CN115879625A - Two-dimensional strip defect layout method and system for coiled material - Google Patents
Two-dimensional strip defect layout method and system for coiled material Download PDFInfo
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Abstract
A two-dimensional strip defect layout method and a system for coil section bars are disclosed, wherein the method comprises the following steps: acquiring an optimal solution of two-dimensional rectangular layout in the coil section with the defects of the target block, wherein the optimal solution comprises an upper bound value Uh and a lower bound value Lh; calling a cutting position discrete point subtraction algorithm, and searching a minimum cutting position discrete point set; converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects of which the Lh width is W, relaxing the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and establishing a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position; and solving the one-dimensional continuous packing model, if the one-dimensional continuous packing model has a solution, calling a check detection algorithm to judge whether the solution meets the requirement of solving the two-dimensional rectangular layout problem, and if so, outputting the optimal solution Lh of the problem. The method has the advantages of clear evolution direction, high evolution efficiency, high convergence rate and the like.
Description
Technical Field
The invention relates to the technical field of plate stock layout, in particular to a two-dimensional strip defect stock layout method and system for coiled materials.
Background
Since the twenty-first century, with the rapid development of economy, the production scale of enterprises is gradually enlarged, and the resource consumption is more and more. The stock layout problem is closely related to daily life, the effect excellence of stock layout directly influences the utilization ratio of raw materials, and the resource is not fully utilized to cause waste, and simultaneously, the pollution is brought to the environment. As a large manufacturing country, china annually needs a large amount of raw materials for manufacturing various products. A considerable portion of the material needs to be cut, and if the utilization rate of the material can be improved by one percentage, the economic benefit is very remarkable.
In many manufacturing industries, it is often necessary to cut raw materials into different types of parts for manufacturing. Such as cutting of wooden boards and glass, this problem is known as two-dimensional lay-out optimization. However, due to its nature and the influence of the manufacturing process, there may be defects in the raw material that cannot be used for production. For example, knots contained in wood, bubbles occurring during the processing of glass, contaminated areas contained in steel, holes present in natural leather. Therefore, in the cutting of the raw material, it is necessary to avoid these areas and make the utilization rate of the raw material as large as possible. In addition to this, several constraints need to be met, such as "one-knife" and "non-one-knife", whether the maximum number of goods is limited, whether the goods cutting direction is rotatable, etc. Despite the various constraints imposed by the stock layout in different industrial fields, they have in common the fundamental problem of finding an effective arrangement of the required components on the raw material, so that the area utilization of the planar regions on the raw material is high, in order to save the raw material as much as possible.
At present, the prior art mainly aims at the problem of flawless stock layout, and the main methods can be divided into an accurate solution algorithm, an intelligent optimization algorithm and a heuristic algorithm. At present, research is less for the problem of stock layout of roll profiles with defects, and a heuristic algorithm and an intelligent optimization algorithm are mainly used. The heuristic algorithm is an algorithm constructed based on intuition or experience, a feasible solution is obtained within a certain time, but the quality of the feasible solution cannot be guaranteed, and the feasible solution obtained each time is unstable, and whether the feasible solution is the optimal solution cannot be judged. The intelligent optimization algorithm is generally based on a random search algorithm based on biological intelligence or physical phenomena, and mainly comprises a simulated annealing algorithm, a genetic algorithm and the like. Simulated annealing is a problem solving method that has the potential to obtain a globally optimal solution to an optimization problem, and has gradually become a general, general method for optimization problem solving, but this is at the cost of an extremely lengthy annealing process, i.e., a problem solving process, and the solving efficiency is low. The genetic algorithm has good global search capability, but has the defects of long search time, low evolution efficiency, low convergence rate and easy trapping in local optimal solution. Therefore, a layout method capable of greatly reducing the search space of the algorithm and improving the convergence rate of the algorithm is urgently needed.
