CN116618597A - Continuous casting cutting optimization method and system based on mixed integer programming - Google Patents
Continuous casting cutting optimization method and system based on mixed integer programming Download PDFInfo
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- 238000005520 cutting process Methods 0.000 title claims abstract description 207
- 238000005457 optimization Methods 0.000 title claims abstract description 126
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- 238000004519 manufacturing process Methods 0.000 claims abstract description 17
- 229910000831 Steel Inorganic materials 0.000 claims abstract description 15
- 239000010959 steel Substances 0.000 claims abstract description 15
- 230000005856 abnormality Effects 0.000 claims description 37
- 239000002699 waste material Substances 0.000 claims description 28
- 238000005266 casting Methods 0.000 claims description 16
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B22—CASTING; POWDER METALLURGY
- B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
- B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
- B22D11/16—Controlling or regulating processes or operations
- B22D11/163—Controlling or regulating processes or operations for cutting cast stock
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
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- G—PHYSICS
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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Abstract
The invention discloses a continuous casting cutting optimization method and system based on mixed integer programming, and belongs to the technical field of data processing, wherein the continuous casting cutting optimization method comprises the following steps: according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters, extracting to obtain known conditions, constraint conditions and optimization targets; performing mathematical abstraction aiming at known conditions, constraint conditions and optimization targets, and establishing a mixed integer programming model according to the mathematical abstraction; and (3) carrying out software programming based on an open source optimization solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimization solver for solving to obtain a continuous casting slab cutting plan. According to the technical scheme, the precise and optimal solution of tail blank optimization is realized, various abnormal conditions faced by the site are considered, and the tail blank optimization method can be adjusted and expanded according to specific requirements.
Description
Technical Field
The invention relates to the technical field of data processing, in particular to a continuous casting cutting optimization method based on mixed integer programming and a continuous casting cutting optimization system based on mixed integer programming.
Background
Continuous casting (continuous casting) of steel is a process of casting molten steel into a billet, as shown in fig. 1: molten steel enters a tundish from the ladle, is poured into a crystallizer from the tundish, is pulled downwards from the crystallizer at a certain speed, enters a subsequent device such as secondary cooling and the like, and is cooled to form a solid steel billet. And then cutting the billet according to certain size requirements. The distance from the crystallizer to the cutting position is typically several tens of meters.
In continuous casting processes, billets with a total count of hundreds of meters are typically cast continuously. In general, a cutter cuts a billet into slabs of a target size according to an order requirement. In actual production, the target size typically has a tolerance (e.g., target cut length 9.5m, acceptable cut range 9 m-10 m).
When some abnormal conditions occur (e.g., a ladle is replaced, the pulling speed is abnormal, etc.), an abnormal region having a different length is formed at the mold according to the kind of the abnormal condition. At this time, if cutting is performed according to the target size, an abnormal region may fall in the middle of a certain slab, as shown in fig. 2.
The abnormal region is cut off in the subsequent process. When the abnormal region falls in the center of the slab, it may cause the remaining portion after cutting to be scrapped without satisfying the required size, as shown in the target length cutting scheme of fig. 2. In the target length cutting scheme, the abnormal region falls in the middle of the 3 rd slab from left to right. After the abnormal region is cut off, the slab is divided into a left slab and a right slab of the abnormal region. The right side plate blank after being divided is still above the acceptable lower limit and can be regarded as a normal plate blank; while the left side panel blank is less than the acceptable lower limit and therefore requires complete scrap. This normal portion that is discarded is the loss of cut. Therefore, when an abnormal region occurs, it is necessary to appropriately optimize the cutting plan, for example, to change the cutting size of a part of the slab so that the abnormal region falls on the tail of a certain normal slab, to reduce the cutting loss.
In the prior art, a method and a device for optimizing and cutting the continuous casting tail blank fixed length by using a computer program are disclosed, wherein the method for optimizing and cutting the continuous casting tail blank fixed length by using the computer program is used for evenly distributing the redundant molten steel quantity less than one single fixed length into a plurality of qualified casting blanks in advance under the condition that the molten steel quantity is not equal to the integral multiple of the casting blank fixed length. The cutting optimization method adopted by the method adopts a heuristic algorithm based on greedy ideas, and can not ensure that an optimal solution meeting the requirements is obtained; and the situation that the lengths of the waste blanks are different under different anomalies on site is not considered, and the situation that the anomalies occur continuously.
