound of the objective function based on a scenario, and the upper bound estimation solution unit is used to estimate and solve the upper bound of the objective function based on semi-positive programming.

[0023] In a possible embodiment, the multi-commodity flow decision-making is based on the construction of a linear representation of the rolling start time of each slab: including the construction of auxiliary variables Among them, the variable Whether the slab i passes through the directed arc a when it starts to process, when It means that when the slab i is processed, it passes through the directed arc a. It means that the slab i is processed without passing through the directed arc a when it starts. It is a set of directed arcs. |A| represents the number of elements in the set. The superscript |A| indicates s iThe dimension of this vector is |A|, where the elements in A are arcs. The rolling time of slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i. The time of starting rolling of slab i is expressed as the linear form t i (x) = q T s i , where t i (x) is the starting rolling time of slab i, x is x i,j The decision matrix, x i,j is the decision variable, x i,j is whether slab j is rolled immediately after slab i; q is the rolling time of the slab.

[0024] In one possible embodiment, the time constraint includes: limiting the flow balance of slab rolling, using a virtual slab as the first slab to start rolling, and if the directed arc a is not passed in the rolling sequence, then when rolling slab i, the directed arc a must not be passed.

[0025] (3) Beneficial effects

[0026] By accounting for the uncertainty of slab rolling times and utilizing limited probability distribution information, the rolling sequence and rolling time for each slab are determined. This robust scheduling solution can be developed using this limited probability distribution information even when rolling times fluctuate significantly. This avoids the impact of uncertain delays in the previous production process, improves scheduling efficiency, and reduces costs associated with variations in slab width, thickness, and hardness.

[0027] Other advantages, objectives, and features of the present application will be described in detail in the following description and, to some extent, will be apparent to those skilled in the art upon examination and study of the following, or may be taught from practice of the present application. The objectives and other advantages of the present application may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain and illustrate the present application, but should not be construed as limiting the scope of protection of the present application.

[0029] Figure 1 This is the flow chart of the application system;

[0030] Figure 2 This is the system structure diagram of this application;

[0031] Among them: 1. Objective function construction module; 2. Constraint condition construction module; 3. Solution module; 201. Linear representation construction unit; 202. Uncertain set construction unit; 203. Opportunity constraint construction unit; 204. Time constraint construction unit; 205. Hot rolling process constraint construction unit; 301. Equivalent transformation unit; 302. Lower bound estimation solution unit; 303. Upper bound estimation solution unit. DETAILED DESCRIPTION

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments in the present application without creative work are within the scope of protection of the present application.

[0034] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0035] In the above description of this application, it should be noted that the terms "one side" and "the other side" and the like indicate positions or locations based on the positions or locations shown in the accompanying drawings, or the positions or locations in which the product of the application is typically placed when in use. These terms are intended solely to facilitate the description of this application and simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limiting this application. Furthermore, the terms "first" and "second" and the like are used solely to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0036] Furthermore, the term "identical" and similar terms do not necessarily require that the components be absolutely identical; slight variations are permitted. The term "perpendicular" simply refers to the positional relationship between components being more perpendicular than "parallel," not that the structure must be perfectly vertical; rather, it can be slightly tilted.

[0037] like Figure 1 As shown, this embodiment provides a hot rolling scheduling method considering uncertain rolling time, including the following steps:

[0038] S1, constructing an objective function (P) based on the total penalty of width, thickness and hardness differences between rolling adjacent slabs; Among them, c I,j represents the penalty caused by the difference in width, thickness and hardness between slab i and j, N + is a set with two virtual slabs at the beginning and end, c 0,i =c I,n+1 =c 0,n+1 =0,c I,0 =c n+1,i =c I,i =+∞,x I,j is the decision variable, x I,j is whether slab j is rolled immediately after slab i, where x is the value of the rolling ratio when slab j is rolled immediately after slab i. I,j = 1, when slab j is not rolled immediately after slab i, x I,j =0.