Disclosure of Invention
In view of the above defects, the present invention provides a two-dimensional strip defect layout method and system for coil section bar, so as to improve the convergence rate of the algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme: a two-dimensional strip defect layout method facing a coiled section comprises the following steps:
step S1: acquiring an optimal solution of a two-dimensional rectangular layout in a coil profile with defects of a target block, wherein the optimal solution comprises an upper bound value Uh and a lower bound value Lh;
step S2: calling a cutting position discrete point subtraction algorithm, and searching a minimum cutting position discrete point set without losing a stock layout optimal solution;
and step S3: converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and establishing a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
and step S4: solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, calling a check detection algorithm, judging whether the solution meets the requirement for solving the two-dimensional rectangular layout problem, if so, outputting the optimal solution Lh of the problem, if not, adjusting the one-dimensional continuous boxing model, and repeating the step S4;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh +1, and judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and repeating the step S1, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
Preferably, the obtaining manner of the upper bound value Uh in the step S1 is as follows:
step A1: sequencing the target blocks according to the sequence of the areas from large to small to obtain a target block set, and initializing a skyline in the roll profile with the defects;
step A2: searching the lowest placeable point of the skyline in the roll profile with the defects;
step A3: sequentially placing the target blocks into the lowest placeable point, respectively obtaining the fitness values of the target blocks, and placing the target block with the largest fitness value into the lowest placeable point;
step A4: and updating the target block set and searching for the lowest placeable point of the skyline in the roll profile with the defect again, and repeating the step A3 until all the target blocks in the target block set are placed in the roll profile with the defect.
Preferably, the manner of obtaining the fitness value of the target block in step A3 is as follows:
respectively judging whether the height of the target block is equal to the left height of the lowest placeable point of the skyline or not, whether the height of the target block is equal to the right height of the lowest placeable point of the skyline or not and whether the height of the target block is equal to the bottom width of the lowest placeable point of the skyline or not;
and accumulating a number of satisfied conditions, the fitness value being in direct proportion to the number of satisfied conditions.
Preferably, the lower threshold Lh in step S1 is obtained as follows:
the lower bound Lh is obtained by the following formula:
wherein Lh = min { L1, L2};
wherein the obtaining formula of L1 is as follows:
wherein w i And h i Width and length, w, of the target block i, respectively d And h d The width and the length of the defect d are respectively, and W is the width of the roll profile;
the acquisition model for L2 is as follows:
min h; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (1);
wherein r is xi Is a variable of 0-1, and represents whether the lower left corner of the target block i is on the x-th target block, if yes, r xi =1, otherwise r xi ＝0，D q Denotes the total length of the q-th column defect, h i Denotes the length of the target block i, h denotes the total length of the coil profile used, X 0 Representing a set of discrete points.
Preferably, the cutting position discrete point subtraction algorithm in the step S2 is specifically as follows:
obtaining the size information of the target block and the position information of the defect in the coil section bar, and calculating to obtain the wide linear combination value N of the target block v (w)；
Calculating a plurality of discrete point sets N which do not exceed the side length of the raw material by taking the right boundary of the defect as a reference v (x,y,w,h)；
Selecting an arbitrary positive integert, wherein 0<t<W, respectively acquiring the calculation point sets on two sides of t
And the set of calculation points->
And a total set M w (t,x,y,w,h)，
Traversing all the t values, and finally selecting the total set M w (t, x, y, w, h) t with the least number of points;
wherein
N v (x,y,w,h)＝N v (w)∪{z|z＝x j +w d +v,j∈D,v∈N v (w),0≤z≤W}；
The minimum cut position discrete point set is:
M w (x,y,w,h)＝{M w (t,x,y,w,h)|t＝argmin{M w (t,x,y,w,h)}|}；
middle w i And h i Width and length, w, of the target block i, respectively d And h d Width and length of defect d, W and h width and length of coil profile, x j And y j The left lower corner abscissa and ordinate of defect D, D defect set, I target block set, a i Is a variable from 0 to 1, z has no specific meaning but one symbol in the set;
|t＝argmin{M w (t, x, y, w, h) } denotes that M is caused to be M w And (t, x, y, w, h) the value of t with the minimum value.
Preferably, the one-dimensional continuous packing model in step S3 is specifically as follows:
wherein r is yi Is a variable from 0 to 1 and indicates whether the lower left corner of the target block i is on the y-th long-bar target block, and if so, r yi =1, otherwise r yi ＝0，W q Indicates the usable width, Y, of the qth slice object block 0 Representing a set of discrete points of a vertical cut line in the y-axis direction, w i And h i Width and length, w, respectively, of the target block i d And h d Width and length, x, of defect d, respectively d And y d The abscissa and ordinate of the lower left corner coordinate of the defect d are respectively indicated.