In the prior art, an online optimization method of continuous casting cutting is also disclosed, and a scheme for optimizing tail blank cutting is designed by carrying out classified and separated condition discussion on the lengths of different tail blanks, but the method is designed based on two specific sample problems and has no universality.
In addition, an online optimization model of continuous casting cutting is also disclosed, and an integer linear programming model is established under three conditions: the first case is that for tail blanks with different lengths, an optimized cutting model which can minimize the total cutting loss under the condition of meeting basic requirements and customer requirements is formulated; the second condition is to formulate an optimized cutting model for minimizing the total loss of the tail blank under the condition of meeting basic requirements and customer requirements at any two abnormal crystallization moments when abnormal crystallization points appear in the forming process of the tail blank; the third case is to formulate an optimized cutting model with minimum loss of tail blank cutting when the constraint condition is the same as the second case and different requirements of customers are increased. All three integer optimization models are used for obtaining an optimal cutting scheme by writing a LINGO program and operating by using LINGO software. However, in the technical scheme, discretization approximation treatment is performed on the cutting length of the slab on one hand, and no method for accurately solving the cutting length is available; on the other hand, the situation that the lengths of the waste billets are different under different anomalies and the anomalies continuously occur is not considered.
Disclosure of Invention
Compared with a greedy heuristic method or an integer programming method modeling by using discretization skills in the prior art, the continuous casting cutting optimization method and system based on mixed integer programming provided by the invention realize accurate optimal solution of tail blank optimization, consider main abnormal conditions (including tundish replacement, ladle casting stopping and the like) faced by the site, consider various abnormal conditions, and adjust and expand the mixed integer programming model according to specific requirements (different optimization targets and different abnormal conditions) of enterprises, thereby overcoming the problem of difficult popularization.
In order to achieve the above object, the present invention provides a continuous casting cutting optimization method based on mixed integer programming, comprising:
according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters, extracting to obtain known conditions, constraint conditions and optimization targets;
performing mathematical abstraction on the known conditions, constraint conditions and optimization targets, and establishing a mixed integer programming model according to the mathematical abstraction;
and (3) carrying out software programming based on an open source optimization solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimization solver for solving to obtain a continuous casting slab cutting plan.
In the above technical solution, preferably, the known information of the slab cutting plan includes a target length of the slab, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value, and the known information of the abnormality parameters includes an abnormality type, an abnormality occurrence position, and an abnormality region length.
In the above technical solution, preferably, the constraint condition includes:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal occurrence position must be at the head or tail of the cut slab;
if the slab cutting length cannot be cut according to the target length, the slab cutting length should be as far as possible between the target length upper limit value and the target length lower limit value;
the optimization objectives include:
the number of slabs cut according to the target length is as large as possible;
if the occurrence of the abnormal waste blank cannot be avoided, the total length of the waste blank is as small as possible, wherein when the cutting length of the plate blank exceeds the upper limit value of the target length, the part exceeding the upper limit is the waste blank, and when the cutting length of the plate blank is smaller than the lower limit value of the target length, the whole plate blank is the waste blank.
In the above technical solution, preferably, the specific process of establishing the mixed integer programming model includes:
assuming that the abnormal occurrence position is x, and the abnormal region length is c;
the following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0，L]: a start cutting position of a j-th slab;
q j ∈[0，L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss;
constructing a constraint function of the mixed integer programming model with the model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
Cutting the j-th plate blank according to the plan, and then the next plate blankThe initial cutting position of the slab is the end of the j-th slab, namely: p is p j ＝p j-1 +q j-1 ，(-s j )M≤q j ≤(sj)M，/>
Only the slab exceeding the upper limit value and the lower limit value of the target length is allowed to be the last block, namely:
judging whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length, namely:
judging whether the last slab is a waste slab or not, namely:
if the cutting length of the last slab is not between the target length lower limit value and the target length upper limit value, cutting loss is formed, namely:
when the cut length of the last slab is below the target length lower limit valueThen
When the cutting length of the last slab is above the target length upper limit valueThen
Comprehensively obtain cutting loss
The objective function of constructing the mixed integer programming model is as follows:
minw 1 l-w 2 ∑ j d j
wherein min l represents the minimum cutting loss, max j d j Representing the number of slabs cut according to said target length as much as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
In the above technical solution, preferably, the process of performing software programming based on the open source optimization solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimization solver for solving is as follows:
aiming at constraint conditions and optimization targets of the mixed integer programming model, based on a Python interface provided by an open source optimization solver SCIP (Solving Constraint Integer Programs, solving constraint integer program), the solution of the mixed integer programming model is realized by adopting Python language programming.
