CN111783254B - Steel cutting control method and device based on multi-target mixed integer programming - Google Patents

Steel cutting control method and device based on multi-target mixed integer programming Download PDF

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CN111783254B
CN111783254B CN202010710301.9A CN202010710301A CN111783254B CN 111783254 B CN111783254 B CN 111783254B CN 202010710301 A CN202010710301 A CN 202010710301A CN 111783254 B CN111783254 B CN 111783254B
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邹晓峰
朱彭生
郑东源
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Ouye Yunshang Co ltd
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Abstract

The invention relates to a steel cutting control method and a steel cutting control device based on multi-target mixed integer programming, which comprises the following steps: 1) acquiring input data; 2) constructing a multi-target mixed integer programming model based on a set target, pre-calculating the scale of a cutting scheme matrix, judging whether the scale is larger than the set scale, if so, executing the step 3 after executing dimension reduction processing, and if not, directly executing the step 3); 3) solving the multi-target mixed integer programming model based on the input data to obtain a primary optimal cutting scheme matrix; 4) judging whether the initial optimal cutting scheme matrix is feasible, if so, directly executing the step 5), otherwise, adjusting the constraint and returning to the step 3) to solve again; 5) performing dynamic parameter adjustment on the initial optimal cutting scheme matrix by adopting a multi-target-based dynamic parameter adjustment algorithm to obtain a final cutting scheme matrix; 6) and controlling the implementation of steel cutting based on the final cutting scheme matrix. Compared with the prior art, the method has the advantages of improving the acquisition speed of the steel cutting scheme and the like.

Description

Steel cutting control method and device based on multi-target mixed integer programming
Technical Field
The invention belongs to the technical field of steel industry and transaction, relates to a steel cutting method, and particularly relates to a steel cutting control method and device based on multi-target mixed integer programming.
Background
The problem of steel cutting and coiling refers to that a batch of raw materials are selected from given steel raw materials and cut into coils and plates with required scales, and the yield of the steel raw materials is guaranteed while the processing technology is met. The problem belongs to the problem of NP-difficult combination optimization, people cannot provide a complete, accurate, rapid and efficient bundling method so far, and various difficulties to be solved, such as low efficiency caused by the fact that a model is not in line with production practice and too many combinations, still exist.
For the raw material cutting problem, a heuristic algorithm is traditionally adopted because the problem is large in scale:
(1) the cluster search algorithm solves the problem of unconstrained stock layout of rectangular pieces on a single raw material, but cannot solve the constraint problem of actual steel coil cutting.
(2) A simulated annealing algorithm and a genetic algorithm belong to a stochastic algorithm, and the existing algorithms are mature and high in operating efficiency, but have the problem of unstable solution. However, the heuristic algorithm has the defects that the solution is unstable, the difference between the solution result and the optimal scheme cannot be evaluated, and the improvement cannot be carried out.
With the continuous development of operational research, the computing power is continuously improved, and in order to solve the defects of heuristic algorithms, deterministic algorithms are continuously developed. Among them, the column production method is a very efficient algorithm for solving the large-scale optimization problem. The theoretical basis is set forth by Danzig, et al 1960. In essence, the column generation algorithm is a form of simplex method, which is used to solve the linear programming problem. However, the column production algorithm requires a smaller sub-problem scale, and the target and constraint in the raw material cutting project are too much, which easily causes the difficulty in reducing the sub-problem scale, so that the application of the column production algorithm in the steel cutting and coiling problem cannot effectively improve the solving efficiency, i.e. the operation speed is very slow.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a steel cutting control method and device based on multi-target mixed integer programming, which can improve the acquisition speed of a steel cutting scheme.