[0039] S2. Construct the constraints of the objective function based on the uncertainty of the rolling time distribution of the slabs. The rolling time distribution is established based on the randomly collected rolling time of each slab, calculated based on the start and end time of each slab. The target slabs are randomly sampled and their rolling times are recorded. The rolling time distribution is determined based on the rolling time of each target slab. The uncertainty of the rolling time distribution is analyzed by analyzing the rolling time distribution. The constraints of the objective function are established based on the uncertainty of the rolling time distribution. Consider a directed network G = (N+, A), where N+ = {0, 1, ···, n, n+1} represents a point set, i.e., a set of slabs. Slabs 0 and n+1 are both virtual slabs. Slab 0 is the first slab to be rolled, and slab n+1 is the last slab to be rolled. The length and rolling time of both are 0. A is a set of network arcs. We use (i, j) or a to represent the arcs in A, where i, j∈N+, (i, j) and a are interchangeable. Specifically, S21. Constructing a linear representation of the start rolling time of each slab based on the multi-commodity flow decision; Constructing a linear representation of the start rolling time of each slab based on the multi-commodity flow decision includes: constructing auxiliary variables Among them, the variable Indicates whether the slab i is processed through the directed arc a. It means that when the slab i is processed, it passes through the directed arc a. It means that the directed arc a is not passed when the slab i is processed. Introducing variables can improve the operation speed. + represents a positive real number, A is a set of directed arcs, |A| represents the number of elements in the set, The superscript |A| indicates s iThe dimension of this vector is |A|. The elements in A are directed arcs and do not represent time. The time for rolling slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i. The time for starting rolling of slab i is expressed as the linear form t i (x) = q T s i , where t i (x) is the starting rolling time of slab i, x is x i,j The decision matrix, x i,j is the decision variable, x i,j Is slab j rolled immediately after slab i?; q is the rolling time of the slab. S22. Construct an uncertain set D of rolling time distribution based on the support set, mean, and covariance of the slab rolling time. Directly calculate the mean, covariance, and support set of the rolling time of each slab based on previous data. Then, construct an uncertain set of rolling time distribution based on the mean and other information:

[0040] D={F|P(q∈[L,U])=1,E F [q] = μ, Cov(q) = Γ}, where q is the rolling time, [L, U] is the support set of q, μ is the mean of the rolling time, and Γ is the covariance of the rolling time. S23. Based on the linear representation and the set, a chance constraint for the latest rolling start time of each slab is constructed using conditional value at risk. The chance constraint is:

[0041]

[0042] Where F is the rolling time distribution, D is the set of uncertain rolling time distribution, sup is CVaR α (t i (x))≤d i The optimal solution, d i is the latest rolling start time of slab i, where i∈N, N is the set without the first and last two virtual slabs, is any slab, and N is an integer set without two virtual slabs at the beginning and end. S24. Construct the time constraint Ξ of the slab rolling based on the directed arc:

[0043]

[0044] where δ + (i) is the set of arcs going out from point i; δ - (i) is the set of arcs from entry point i. a is a directed arc, a∈A;

[0045] and

[0046] Limits the flow balance of slab rolling; The constraint means that if the rolling sequence does not pass through the directed arc a, then when rolling slab i, it must not pass through the directed arc a. The constraint representation is that the virtual slab 0 is used as the first slab to be rolled. The slab rolling time constraint also restricts the rolling process to not have sub-loops and restricts the feasible solution of s to a unique integer solution. Therefore, the starting rolling time of each slab can be expressed as t i (x) = q T s i S25. Construct hot rolling process constraint Z based on the differences in width, thickness and hardness of adjacent slabs during the actual hot rolling process:

[0047]