The invention also provides a continuous casting cutting optimization system based on mixed integer programming, and the continuous casting cutting optimization method based on mixed integer programming disclosed by any one of the technical schemes comprises the following steps:
the mathematical condition refining module is used for refining to obtain known conditions, constraint conditions and optimization targets according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters;
the mathematical model construction module is used for carrying out mathematical abstraction on the known conditions, the constraint conditions and the optimization targets and establishing a mixed integer programming model according to the mathematical abstraction;
and the cutting parameter solving module is used for carrying out software programming based on the open source optimizing solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimizing solver for solving to obtain a continuous casting slab cutting plan.
In the above technical solution, preferably, in the mathematical condition refinement module, the known information of the slab cutting plan includes a target length of the slab, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value, and the known information of the abnormality parameters includes an abnormality type, an abnormality occurrence position, and an abnormality region length.
In the foregoing technical solution, preferably, in the mathematical model building module, the constraint condition includes:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal occurrence position must be at the head or tail of the cut slab;
if the slab cutting length cannot be cut according to the target length, the slab cutting length should be as far as possible between the target length upper limit value and the target length lower limit value;
the optimization objectives include:
the number of slabs cut according to the target length is as large as possible;
if the occurrence of the abnormal waste blank cannot be avoided, the total length of the waste blank is as small as possible, wherein when the cutting length of the plate blank exceeds the upper limit value of the target length, the part exceeding the upper limit is the waste blank, and when the cutting length of the plate blank is smaller than the lower limit value of the target length, the whole plate blank is the waste blank.
In the above technical solution, preferably, the specific process of establishing the mixed integer programming model by the mathematical model construction module includes:
assume that the abnormality occurrence position is x The length of the abnormal region is c ；
The following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0，L]: the j-th slabIs used for cutting the workpiece;
q j ∈[0，L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss;
constructing a constraint function of the mixed integer programming model with the model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
Cutting the jth slab according to the plan, wherein the initial cutting position of the next slab is the tail of the jth slab, namely: p is p j ＝p j-1 +q j-1 ，(-s j )M≤q j ≤(s j )M，/>
Allowing only the target length upper limit sum to be exceededThe slab with the lower limit value of the target length is the last block, namely:
judging whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length, namely:
judging whether the last slab is a waste slab or not, namely:
if the cutting length of the last slab is not between the target length lower limit value and the target length upper limit value, cutting loss is formed, namely:
when the cut length of the last slab is below the target length lower limit valueThen
When the cutting length of the last slab is above the target length upper limit valueThen
Comprehensively obtain cutting loss
The objective function of constructing the mixed integer programming model is as follows:
minw 1 l-w 2 ∑ j d j
wherein min l represents the minimum cutting loss, max j d j Representing a slab cut according to said target lengthAs many as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
In the above technical solution, preferably, the specific method for implementing the open source optimization solver for the mixed integer programming model by the cutting parameter solving module through software programming includes:
and aiming at constraint conditions and optimization targets of the mixed integer programming model, adopting Python language programming to realize an open-source optimization solver SCIP.
Compared with the prior art, the invention has the beneficial effects that: compared with a greedy heuristic method or an integer programming method modeling by using discretization skills in the prior art, the optimization method based on the mixed integer programming model is adopted for continuous casting cutting optimization, so that the precise optimal solution of tail blank optimization is realized, main abnormal conditions (including tundish replacement, ladle casting stopping and the like) faced by the site are considered, various abnormal conditions are considered, and the mixed integer programming model can be adjusted and expanded according to specific requirements (different optimization targets and different abnormal conditions) of enterprises, so that the problem of difficult popularization can be solved.