The purpose of the invention can be realized by the following technical scheme:
a steel cutting control method based on multi-target mixed integer programming comprises the following steps:
1) acquiring input data;
2) constructing a multi-target mixed integer programming model based on a set target, taking an order with the narrowest width and a raw material with the largest width to pre-calculate the scale of a cutting scheme matrix, judging whether the scale is larger than the set scale, if so, executing step 3 after executing dimension reduction processing, and if not, directly executing step 3);
3) solving the multi-target mixed integer programming model based on the input data to obtain a primary optimal cutting scheme matrix;
4) judging whether the initial optimal cutting scheme matrix is feasible, if so, directly executing the step 5), otherwise, adjusting the constraint and returning to the step 3) to solve again;
5) performing dynamic parameter adjustment on the initial optimal cutting scheme matrix by adopting a multi-target-based dynamic parameter adjustment algorithm to obtain a final cutting scheme matrix;
6) and realizing steel cutting based on the final cutting scheme matrix.
Further, the input data comprises steel product demand data and raw material data.
Further, the target of the multi-target mixed integer programming model comprises a plurality of the yield, the short overflow area, the number of row cutters, the auxiliary material using area, the excess material generating area, the overflow short area and the number of whole roll cutting.
Further, the constraints of the multi-objective mixed integer programming model comprise order demand constraints, raw material inventory constraints, industrial processing constraints, coil material bundling requirements constraints and whole coil use constraints.
Further, the dimension reduction processing is realized based on a heuristic algorithm.
Further, the dimension reduction processing comprises multiple dimension reduction and yield screening dimension reduction.
Further, the dynamic parameter adjustment algorithm specifically includes:
and (3) constructing a mathematical programming model by taking each target as a single target respectively, sequentially solving an optimal solution, and taking the single target as a constraint and relaxing in the mathematical programming model solution of the current single target.
Further, the single targets include a yield single target, a row number single target and a full roll use single target.
Further, the set scale is at least 50000.
The invention also provides a steel cutting control device based on multi-target mixed integer programming, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the method according to claim 1 so as to control the implementation of steel cutting.
Compared with the prior art, the invention has the following beneficial effects:
(1) and a multi-target mixed integer program is constructed, and the constraint problem of actual steel coil cutting is solved.
(2) The solution of the multi-target mixed integer programming model adopts a deterministic algorithm, and the robustness problem of a heuristic algorithm is solved, namely the problem of unstable solution results is solved.
(3) And the heuristic algorithm is utilized to reduce the scale of the scheme matrix and improve the operational efficiency of the whole model.
(4) The effective combination of the deterministic algorithm and the heuristic algorithm solves the balance problem of the solving stability and the solving efficiency.
(5) Aiming at the multi-target problem, a dynamic parameter adjusting algorithm is constructed, and the problem of stability of the algorithm in balancing the multi-target is solved.
(6) By means of multi-target mixed integer programming and dynamic parameter adjusting algorithm, the problem that the algorithm is difficult to add new targets and the expansibility of constraint is solved.
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FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
The embodiment provides a steel cutting control method based on multi-target mixed integer programming, which is characterized in that defined targets are converted into data programming, effective parameter adjustment is carried out on the optimal solution scheme based on a multi-target mixed integer programming model so as to obtain a more effective cutting scheme, the problem scale is reduced when the scale is large so as to improve the solving efficiency, a dynamic parameter adjustment algorithm is constructed so as to support the solving of multiple targets, and the balance problem of the stability of the solving result and the solving efficiency is solved.
As shown in fig. 1, the method comprises the steps of:
1) acquiring input data;
2) based on the set target, a multi-target mixed integer programming model is constructed, the order with the narrowest width and the raw material with the largest width are taken, and O (n! ) Pre-calculating the scale of the cutting scheme matrix, judging whether the scale is larger than the set scale, if so, executing the step 3 after executing dimension reduction processing, and if not, directly executing the step 3);
3) solving the multi-target mixed integer programming model based on the input data to obtain a primary optimal cutting scheme matrix;
4) judging whether the initial optimal cutting scheme matrix is feasible, if so, directly executing the step 5), otherwise, throwing out an exception, and returning to the step 3) to solve again after automatically relaxing the constraint;
5) performing dynamic parameter adjustment on the initial optimal cutting scheme matrix by adopting a multi-target-based dynamic parameter adjustment algorithm to obtain a final cutting scheme matrix;
6) and realizing steel cutting based on the final cutting scheme matrix.