[0048] in: and Except for the initial slab and the final rolled slab, the other slabs have only one preceding slab and one succeeding slab, where x i,j is the decision variable, x i,j is whether slab j is rolled immediately after slab i, where x is the value of the rolling ratio when slab j is rolled immediately after slab i. i,j = 1, when slab j is not rolled immediately after slab i, x i,j =0,l i represents slab i∈N + The length, N + is a set with the first and last virtual slabs, the length of the first and last virtual slabs is 0, record and The number of slabs of the same width that can be continuously rolled is limited, and the limit is given in the form of the cumulative length of the slabs of the same width that can be continuously rolled. i,j Indicates whether slab i∈N and slab j∈N, i≠j have the same width, L w represents the upper limit of the cumulative length of the continuously rolled slab with equal width, B represents a large positive number, which is the sum of the lengths of all slabs in the rolling unit, |.| represents the number of elements in the set, y i Depends on x i,j The decision variable, y i is the cumulative length of slabs with the same width as slab i and rolled continuously; is the decision variable x i,j and the domain of any slab i and any slab j, N + is a set of two virtual slabs at the beginning and end.

[0049] S26. Construct the constraint condition based on the linear representation, the chance constraint, the slab rolling time constraint, and the hot rolling process constraint:

[0050] (x,y,s)∈Ξ,(x,y)∈Z;

[0051] Among them, (x,y,s)∈Ξ is equivalent to x∈Ξ,y∈Ξ,s∈Ξ; (x,y)∈Z is equivalent to x∈Z,y∈Z; x is x i,j The decision matrix composed of x i,j is the decision variable; y is the decision variable y i The decision matrix composed of i Depends on x i,j The decision variable, y i is the cumulative length of slabs with the same width as slab i and continuously rolled; s is The decision matrix composed of s is first s i The vector composed of s i for The vector composed of , then s is The decision matrix composed of

[0052] x is x i,j The decision matrix composed of x i,j is the decision variable;

[0053]

[0054] S3. Solve the objective function based on the constraint conditions and determine the scheduling plan according to the solution results. The decision variables x and t are the rolling order and the time of starting rolling of the slab, which is the scheduling plan. The objective function value is the penalty for the jump of physical properties of adjacent slabs caused by the rolling plan, with x as the value. i,j For example, if x i,j = 1, which means that slab j is rolled next to slab i. But is it optimal to roll slab j next to slab i? Will it minimize the cost? This requires us to solve the problem, which is the decision-making process. If rolling slab j next to slab i is not optimal, then the x we ​​solve is i,j should be 0, that is, slab j is not rolled next to slab i. If the opposite is true, then x i,j =1. Solving the objective function based on the constraint condition includes: estimating and solving the lower bound of the objective function based on the scenario and estimating and solving the upper bound of the objective function based on semi-positive programming, specifically:

[0055] The generalized duality principle is used to perform equivalent transformations on the linear representations and chance constraints in the constraints:

[0056] According to the definition of conditional risk value, CVaR α (t i (x)) is transformed into the following equivalent form:

[0057]

[0058] Among them, [a] + =max{a,0}. Based on the generalized duality principle, we can give the problem The equivalent dual problem is:

[0059]

[0060]

[0061]

[0062] λ i ∈R,ω i ∈R |A| ,β i =(β i ) T ∈R |A|×|A| ;

[0063] in,

[0064]

[0065] Where M = Γ + μμ T ,I·J=∑ i,j I i,j J i,j ;

[0066] R represents the set of all real numbers, q is the rolling time of the slab, [L, U] is the support set of the rolling time q, Γ is the covariance matrix of the rolling time q, μ is the mean (vector) of the rolling time q, θ i ,ω i and β i To derive The dual variable θ is introduced in the dual problem process. i is a one-dimensional decision variable, ω i is the decision vector, β i is the decision matrix.