Drawings
FIG. 1 is a schematic flow chart of a continuous casting process for steel in the prior art;
FIG. 2 is a schematic illustration of a prior art slab cutting scheme and scrap position;
FIG. 3 is a schematic flow chart of a continuous casting cutting optimization method based on mixed integer programming according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a slab cutting scheme after adjustment according to a mixed integer programming-based continuous casting cutting optimization method according to an embodiment of the present invention;
fig. 5 is a schematic block diagram of a continuous casting cutting optimization system based on mixed integer programming according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention is described in further detail below with reference to the attached drawing figures:
as shown in fig. 3, the continuous casting cutting optimization method based on mixed integer programming provided by the invention comprises the following steps:
according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters, extracting to obtain known conditions, constraint conditions and optimization targets;
performing mathematical abstraction aiming at known conditions, constraint conditions and optimization targets, and establishing a mixed integer programming model according to the mathematical abstraction;
and (3) carrying out software programming based on an open source optimization solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimization solver for solving to obtain a continuous casting slab cutting plan.
In the embodiment, compared with a greedy heuristic method or an integer programming method modeling by using discretization skills in the prior art, the optimization method based on the mixed integer programming model is adopted for continuous casting cutting optimization, so that the precise optimal solution of tail blank optimization is realized, main abnormal conditions (including tundish replacement, ladle casting stopping and the like) faced by the site are considered, various abnormal conditions are considered, and the mixed integer programming model can be adjusted and expanded according to specific requirements (different optimization targets and different abnormal conditions) of enterprises, so that the problem of difficult popularization can be overcome.
Specifically, the whole technical scheme comprises three parts: firstly, mixed integer programming modeling; secondly, programming is realized; thirdly, solving the application. According to the actual condition of continuous casting cutting optimization, known conditions, constraint conditions and optimization targets are extracted, mathematical abstraction is carried out, and then a mixed integer programming model is established. And then solving the actual data by adopting software programming and a third party optimization solver to obtain a specific cutting plan for guiding actual production.
Firstly, the cutting optimization problem under different abnormal conditions is unified and abstracted into 'tail blank optimization'. The so-called tail stock optimization, i.e. the problem of optimizing the tail of the last optimized slab always placed with the abnormal section, corresponds to the necessity of cutting once at the tail of each abnormal zone. For different abnormal conditions, the lengths of the generated abnormal areas are not necessarily the same, the problems under different abnormal conditions can be uniformly modeled into tail blank optimization by taking the abnormal area length as a super-parameter form of the tail blank optimization problem, and the cutting length of each slab is obtained by establishing and solving the tail blank optimization problem.
In the above embodiment, preferably, the known information of the slab cutting plan includes a target length of the slab, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value, and the known information of the abnormality parameters includes an abnormality type, an abnormality occurrence position, and an abnormality region length.
In the above embodiment, preferably, the constraint condition includes:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal position must be at the head or tail of the cut slab;
if the cutting length of the slab cannot be cut according to the target length, the cutting length of the slab is between the upper limit value of the target length and the lower limit value of the target length as far as possible;
the optimization targets include:
the number of slabs cut according to the target length is as large as possible;
if it is unavoidable that the abnormal blank is contained, the total length of the blank is as small as possible, wherein the portion exceeding the upper limit is the blank when the cut length of the slab exceeds the upper limit value of the target length, and the whole slab is the blank when the cut length of the slab is less than the lower limit value of the target length.
According to the continuous casting cutting optimization method disclosed by the embodiment, the continuous casting cutting optimization problem is refined and abstracted, and mainly known information, conditions to be met, cutting targets and the like in the production process are refined and abstracted into problems which can be described by using mathematical languages, so that the known information, constraint conditions and optimization targets are obtained, and a mixed integer programming model is built.