The objectives of the multi-objective mixed integer programming model may include:
yield of finished product: the desired (finished product area + excess material area)/total amount area target is achieved.
Area of use of auxiliary materials: the cutting scheme preferentially uses auxiliary materials, and the auxiliary materials are large in use area.
Excess area (wide) produced: the width remains the target of small area of the produced residue.
The number of rows of blades: the target with small number of cutting row knives.
Use of the whole volume: the whole roll is preferred to be used, so that the operation efficiency is improved; the aim of small excess material area caused by length surplus is also fulfilled.
Order requirements: the goal of meeting the order specification requirement and the total amount requirement is achieved.
Number of partial volumes: the order requirement is to achieve the goal of the maximum number of partial rolls allowable for each order.
Raw stock: the total amount of raw material inventory area should meet the target of order demand.
The process requirements are: the shortest length of the cutting machine set is required.
The multi-target mixed integer programming model also needs to consider algorithm performance and efficiency targets during construction, wherein the algorithm performance and the efficiency targets comprise algorithm robustness and algorithm expansibility, and the algorithm robustness refers to a stability target of a model solution scheme result; algorithm extensibility refers to the addition of new goals and constraints to an algorithm.
Description of the symbols:
standard raw material (non-auxiliary material) specification
Figure BDA0002596298990000041
N in total1And (4) seed preparation. Wherein liDenotes the length of the raw material, wiIs the width of the raw material, numiIs the number of raw materials, gi＝numi*lIThe total length of the type of feedstock is indicated.
Specification of auxiliary materials
Figure BDA0002596298990000042
The type is remainder, n2And (4) seed preparation.
Definitions n ═ n1+n2,gT＝{g1,...,gn}。
Specification of sheet material order
Figure BDA0002596298990000043
Sheet type s1In which
Figure BDA0002596298990000044
Indicates the total number of orders, then
Figure BDA0002596298990000045
Indicating the total length requirement of the order.
Specification of coil order
Figure BDA0002596298990000046
S in total2In the method for preparing the seed coating,
Figure BDA0002596298990000047
indicating rollThe total length of the cable needs to be,
Figure BDA0002596298990000048
indicating the coil number requirement.
Definition s ═ s1+s2。dT＝{d1,...,ds}。
·aiA cutting plan of the raw material, wherein
Figure BDA0002596298990000051
Representing the number of cuts of different widths for this scheme.
·
Figure BDA0002596298990000052
The cutting plan generates a matrix, i.e.
Figure BDA0002596298990000053
·R1：
Figure BDA0002596298990000054
The vector is judged according to the excess material,
Figure BDA0002596298990000055
the cutting residual part of the scheme i meets the requirement of the excess material width and can be used as the excess material, and if the cutting residual part cannot be used as the excess material, the cutting residual part can be used as the excess material
Figure BDA0002596298990000056
·R2：
Figure BDA0002596298990000057
And (4) a remainder width vector, wherein if the cutting remainder of the scheme i meets the requirement of the remainder width, the width of the remainder is marked, and if the cutting remainder cannot be used as the remainder, the width of the remainder is 0.
The loss scrap width vector, the width of scrap,
Figure BDA0002596298990000058
if scheme i cuts the rest fullThe width of the remaining portion is marked as the width of the scrap width requirement, and if the width of the scrap is not satisfied, the width is 0.
·
Figure BDA0002596298990000059
The feedstock-recipe uses a matrix, in which the ith row
Figure BDA00025962989900000510
Cl represents the short spill range of the order, respectively. Wherein cl ═ { cl ═1,...,cls}。
·α1Representing a variable inventory vector.