Preferably, the check detection algorithm in step S4 is specifically as follows:
x i +(1-z ij )M≥x j +w j ,{i,j∈I|y i +w i ≥y i ∩y i +w i ≥y i -formula (9);
x i +(1-z ij )M≥x d +w d ,{i∈I,d∈D|y i +w i ≥y d ∩y d +w d ≥y i formula (ii) } -formula(10)；
0≤x i ≤W-w i -formula (11);
wherein M represents a very large number, z ij ∈{0，1}，z ij Is a variable from 0 to 1, indicating whether the target block i is to the right of the target block j, if z ij =1, otherwise z ij ＝0,x i Are defined variables.
Preferably, the method for adjusting the one-dimensional continuous binning model in step S4 is to add a constraint condition to the one-dimensional continuous binning model, where the constraint condition is:
A two-dimensional strip defect layout system for coil section bars uses the two-dimensional strip defect layout method for the coil section bars, and comprises a boundary value acquisition module, a point set acquisition module, a model construction module and a judgment module;
the boundary value acquisition module is used for acquiring an optimal solution of two-dimensional rectangular layout in the coil section with the defects of the target block, wherein the optimal solution comprises an upper boundary value Uh and a lower boundary value Lh;
the point set acquisition module is used for calling a cutting position discrete point subtraction algorithm and searching a minimum cutting position discrete point set without losing a stock layout optimal solution;
the model building module is used for converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and building a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
the judging module is used for solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, a check detection algorithm is called to judge whether the solution meets the requirement for solving the two-dimensional rectangular layout problem, if so, the optimal solution Lh of the problem is output, and if not, the one-dimensional continuous boxing model is adjusted and the judging module is called again;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh + 1, and judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and calling the bound value acquisition module again, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
One of the above technical solutions has the following advantages or beneficial effects: the invention relaxes the arrangement problem into a one-dimensional continuous packing problem which can be solved by establishing a one-dimensional continuous packing model to obtain a result. When the one-dimensional continuous boxing model has a solution, further verification is needed, a check detection algorithm is called at the moment, whether the solution meets the requirement for solving the two-dimensional rectangular layout problem or not is judged, and if the solution meets the requirement, the optimal solution Lh of the problem is output. When the one-dimensional continuous boxing model has no solution, the coil section with the length of the lower bound value Lh cannot meet the requirement of stock layout, the lower bound value Lh is updated to enable the length of the coil section to be +1, then the steps are continuously repeated, and a new one-dimensional continuous boxing model is constructed to be solved continuously.
Drawings
FIG. 1 is a flow chart of one embodiment of the method of the present invention.
Figure 2 is a schematic block diagram of one embodiment of the system of the present invention.
FIG. 3 is a skyline representation spread diagram of one embodiment of the system of the present invention.
FIG. 4 is a state diagram of an algorithm arrangement for cutting position discrete point subtraction according to an embodiment of the system of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the embodiments of the present invention, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implying any number of technical features indicated. Thus, features defined as "first", "second", may explicitly or implicitly include one or more of the described features. In the description of the embodiments of the present invention, "a plurality" means two or more unless specifically limited otherwise.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless otherwise specified. The specific meanings of the above terms in the present invention can be understood in a specific case to those of ordinary skill in the art.
As shown in fig. 1 to 4, a two-dimensional strip defect layout method for coil section bar comprises the following steps:
step S1: acquiring an optimal solution of two-dimensional rectangular layout in a coil profile with defects of a target block, wherein the optimal solution comprises an upper bound value Uh and a lower bound value Lh;
step S2: calling a cutting position discrete point subtraction algorithm to search a minimum cutting position discrete point set without losing a stock layout optimal solution;
and step S3: converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and establishing a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
and step S4: solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, calling a check detection algorithm, judging whether the solution meets the requirement for solving the two-dimensional rectangular layout problem, if so, outputting the optimal solution Lh of the problem, if not, adjusting the one-dimensional continuous boxing model, and repeating the step S4;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh + 1, and judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and repeating the step S1, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
In the invention, I = {1,2, \8230;, n } different types are cut in a defective roll section with width W and unlimited length, and the width and the height are W respectively i And h i Value v i The target block (area) is cut out, the cut target block cannot intersect with the defect area, the direction of the target block is fixed, and the target block cannot rotate.