Specifically, in practice, known information includes, but is not limited to:
(1) A slab plan issued by a production line (comprising a slab target length, a target length upper limit value and a target length lower limit value);
(2) The type of abnormality (including the abnormality of RB point, tundish change, head cutting, tail cutting, etc.), the position of abnormality occurrence, and the length of the abnormality region;
(3) Casting line length (length from the crystallizer to the cutting position, which is the total length of the optimized cutting in the production process);
(4) Minimum value of the cuttable length, also called lower limit of the transportable slab (i.e. minimum value of the cuttable length, determined by the design of the machine itself);
(5) Maximum value of the length that can be cut, also called upper limit of the slab that can be conveyed (i.e. maximum value of the length that can be cut, determined by the design of the machine itself);
(6) Other known conditions.
Depending on the requirements in an actual implementation, constraints may include, but are not limited to:
(1) The cutting length of the slab is required to be within the upper limit and the lower limit of the transportable slab;
(2) The abnormal section/waste blank must fall on the tail/head of the blank;
(3) If the cutting length cannot be cut according to the target length, the cutting length should fall within the upper and lower limits of the target length as much as possible.
Depending on the requirements in the actual implementation, optimization objectives may include, but are not limited to:
(1) The number of the target long cutting slabs is as large as possible;
(2) If the occurrence of the scrap is unavoidable, the total length of the scrap is as small as possible.
Wherein, the definition of the waste blank is as follows: when the cutting length exceeds the upper limit of the target length, the part exceeding the upper limit is a waste blank; and when the cutting length is smaller than the lower limit of the target length, the whole slab is a waste slab.
According to the continuous casting cutting optimization method based on mixed integer programming disclosed in this embodiment, in a specific implementation process, a specific process of establishing a mixed integer programming model is described with the following examples.
Example 1:
it is assumed that the known information refined in this embodiment includes:
the slab cutting plan issued by the production line specifically comprises:
(1) The target length of the j-th slab plan is aj, and the acceptable lower limit isThe upper acceptable limit is->Planning the total number of slabs to be j * ；
(2) Abnormal occurrence position, x= { X 1 ，x 2 ，...，x n -corresponding to abnormal relative positions occurring in sequence from the cutting head;
(3) Abnormal region length, c= { C 1 ，c 2 ，...，c n -corresponding to the length of the abnormal region occurring in sequence from the cutting head;
(4) Upper limit a of transportable slab mx ；
(5) Lower limit a of transportable slab min ；
(6) Casting a length L.
In this embodiment, since the occurrence position and the length of the abnormal region are paid attention to different types of abnormalities, the abnormality occurrence position and the length of the corresponding abnormal region are directly used as the distinction between different abnormalities when the problem is abstracted. Wherein it is required that the abnormal region always falls on the tail of a slab, i.e. that a cut must be made at the end of each abnormal region, thereby converting the situation of multiple abnormal occurrences into a "tail blank optimization" problem of abnormal occurrence on the tail.
At this time, there is always only one abnormal region in the casting length to be optimized, and the abnormal region always falls at the end of the casting length. In the present embodiment, only the case where one abnormality occurs is considered, and the abnormality occurrence position is assumed to be x and the abnormality region length is assumed to be c.
Then, the mixed integer programming modeling step includes:
the following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0，L]: a start cutting position of a j-th slab;
q j ∈[0，L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss.
In actual production, the number of planned cut slabs is often larger than the number of actual castable slabs of molten steel; in order to minimize cutting loss, when an abnormality occurs, it is necessary to select an appropriate length from the planned slabThe slab is cut, thus introducing the variable s j E {0,1}, indicating whether the j-th plan slab is cut.
Constructing a constraint function of the mixed integer programming model with model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
If the jth slab is cut according to the plan, the initial cutting position of the next slab is the tail of the jth slab, namely: p is p j ＝p j-1 +q j-1 ，(-s j )M≤q j ≤(s j )M，/> Wherein M is a sufficiently large constant;
meanwhile, in order to reduce the number of unreasonable cut slabs, only slabs exceeding the upper limit value of the target length and the lower limit value of the target length are allowed to be the last block, namely:
with this arrangement, if the slab other than the last slab is cut, the cutting length thereof is necessarily within the upper and lower limits of the cutting plan.