Q represents the order split number requirement,
Figure BDA00025962989900000511
x this variable represents the cut length of the protocol, where
Figure BDA00025962989900000512
·x1Representing standard type stock cut length, x2Denotes the cut length of the adjunct, so that x ═ x1,x2)
T auxiliary variable, the purpose of which is to convert the absolute value form into a linear form.
Z this variable indicates whether a scheme is used, a variable of type 0-1.
E, the variable indicates whether a certain raw material is used, a variable of type 0-1, and e ═ e1,...,en。
·yiThe variable indicates whether the material is in a certain interval, a type 0-1 variable.
·viThe variable indicates whether the raw material i is used in its entirety, and the variable is a type 0-1 variable.
1. Multi-objective mixed integer programming model
The multi-objective mixed integer programming model P1 introduced in this embodiment defines 6 objective functions, which are:
·(Ax-d)Tw2indicating the short overflow area of the order, c1Punishment parameters for short overflow area of the order;
·
Figure BDA00025962989900000513
indicates the area of scrap, c2Punishment parameters for the waste area;
·(R2)Tx represents the area of the used auxiliary material, c3Exciting parameters for the use area of auxiliary materials;
·
Figure BDA00025962989900000514
indicates the area of excess material generation, c4A penalty parameter for generating the excess material area;
·
Figure BDA00025962989900000515
indicates the total number of gang tools, c5A penalty parameter which is the total cutter arrangement number;
·
Figure BDA00025962989900000516
indicates the remaining number of raw material lengths, c6The penalty parameter is the residual number of the length of the raw material. (Note: business preference: complete volume, reduced operation, increased efficiency, reduced excess material generation)
The multi-objective mixed integer programming model P1 of this embodiment defines 6 basic constraints, and meets the requirements of orders and production processes:
order demand constraints: d is less than or equal to Ax and less than or equal to d + cl, the constraint is mainly to ensure that the cutting scheme meets the actual order requirement, and if a short overflow condition occurs, the short overflow range is defined within a certain range.
Raw stock constraints: bx is less than or equal to g, and the constraint mainly ensures that the raw materials required by the cutting scheme cannot exceed the current inventory upper limit.
Industrial process constraints:
Figure BDA0002596298990000061
this constraint mainly ensures that the cutting length cannot be less than the shortest machining length of the machining unit.
Coil splitting requirement constraints:
Figure BDA0002596298990000062
this constraint primarily ensures that the number of split plans is less than the split requirements in the order requirements.
Whole volume usage constraint 1:
Figure BDA0002596298990000063
because of yjIs a variable from 0 to 1, the whole volume uses constraint 1 and only one variable is taken 1, also show
Figure BDA0002596298990000064
Indicates the standard length liA certain integer multiple.
Whole volume usage constraint 2:
Figure BDA0002596298990000065
indicates the total length of the feedstock i used.
The two whole rolls are restricted to ensure that the cutting scheme tends to select the whole rolls for use, so that the operation efficiency is improved; and also takes into account the smaller excess material area generated by the length surplus.
2. Dimensionality reduction treatment
In this embodiment, the set scale is 50000, and when the specification of the scheme matrix is greater than 50000, a heuristic algorithm needs to be used to reduce the scale of the problem. The reduction processing includes:
2.1) multiple dimensionality reduction: in model P1, the size of the solution matrix a will increase as the order volume and material type increase, and the order width decreases. A heuristic algorithm is adopted to reduce the scale of the scheme matrix A, a proper coefficient k is calculated through experiments in the generation process of the scheme aiN) are only multiples of k, so that the number of schemes is not excessive.
2.2) screening yield and reducing dimension: and after the scheme is generated, screening all schemes meeting the requirements by using the yield as a screening standard, and removing the schemes which are not met from the scheme matrix A so as to select the scheme with higher yield on the basis of meeting the yield target.
Through the 2 steps, the problem scale is reduced, and the solving efficiency of the mixed integer programming in the subsequent steps is improved.