Firstly, obtaining an optimal solution of two-dimensional rectangular layout in a rolled section, wherein the optimal solution comprises an upper boundary value Uh and a lower boundary value Lh, the upper boundary value Uh is the length which uses the most plates, and the lower boundary value Lh is the length which uses the shortest plates, then verifying the result, and judging whether a lower boundary value Lh scheme is used for smoothly cutting all target blocks in the rolled section, so that a cutting position discrete point minus point algorithm is called according to the cutting point of each target in the optimal solution lower boundary value scheme to search a minimum cutting position discrete point set which does not lose the optimal solution of the layout, and then converting the two-dimensional rectangular layout problem of the rolled section with defects into a one-dimensional continuous boxing problem with the length of h and the width of w by using the layout scheme of the layout, wherein the one-dimensional continuous boxing problem can be solved by establishing a one-dimensional continuous boxing model to obtain a result. When the one-dimensional continuous boxing model has a solution, further verification is needed, a check detection algorithm is called at the moment, whether the solution meets the requirement for solving the two-dimensional rectangular layout problem or not is judged, and if the solution meets the requirement, the optimal solution Lh of the problem is output. And when the one-dimensional continuous encasement model is not solved, which indicates that the roll profile with the length of the lower bound value Lh cannot meet the requirement of stock layout, updating the lower bound value Lh to enable the length of the roll profile to be +1, and then continuously repeating the steps to construct a new one-dimensional continuous encasement model to continuously solve.
The method provided by the invention has the advantages of clear evolution direction, high evolution efficiency, high convergence rate and the like.
Preferably, the upper bound value Uh in step S1 is obtained as follows:
step A1: sequencing the target blocks according to the sequence of the areas from large to small to obtain a target block set, and initializing skylines in the roll profiles with the defects;
step A2: searching the lowest placeable point of the skyline in the roll profile with the defects;
step A3: sequentially placing target blocks into the lowest placeable point, respectively obtaining the fitness values of the target blocks, and placing the target block with the largest fitness value into the lowest placeable point;
step A4: and updating the target block set, searching the lowest placeable point of the skyline in the roll profile with the defects again, and repeating the step A3 until all the target blocks in the target block set are placed in the roll profile with the defects.
In the invention, an optimal adaptation heuristic method is used for calculating the upper bound value Uh of the defective roll profile two-dimensional rectangular layout problem, the optimal adaptation heuristic method uses skylines to represent the arrangement state, the skylines are the external top contour lines of the arrangement state, as shown by dotted lines in figure 3, the skylines are placeable points, and shadow parts are wasted areas. And selecting a lower left angular point (0, 0) of the raw material plate as a feasible placing point at the initial lowest position of the skyline, then calculating the fitness value, and selecting a target block to place. And sequentially carrying out iterative computation to obtain a final arrangement method scheme. This process is a heuristic, with the resulting value being the upper bound of the original problem.
It is worth mentioning that when the fitness values of a plurality of target blocks are equal, the target block with the highest rank in the target block set is placed.
Preferably, the manner of obtaining the fitness value of the target block in step A3 is as follows:
respectively judging whether the height of the target block is equal to the left height of the lowest placeable point of the skyline, whether the height of the target block is equal to the right height of the lowest placeable point of the skyline, and whether the height of the target block is equal to the bottom width of the lowest placeable point of the skyline;
and accumulating a number of satisfied conditions, the fitness value being in direct proportion to the number of satisfied conditions.
For example, when all three conditions are satisfied, the fitness value is recorded as 3; when two conditions are met, the fitness value is recorded as 2; when a condition is met, recording the fitness value as 1; the fitness value is noted as 0 when none of the three conditions are met.