Meanwhile, considering that the site generally hopes to cut according to the target length as much as possible, constraint conditions are added to judge whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length (within the upper and lower limits of the portability), namely:
judging whether the last slab is waste, if the length is above the acceptable upper limit, thenIf it is above the lower acceptable limit +.>And vice versa is 0, namely:
if the last slab cut length is not between the target length lower limit value and the target length upper limit value, a cut loss (excluding the abnormal region included in itself) is formed, that is:
when the cutting length of the last slab is below the target length lower limit value, the whole slab belongs to the scrapped slab,then->I.e. the cutting loss should be at least the length of the last slab;
when the cut length of the last slab is above the upper limit value of the target length, only the part exceeding the upper limit is the cut lossThen->
Comprehensively obtain cutting loss
In the specific implementation process, according to the optimization target:
(1) Minimizing cutting losses
min l
(2) So that the number of slab blocks exactly the target length is as large as possible
max∑ j d j
The optimization targets are integrated, and the objective function for constructing the mixed integer programming model is as follows:
minw 1 l-w 2 ∑ j d j
wherein min l represents the minimum cutting loss, max j d j Indicating that the number of slabs cut according to the target length is as large as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
In the above embodiment, preferably, the process of modeling actual production data into a mixed integer programming model based on software programming of the open source optimization solver and then inputting the model into the open source optimization solver for solving is as follows:
and aiming at constraint conditions and optimization targets of the mixed integer programming model, based on a Python interface provided by an open source optimization solver SCIP, adopting Python language programming to realize solving of the mixed integer programming model.
In this embodiment, other existing open source solvers, such as BARON and anigle, may be written in other existing programming languages, according to the implementation scenario and specific application of the continuous casting cutting optimization method, for solving the specific results of the mixed integer programming model, which is not exemplified herein.
According to the continuous casting cutting optimization method disclosed in the above embodiment, compared with the cutting scheme shown in fig. 2, after the optimization method is executed, the cutting scheme is shown in fig. 4, and besides the cutting loss is reduced, the requirement of the order target length is met as much as possible, and the cutting loss is reduced as much as possible, and meanwhile, the target long slab is cut as much as possible.
As shown in fig. 5, the present invention further provides a continuous casting cutting optimization system based on mixed integer programming, and the continuous casting cutting optimization method based on mixed integer programming disclosed in any one of the above embodiments is applied, including:
the mathematical condition refining module is used for refining to obtain known conditions, constraint conditions and optimization targets according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters;
the mathematical model construction module is used for carrying out mathematical abstraction aiming at known conditions, constraint conditions and optimization targets, and establishing a mixed integer planning model according to the mathematical abstraction;
and the cutting parameter solving module is used for carrying out software programming based on the open source optimizing solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimizing solver for solving to obtain a continuous casting slab cutting plan.
In the above embodiment, preferably, in the mathematical condition refinement module, the known information of the slab cutting plan includes a target length of the slab, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value, and the known information of the abnormality parameters includes an abnormality type, an abnormality occurrence position, and an abnormality region length.
In the above embodiment, preferably, in the mathematical model building block, the constraint condition includes:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal position must be at the head or tail of the cut slab;
if the cutting length of the slab cannot be cut according to the target length, the cutting length of the slab is between the upper limit value of the target length and the lower limit value of the target length as far as possible;
the optimization targets include:
the number of slabs cut according to the target length is as large as possible;
if it is unavoidable that the abnormal blank is contained, the total length of the blank is as small as possible, wherein the portion exceeding the upper limit is the blank when the cut length of the slab exceeds the upper limit value of the target length, and the whole slab is the blank when the cut length of the slab is less than the lower limit value of the target length.
In the foregoing embodiment, preferably, the specific process of establishing the mixed integer programming model by the mathematical model construction module includes:
assume that the abnormality occurrence position is x The length of the abnormal region is c ；
The following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0，L]: a start cutting position of a j-th slab;
q j ∈[0，L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss;
constructing a constraint function of the mixed integer programming model with model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
Cutting the jth slab according to the plan, wherein the initial cutting position of the next slab is the tail of the jth slab, namely: p is p j ＝p j-1 +q j-1 ，(-s j )M≤q j ≤(s j )M，/>
Only the slab exceeding the upper limit value and the lower limit value of the target length is allowed to be the last block, namely:
judging whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length, namely:
judging whether the last slab is a waste slab or not, namely:
if the cutting length of the last slab is not between the lower limit value of the target length and the upper limit value of the target length, cutting loss is formed, namely:
when the cut length of the last slab is below the target length lower limit valueL is not less than%>
When the cut length of the last slab is above the target length upper limit valueL is not less than
Comprehensively obtain cutting loss
The objective function of constructing the mixed integer programming model is:
minw 1 l-w 2 ∑ j d j
wherein min l represents the minimum cutting loss, max j d j Indicating that the number of slabs cut according to the target length is as large as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
In the above technical solution, preferably, the specific method for implementing the open source optimization solver for the mixed integer programming model by the cutting parameter solving module through software programming includes:
and aiming at constraint conditions and optimization targets of the mixed integer programming model, adopting Python language programming to realize an open-source optimization solver SCIP.