3. Dynamic parameter adjusting algorithm
Based on a mixed integer programming model, effective parameter adjustment is carried out on the solution optimal scheme, and the method specifically comprises the following steps:
3.1) solving by taking the yield (for the convenience of mathematical modeling, the minimum waste area is converted into the target function), the number of arranged cutters, the whole roll, the overflow short-loading area, the excess material generating area (width) and the auxiliary material using area as single targets respectively, and providing parameters for the automatic updating of the relaxation parameter beta according to the solved result.
3.2) construct a mathematical programming model P2 with yield (scrap area) as a single objective.
3.3) solving the mathematical programming P2 to obtain an optimal solution V2, then taking the yield as constraint, and constructing a mathematical programming model P3 with the minimum number of row knives as a single target. And the relaxation parameter beta 2 is automatically updated based on the solving process, so that the last single-target yield is taken as constraint and relaxed.
3.4) assuming that the optimal solution of P3 is V3, adding row number constraints and constructing a mathematical programming model P4 with a single target for use of the whole roll. And the relaxation parameter beta 3 is automatically updated based on the solving process, so that the last single-target cutter arranging number is used as constraint and is relaxed.
3.5) assuming the optimal solution of P4 is V4, adding the full volume usage constraint and constructing the final mathematical programming problem P5. P5 is a multi-objective mathematical programming model, with the objectives: a yield (waste area) target, an overflow short-loading area target, a residual material residual area target and an auxiliary material using area target. In model P5 we define the target weights according to importance: the target of yield is equal to or larger than the target of overflow short-loading area and equal to or larger than the target of residual material area, namely the target of auxiliary material using area.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (7)

1. A steel cutting control method based on multi-target mixed integer programming is characterized by comprising the following steps:
1) acquiring input data;
2) constructing a multi-target mixed integer programming model based on a set target, pre-calculating the scale of a cutting scheme matrix, judging whether the scale is larger than the set scale, if so, executing the step 3 after executing dimension reduction processing, and if not, directly executing the step 3);
3) solving the multi-target mixed integer programming model based on the input data to obtain a primary optimal cutting scheme matrix;
4) judging whether the initial optimal cutting scheme matrix is feasible, if so, directly executing the step 5), otherwise, adjusting the constraint and returning to the step 3) to solve again;
5) performing dynamic parameter adjustment on the initial optimal cutting scheme matrix by adopting a multi-target-based dynamic parameter adjustment algorithm to obtain a final cutting scheme matrix;
6) controlling the realization of steel cutting based on the final cutting scheme matrix;
the targets of the multi-target mixed integer programming model comprise a plurality of targets of a yield, a short overflowing area, the number of row cutters, an auxiliary material using area, a surplus material generating area, an overflowing and short loading area and a whole roll cutting number, and the constraints comprise an order demand constraint, a raw material inventory constraint, an industrial processing constraint, a coil material bundling requirement constraint and a whole roll using constraint;
the dynamic parameter adjusting algorithm specifically comprises the following steps: and (3) constructing a mathematical programming model by taking each target as a single target respectively, sequentially solving an optimal solution, and taking the single target as a constraint and relaxing in the mathematical programming model solution of the current single target.
2. The steel cutting control method based on multi-objective mixed integer programming according to claim 1, wherein the input data comprises steel demand data and raw material data.
3. The steel cutting control method based on multi-objective mixed integer programming according to claim 1, characterized in that the dimension reduction processing is realized based on a heuristic algorithm.
4. A steel cutting control method based on multi-objective mixed integer programming according to claim 3, wherein the dimension reduction process comprises multiple dimension reduction and yield screening dimension reduction.
5. The method of claim 1, wherein the single targets include a yield single target, a number of rows of knives single target, and a full roll use single target.
6. A steel cutting control method based on multi-objective mixed integer programming according to claim 1, characterized in that the set scale is at least 50000.
7. A steel product cutting control device based on multi-objective mixed integer programming, comprising a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of the method according to claim 1 so as to control the implementation of the steel product cutting.
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