[0067] Will By bringing the equivalent dual form of into the objective function, we can get the equivalent form DP of the objective function P:

[0068]

[0069] The constraints of DP are as follows:

[0070] (x,y,s)∈Ξ;

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Solve the lower bound of the objective function based on the scenario and the equivalent transformation: DP constraints and The rolling time q of the slab belongs to its support set [L, U], which essentially represents an infinite number of constraints. The difficulty of solving the model depends on the range of the support set. Therefore, the lower bound of the objective function is estimated based on the scenario by sampling the q value in [L, U], which originally represents an infinite number of constraints. and Replace with a finite number of constraints; the lower bound estimate of the objective function is solved as follows:

[0077] If the Slater interior point condition holds, the sample set Then the 0-1 mixed linear programming problem LP provides a lower bound for DP:

[0078]

[0079] st(x,y,s)∈Ξ;

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Based on the semi-positive programming and the equivalent transformation, the upper bound of the objective function is estimated and solved. The constraints of DP and constraints The rolling time q of the slab belongs to its support set [L, U], which essentially represents an infinite number of constraints. The difficulty of solving the model depends on the range of the support set. Therefore, the upper bound of the objective function is estimated based on semi-positive programming. By sampling the q value in [L, U], the original infinite number of constraints is converted to and Replace with a finite number of constraints; the upper bound of the objective function is estimated and solved as follows:

[0086] If the Slater interior point condition holds, then the mixed 0-1 semidefinite programming problem UP provides an upper bound on DP:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] in,

[0094]

[0095]

[0096] Compared with the existing technology, by considering the uncertainty of slab rolling time and utilizing limited probability distribution information, the rolling sequence of slabs and the rolling time of each slab are determined. In the case of large fluctuations in rolling time, limited probability distribution information can be utilized to provide a feasible scheduling plan with good robustness, avoiding the impact of uncertain delays in the previous production process, improving scheduling efficiency, and reducing cost losses caused by differences in width, thickness and hardness between slabs.

[0097] like Figure 2As shown, as the second aspect of the present application, a hot rolling scheduling system considering uncertain rolling time is also provided, including an objective function construction module 1, a constraint condition construction module 2 and a solution module 3; wherein, the objective function construction module 1 is used to construct an objective function based on the total penalty of the width, thickness and hardness differences between adjacent slabs; the constraint condition construction module 2 is used to construct the constraint conditions of the objective function based on the uncertainty of the rolling time distribution of the slab; the solution module 3 is used to solve the objective function based on the constraint conditions, and determine the scheduling plan according to the solution result.

[0098] The constraint condition construction module includes a linear representation construction unit 201 , an uncertainty set construction unit 202 , a chance constraint construction unit 203 , a time constraint construction unit 204 , a hot rolling process constraint construction unit 205 and a constraint condition construction unit 206 .

[0099] The linear representation construction unit 201 is used to construct a linear representation of the rolling start time of each slab based on the multi-commodity flow decision. The linear representation construction unit 201 is used to construct a linear representation of the rolling start time of each slab based on the multi-commodity flow decision. The linear representation construction unit 201 comprises: constructing auxiliary variables Indicates whether the slab i passes through the directed arc a when it starts to process. It means that when the slab i is processed, it passes through the directed arc a. Indicates that the slab i does not pass through the directed arc a when it starts to be processed; R + represents a positive real number, A is a set of directed arcs, |A| represents the number of elements in the set, The superscript |A| indicates s i The dimension of this vector is |A|. The elements in A are arcs, not time. The time for rolling slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i; the time for starting rolling of slab i is expressed as the linear form t i (x) = q T s i , where t i (x) is the starting rolling time of slab i, x is x i,j The decision matrix, x i,j is the decision variable, x i,j is whether slab j is rolled immediately after slab i; q is the rolling time of the slab.

[0100] The uncertain set construction unit 202 is used to construct an uncertain set D of rolling time distribution based on the support set, mean and covariance of the rolling time of the slab. The mean, covariance and support set of the rolling time of each slab are directly calculated based on previous data, and then the uncertain set of rolling time distribution is constructed based on the mean and other information:

[0101] D={F|P(q∈[L,U])=1,E F [q] = μ, Cov(q) = Γ};

[0102] Where q is the rolling time, [L,U] is the support set of q, μ is the mean of the rolling time, and Γ is the covariance of the rolling time.