According to the continuous casting cutting optimization system based on mixed integer programming disclosed in the above embodiment, functions to be realized by each module correspond to each step of the continuous casting cutting optimization method disclosed in the above embodiment, and in the implementation process, the implementation is performed with reference to the continuous casting cutting optimization method of the above embodiment, which is not described herein.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. The continuous casting cutting optimization method based on mixed integer programming is characterized by comprising the following steps of:
according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters, extracting to obtain known conditions, constraint conditions and optimization targets;
performing mathematical abstraction on the known conditions, constraint conditions and optimization targets, and establishing a mixed integer programming model according to the mathematical abstraction;
and (3) carrying out software programming based on an open source optimization solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimization solver for solving to obtain a continuous casting slab cutting plan.
2. The continuous casting cutting optimization method based on mixed integer program according to claim 1, wherein the known information of the slab cutting program includes a target length, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value of the slab, and the known information of the abnormality parameters includes an abnormality kind, an abnormality occurrence position, and an abnormality region length.
3. The mixed integer programming-based continuous casting cut optimization method of claim 2, wherein the constraints include:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal occurrence position must be at the head or tail of the cut slab;
if the slab cutting length cannot be cut according to the target length, the slab cutting length should be as far as possible between the target length upper limit value and the target length lower limit value;
the optimization objectives include:
the number of slabs cut according to the target length is as large as possible;
if the occurrence of the abnormal waste blank cannot be avoided, the total length of the waste blank is as small as possible, wherein when the cutting length of the plate blank exceeds the upper limit value of the target length, the part exceeding the upper limit is the waste blank, and when the cutting length of the plate blank is smaller than the lower limit value of the target length, the whole plate blank is the waste blank.
4. The continuous casting cutting optimization method based on mixed integer programming according to claim 3, wherein the specific process of establishing the mixed integer programming model comprises the following steps:
assuming that the abnormal occurrence position is x, and the abnormal region length is c;
the following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0,L]: a start cutting position of a j-th slab;
q j ∈[0,L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss;
constructing a constraint function of the mixed integer programming model with the model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
Cutting the jth slab according to the plan, wherein the initial cutting position of the next slab is the tail of the jth slab, namely:
only the slab exceeding the upper limit value and the lower limit value of the target length is allowed to be the last block, namely:
judging whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length, namely:
judging whether the last slab is a waste slab or not, namely:
if the cutting length of the last slab is not between the target length lower limit value and the target length upper limit value, cutting loss is formed, namely:
when the cut length of the last slab is below the target length lower limit valueThen
When the cutting length of the last slab is above the target length upper limit valueThen
Comprehensively obtain cutting loss
The objective function of constructing the mixed integer programming model is as follows:
min w 1 l-w 2 ∑ j d j
wherein min l represents minimum cutting loss, max Σ j d j Representing the number of slabs cut according to said target length as much as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
5. The continuous casting cutting optimization method based on mixed integer programming according to claim 4, wherein the process of modeling actual production data into a mixed integer programming model and inputting the model into the open source optimization solver for solving is as follows:
and aiming at constraint conditions and optimization targets of the mixed integer programming model, based on a Python interface provided by an open source optimization solver SCIP, adopting Python language programming to realize solving of the mixed integer programming model.