Preferably, the lower threshold Lh in step S1 is obtained as follows:
the lower bound Lh is obtained by the following formula:
wherein Lh = min { L1, L2};
wherein the acquisition formula of L1 is as follows:
wherein w i And h i Width and length, w, of the target block i, respectively d And h d The width and the length of the defect d are respectively, and W is the width of the roll profile;
the acquisition model for L2 is as follows:
min h; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (1);
wherein r is xi Is a variable from 0 to 1 and indicates whether the lower left corner of the target block i is on the x-th target block, and if so, r xi =1, otherwise r xi ＝0，D q Denotes the total length of the q-th column defect, h i Denotes the length of the target block i, h denotes the total length of the coil profile used, X 0 Representing a discrete set of points.
In the present invention, equation (1) represents minimizing the coil length, equation (2) constrains that all target blocks must be cut, equation (3) constrains that the total length of the patch covering the qth row length entry does not exceed the usable length of the strip, and equation (4) represents a variable of 0-1. L2 of the lower bound is relaxed linearly by solving the model, i.e. the decision variable r xi Relaxation is 0-r xi And (3) solving the linear value less than or equal to 1 to obtain a lower bound of the two-dimensional rectangular layout problem which can be closely attached with the defects.
Preferably, the cutting position discrete point subtraction algorithm in the step S2 is specifically as follows:
obtaining the size information of the target block and the position information of the defect in the coil section bar, and calculating to obtain the wide linear combination value N of the target block v (w); calculating a plurality of discrete point sets N which do not exceed the side length of the raw material by taking the right boundary of the defect as a reference v (x,y,w,h)；
Selecting an arbitrary positive integer t, wherein 0<t<W, respectively acquiring the calculation point sets on two sides of t
And a set of calculation points>
And a total set M w (t,x,y,w,h)，
Traversing all the t values, and finally selecting the total set M w (t, x, y, w, h) t with the least number of points;
wherein
N v (x,y,w,h)＝N v (w)∪{z|z＝x j +w d +v,j∈D,v∈N v (w),0≤z≤W}；
The minimum cut position discrete point set is:
M w (x,y,w,h)＝{M w (t,x,y,w,h)|t＝argmin{M w (t,x,y,w,h)}|}；
middle w i And h i Width and length, w, of the target block i, respectively d And h d Width and length of defect d, W and h are width and length of coil, x j And y j Respectively the abscissa and ordinate of the lower left corner of defect D, D defect set, I target block set, a i Is a variable from 0 to 1, z has no specific meaning, but is a symbol in the set;
|t＝argmin{M w (t, x, y, w, h) } denotes that M is caused to be M w And (t, x, y, w, h) the value of t with the minimum value.
The invention provides an algorithm, which is used for calculating a feasible point set of a cutting position of a plate with a defect, and applying the discrete point set to algorithm solution to reduce the search space of the algorithm. The main idea of the point reduction algorithm is to select a t, divide the space into two parts, and calculate the right boundary x of the zero point and the defect point on the left part of the t j +w j A combined value of target block widths (heights) not greater than t based on the right edge portion of t calculated with the raw material sheet right boundary point W and the defective point left boundary W j Is the combined value of the target block width (height) of the reference, which is not greater than t, and then both sets are stored in the cut discrete point set, as shown in fig. 4, the algorithm traverses all possible values of t, from which the value that minimizes the cut position discrete point set is selected.
Preferably, the one-dimensional continuous packing model in step S3 is specifically as follows:
wherein r is yi Is a variable of 0-1, which indicates whether the lower left corner of the target block i is on the y-th long target block, and if so, r yi =1, otherwise r yi ＝0，W q Indicates the usable width, Y, of the qth slice object block 0 Representing a set of discrete points of the y-axis vertical cut line, w i And h i Width and length, w, respectively, of the target block i d And h d Width and length, x, of defect d, respectively d And y d The abscissa and ordinate of the lower left corner coordinate of the defect d are respectively indicated.
The raw material sheet is horizontally cut into Lh (Lh = (1, 2, \8230;, y, \8230;, lh)) long strips of unit length, and an optimal solution for the utilization of each long strip is solved. By removing the x variable from the original problem, a one-dimensional continuous bin model can be obtained, and in the one-dimensional continuous bin model, formula (5) indicates that the total length of the patch covering the q-th row length entry does not exceed the available length of the strip, formula (6) constrains that all target patches must be cut, and formula (7) indicates that all the patch are larger than x d And is greater than W-x d The target block of (2) cannot cover the strip where the defect d is located.