[0103] The opportunity constraint construction unit 203 is used to construct the opportunity constraint of the latest rolling start time of each slab based on the linear representation and the set using the conditional value at risk, wherein the opportunity constraint is:

[0104]

[0105] Where F is the rolling time distribution, D is the set of uncertain rolling time distribution, sup is CVaR α (t i (x))≤d i The optimal solution, d i is the latest rolling start time of slab i, where i∈N, N is the set without the first and last two virtual slabs, is any slab, and N is an integer set without two virtual slabs at the beginning and end. The time constraint construction unit 204 is used to construct the time constraint Ξ of the slab rolling based on the directed arc:

[0106]

[0107] where δ + (i) is the set of arcs going out from point i; δ - (i) is the set of arcs from entry point i. a is a directed arc, a∈A;

[0108] and Limits the flow balance of slab rolling; The constraint means that if the rolling sequence does not pass through the directed arc a, then when rolling slab i, it must not pass through the directed arc a. The constraint representation is that the virtual slab 0 is used as the first slab to be rolled. The slab rolling time constraint also restricts the rolling process to not have sub-loops and restricts the feasible solution of s to a unique integer solution. Therefore, the starting rolling time of each slab can be expressed as t i (x) = q Ts i .

[0109] The hot rolling process constraint construction unit 205 is used to construct the hot rolling process constraint Z based on the differences in width, thickness and hardness of adjacent slabs during the actual hot rolling process:

[0110]

[0111] in:

[0112] and Except for the initial slab and the final rolled slab, the other slabs have only one preceding slab and one succeeding slab, where x i,j is the decision variable, x i,j is whether slab j is rolled immediately after slab i, where x is the value of the rolling ratio when slab j is rolled immediately after slab i. i,j = 1, when slab j is not rolled immediately after slab i, x i,j =0,l i represents slab i∈N + The length, N + is a set with the first and last virtual slabs, the length of the first and last virtual slabs is 0, record and The number of slabs of the same width that can be continuously rolled is limited, and the limit is given in the form of the cumulative length of the slabs of the same width that can be continuously rolled. i,j Indicates whether slab i∈N and slab j∈N, i≠j have the same width, L w represents the upper limit of the cumulative length of the continuously rolled slab with equal width, B represents a large positive number, which is the sum of the lengths of all slabs in the rolling unit; |.| represents the number of elements in the set, y i Depends on x i,j The decision variable, y i is the cumulative length of slabs with the same width as slab i and rolled continuously; is the decision variable x i,j and the domain of any slab i and any slab j, N + is a set of two virtual slabs at the beginning and end.

[0113] The constraint condition construction unit 206 is used to construct the constraint condition based on the linear representation, chance constraint, arc constraint and penalty constraint:

[0114] (x,y,s)∈Ξ,(x,y)∈Z;where,(x,y,s)∈Ξis equivalent to x∈Ξ,y∈Ξ,s∈Ξ;(x,y)∈Zis equivalent to x∈Z,y∈Z;xis x i,j The decision matrix composed of xi,j is the decision variable; y is the decision variable y i The decision matrix composed of i Depends on x i,j The decision variable, y i is the cumulative length of slabs with the same width as slab i and continuously rolled; s is The decision matrix composed of s is first s i The vector composed of s i for The vector composed of , then s is The decision matrix composed of

[0115] x is x i,j The decision matrix composed of x i,j is the decision variable;

[0116]

[0117] The solution module 3 includes an equivalent transformation unit 301, a lower bound estimation solution unit 302, and an upper bound estimation solution unit 303; wherein the equivalent transformation unit 301 is used to perform an equivalent transformation on the linear representation and chance constraint in the constraint condition using the generalized duality principle, the lower bound estimation solution unit 301 is used to estimate and solve the lower bound of the objective function based on the scenario and the equivalent transformation, and the upper bound estimation solution unit 302 is used to estimate and solve the upper bound of the objective function based on semi-positive programming and the equivalent transformation. Specifically:

[0118] The equivalent transformation unit 301 uses the generalized duality principle to perform equivalent transformation on the linear representation and chance constraint in the constraint conditions:

[0119] According to the definition of conditional risk value and linear representation, CVaR α (t i (x)) is transformed into the following equivalent form:

[0120]

[0121] Among them, [a] + =max{a,0}. Based on the generalized duality principle, we can give the problem The equivalent dual problem is:

[0122]

[0123]

[0124]

[0125]

[0126] Where M = Γ + μμ T ,I·J=∑ i,j I i,j J i,j ;

[0127] R represents the set of all real numbers, q is the rolling time of the slab, [L, U] is the support set of the rolling time q, Γ is the covariance matrix of the rolling time q, μ is the mean (vector) of the rolling time q, θ i ,ω i and β i To derive The dual variable θ is introduced in the dual problem process. i is a one-dimensional decision variable, ω i is the decision vector, β i is the decision matrix.

[0128] Will By bringing the equivalent dual form of into the objective function, we can get the equivalent form DP of the objective function P:

[0129]

[0130] The constraints of DP are as follows:

[0131] (x,y,s)∈Ξ;

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] The lower bound estimation solving unit 302 estimates and solves the lower bound of the objective function based on the scenario: the constraints of DP and The rolling time q of the slab belongs to its support set [L, U], which essentially represents an infinite number of constraints. The difficulty of solving the model depends on the range of the support set. Therefore, the lower bound of the objective function is estimated based on the scenario by sampling the q value in [L, U], and converting the formula that originally represents the infinite number of constraints into and Replace with a finite number of constraints; the lower bound estimate of the objective function is solved as follows:

[0138] If the Slater interior point condition holds, the sample set Then the 0-1 mixed linear programming problem LP provides a lower bound for DP:

[0139]

[0140] st(x,y,s)∈Ξ;

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] The upper bound estimation solving unit 303 estimates and solves the upper bound of the objective function based on semi-positive programming. and The rolling time q of the slab belongs to its support set [L, U], which essentially represents an infinite number of constraints. The difficulty of solving the model depends on the range of the support set. Therefore, the upper bound of the objective function is estimated based on semi-positive programming. By sampling the q value in [L, U], the original infinite number of constraints is converted to and Replace with a finite number of constraints; the upper bound of the objective function is estimated and solved as follows:

[0147] If the Slater interior point condition holds, then the mixed 0-1 semidefinite programming problem UP provides an upper bound on DP:

[0148]

[0149] st(x,y,s)∈Ξ;

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] in,

[0156]

[0157]

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, ordinary technicians in this field should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present application, which should be included in the scope of the claims of the present application.

Claims

1. A hot rolling scheduling method considering uncertain rolling time, characterized in that: The method comprises the following steps: S1, constructing an objective function based on penalties for differences in width, thickness, and hardness between adjacent slabs; S2, constructing constraints for the objective function based on uncertainty in the rolling time distribution of the slabs; S3, solving the objective function based on the constraints, and determining a scheduling plan based on the solution results; The constraint conditions for constructing the objective function based on the uncertainty of the rolling time distribution of the slab include: S21. Construct a linear representation of the rolling start time of each slab based on multi-commodity flow decisions and directed arcs; S22. Construct a nonlinear representation of the rolling time distribution based on the support set, mean and covariance of the rolling time of the slab. S23, based on the linear representation and the set, using the conditional risk value to construct the latest value of each slab Chance constraints on the time to start rolling; S24, constructing a time constraint for slab rolling based on the directed arc; S25, constructing a time constraint for hot rolling based on the difference in width, thickness and hardness of adjacent slabs during the actual hot rolling process. process constraints; S26, constructing the constraint condition based on the linear representation, the chance constraint, the slab rolling time constraint, and the hot rolling process constraint; The linear representation of the rolling start time of each slab is constructed based on the multi-commodity flow decision: including the construction of auxiliary variables , where the variable , Whether the slab i passes through the directed arc a when it starts to process, when It means that when the slab i is processed, it passes through the directed arc a. It means that the slab i does not pass through the directed arc a when it starts to be processed. represents a positive real number, is a set of directed arcs, |A| represents the number of elements in the set, The superscript |A| indicates The dimension of this vector is |A|, where the elements in A are directed arcs. The rolling time of slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i. The time of starting rolling of slab i is expressed as a linear form ,in, is the starting rolling time of slab i, , x is The decision matrix formed by is the decision variable, is whether slab j is rolled immediately after slab i; q is the rolling time of the slab; The time constraints include: limiting the flow balance of slab rolling, taking the virtual slab as the first slab to be rolled, and if the rolling sequence does not pass through the directed arc a, then when rolling slab i, it must not pass through the directed arc a.