6. A mixed integer programming based continuous casting cutting optimization system, characterized by applying the mixed integer programming based continuous casting cutting optimization method according to any one of claims 1 to 5, comprising:
the mathematical condition refining module is used for refining to obtain known conditions, constraint conditions and optimization targets according to the slab cutting plan of the continuous casting process of steel and the known information of abnormal parameters;
the mathematical model construction module is used for carrying out mathematical abstraction on the known conditions, the constraint conditions and the optimization targets and establishing a mixed integer programming model according to the mathematical abstraction;
and the cutting parameter solving module is used for carrying out software programming based on the open source optimizing solver, modeling actual production data into a mixed integer programming model, and inputting the mixed integer programming model into the open source optimizing solver for solving to obtain a continuous casting slab cutting plan.
7. The continuous casting cutting optimization system based on mixed integer programming of claim 6, wherein the known information of the slab cutting plan in the mathematical condition refinement module includes a target length of the slab, a target length upper limit value, a target length lower limit value, a casting line length, a cuttable length minimum value, and a cuttable length maximum value, and the known information of the abnormality parameters includes an abnormality type, an abnormality occurrence position, and an abnormality region length.
8. The mixed integer programming based continuous casting cut optimization system of claim 7, wherein the constraints in the mathematical model building block include:
the slab cut length must be between the minimum and maximum cuttable lengths;
the abnormal occurrence position must be at the head or tail of the cut slab;
if the slab cutting length cannot be cut according to the target length, the slab cutting length should be as far as possible between the target length upper limit value and the target length lower limit value;
the optimization objectives include:
the number of slabs cut according to the target length is as large as possible;
if the occurrence of the abnormal waste blank cannot be avoided, the total length of the waste blank is as small as possible, wherein when the cutting length of the plate blank exceeds the upper limit value of the target length, the part exceeding the upper limit is the waste blank, and when the cutting length of the plate blank is smaller than the lower limit value of the target length, the whole plate blank is the waste blank.
9. The continuous casting cutting optimization system based on mixed integer programming according to claim 8, wherein the mathematical model construction module establishes a concrete process of establishing a mixed integer programming model comprising:
assuming that the abnormal occurrence position is x, and the abnormal region length is c;
the following model parameters were introduced:
n is E N: planning to cut the number of blocks of the slab;
p j ∈[0,L]: a start cutting position of a j-th slab;
q j ∈[0,L]: cutting length of the j-th slab;
s j e {0,1}: j, planning whether the slab is cut or not;
a target length lower limit value of the j-th slab;
the upper limit value of the target length of the j-th slab;
t j e {0,1}: the j-th cutting plate blank is above the lower limit value of the target length;
r j e {0,1}: the j-th cutting plate blank is below the upper limit value of the target length;
d j e {0,1}: the j-th cutting plate blank is a target length or not;
l e [0, L ]: cutting loss;
constructing a constraint function of the mixed integer programming model with the model parameters according to the constraint and the optimization target comprises:
the starting position of the first slab is 0: p is p 1 ＝0，
Cutting the jth slab according to the plan, wherein the initial cutting position of the next slab is the tail of the jth slab, namely:
only the slab exceeding the upper limit value and the lower limit value of the target length is allowed to be the last block, namely:
judging whether the currently cut slab is cut according to the target length, namely:
only the last slab is allowed to be abnormal, namely:
ensuring that the abnormal region appears at the tail of the last slab, i.e
The last slab is allowed to be of any length, namely:
judging whether the last slab is a waste slab or not, namely:
if the cutting length of the last slab is not between the target length lower limit value and the target length upper limit value, cutting loss is formed, namely:
when the cut length of the last slab is below the target length lower limit valueThen
When the cutting length of the last slab is above the target length upper limit valueThen
Comprehensively obtain cutting loss
The objective function of constructing the mixed integer programming model is as follows:
min w 1 l-w 2 ∑ j d j
wherein min l represents minimum cutting loss, max Σ j d j Representing the number of slabs cut according to said target length as much as possible, w 1 And w 2 Respectively representing the weights of the two optimization objectives.
10. The continuous casting cutting optimization system based on mixed integer programming according to claim 9, wherein the specific method for realizing the open source optimization solver for the mixed integer programming model by the cutting parameter solving module through software programming is as follows:
and aiming at constraint conditions and optimization targets of the mixed integer programming model, adopting Python language programming to realize an open-source optimization solver SCIP.
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