2. A hot rolling scheduling method considering uncertain rolling time according to claim 1, characterized in that: Solving the objective function based on the constraint conditions includes: estimating and solving a lower bound of the objective function based on a scenario and estimating and solving an upper bound of the objective function based on semi-definite programming.

3. A hot rolling scheduling system considering uncertain rolling time, characterized in that: The system comprises an objective function construction module, a constraint condition construction module and a solution module; wherein the objective function construction module is used to construct an objective function based on the total penalty of the width, thickness and hardness differences between rolling adjacent slabs; the constraint condition construction module is used to construct the constraint conditions of the objective function based on the uncertainty of the rolling time distribution of the slabs; the solution module is used to solve the objective function based on the constraint conditions and determine the scheduling plan according to the solution results; The constraint condition construction module includes a linear representation construction unit, an uncertain set construction unit, an opportunity constraint construction unit, a time constraint construction unit, a hot rolling process constraint construction unit and a constraint condition construction unit; wherein the linear representation construction unit is used to construct a linear representation of the rolling start time of each slab based on the multi-commodity flow decision; the uncertain set construction unit is used to construct an uncertain set of rolling time distribution based on the support set, mean and covariance of the rolling time of the slab; the opportunity constraint construction unit is used to construct the opportunity constraint of the latest rolling start time of each slab based on the linear representation and the set using conditional risk value; the time constraint construction unit is used to construct the time constraint of slab rolling based on directed arcs; the hot rolling process constraint construction unit is used to construct the hot rolling process constraint based on the differences in width, thickness and hardness of adjacent slabs in the actual hot rolling process; the constraint condition construction unit is used to construct the constraint condition based on the linear representation, opportunity constraint, time constraint and hot rolling process constraint; The linear representation of the rolling start time of each slab is constructed based on the multi-commodity flow decision: including the construction of auxiliary variables , where the variable , Whether the slab i passes through the directed arc a when it starts to process, when It means that when the slab i is processed, it passes through the directed arc a. It means that the slab i does not pass through the directed arc a when it starts to be processed. represents a positive real number, is a set of directed arcs, |A| represents the number of elements in the set, The superscript |A| indicates The dimension of this vector is |A|, where the elements in A are directed arcs. The rolling time of slab i is expressed as the time of the directed arc of rolling slab j after rolling slab i, where j can be any slab except i. The time of starting rolling of slab i is expressed as a linear form ,in, is the starting rolling time of slab i, , x is The decision matrix formed by is the decision variable, is whether slab j is rolled immediately after slab i; q is the rolling time of the slab; The time constraints include: limiting the flow balance of slab rolling, taking the virtual slab as the first slab to be rolled, and if the rolling sequence does not pass through the directed arc a, then when rolling slab i, it must not pass through the directed arc a.

4. The hot rolling scheduling system considering uncertain rolling time according to claim 3, characterized in that: The solution module includes a lower bound estimation solution unit and an upper bound estimation solution unit; the lower bound estimation solution unit is used to estimate and solve the lower bound of the objective function based on the scenario, and the upper bound estimation solution unit is used to estimate and solve the upper bound of the objective function based on semi-definite programming.

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