Preferably, the check detection algorithm in step S4 is specifically as follows:
x i +(1-z ij )M≥x j +w j ,{i,j∈I|y i +w i ≥y i ∩y i +w i ≥y i formula (9);
x i +(1-z ij )M≥x d +w d ,{i∈I,d∈D|y i +w i ≥y d ∩y d +w d ≥y i formula (10);
0≤x i ≤W-w i -formula (11);
wherein M represents a significant number, z ij ∈{0，1}，z ij Is a variable of 0-1, indicating whether the target block i is to the right of the target block j, if z ij =1, otherwise z ij ＝0,x i Are defined variables.
Equation (9) for verifying that in the interval [ x ] j ，x j +w j ]Whether there is only one inner target block to ensure that the target blocks do not overlap, equation (10) is used to verify that there is an interval [ x ] d ,x d +w d ]Whether a target block exists in the defect block or not is determined, so that the target block is not overlapped with the defect. Equation (11) is used to define the variable x i The range of (1).
Preferably, the method for adjusting the one-dimensional continuous binning model in step S4 is to add a constraint condition to the one-dimensional continuous binning model, where the constraint condition is:
A two-dimensional belt defect layout system for coil sectional materials uses the two-dimensional belt defect layout method for the coil sectional materials, and comprises a boundary value acquisition module, a point set acquisition module, a model construction module and a judgment module;
the boundary value acquisition module is used for acquiring an optimal solution of two-dimensional rectangular layout in the coil section with the defects of the target block, wherein the optimal solution comprises an upper boundary value Uh and a lower boundary value Lh;
the point set acquisition module is used for calling a cutting position discrete point subtraction algorithm and searching a minimum cutting position discrete point set without losing a stock layout optimal solution;
the model building module is used for converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and building a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
the judging module is used for solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, a check detection algorithm is called to judge whether the solution meets the requirement of solving the two-dimensional rectangular layout problem, if so, the optimal solution Lh of the problem is output, and if not, the one-dimensional continuous boxing model is adjusted and the judging module is called again;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh + 1, and judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and calling the bound value acquisition module again, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and not to be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (9)
1. A two-dimensional strip defect layout method for coiled materials is characterized by comprising the following steps:
step S1: acquiring an optimal solution of a two-dimensional rectangular layout in a coil profile with defects of a target block, wherein the optimal solution comprises an upper bound value Uh and a lower bound value Lh;
step S2: calling a cutting position discrete point subtraction algorithm, and searching a minimum cutting position discrete point set without losing a stock layout optimal solution;
and step S3: converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and establishing a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
and step S4: solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, calling a check detection algorithm, judging whether the solution meets the requirement for solving the two-dimensional rectangular layout problem, if so, outputting the optimal solution Lh of the problem, if not, adjusting the one-dimensional continuous boxing model, and repeating the step S4;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh +1, and judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and repeating the step S1, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
2. The two-dimensional strip defect layout method for coil section bars according to claim 1, characterized in that the upper bound value Uh in the step S1 is obtained as follows:
step A1: sequencing the target blocks according to the sequence of the areas from large to small to obtain a target block set, and initializing skylines in the roll profiles with the defects;
step A2: searching the lowest placeable point of the skyline in the roll profile with the defects;
step A3: sequentially placing the target blocks into the lowest placeable point, respectively obtaining the fitness values of the target blocks, and placing the target block with the largest fitness value into the lowest placeable point;
step A4: and updating the target block set and searching for the lowest placeable point of the skyline in the roll profile with the defect again, and repeating the step A3 until all the target blocks in the target block set are placed in the roll profile with the defect.
3. The two-dimensional strip defect layout method for the coil section bar according to claim 2, wherein the manner of obtaining the fitness value of the target block in the step A3 is as follows:
respectively judging whether the height of the target block is equal to the left height of the lowest placeable point of the skyline, whether the height of the target block is equal to the right height of the lowest placeable point of the skyline, and whether the height of the target block is equal to the bottom width of the lowest placeable point of the skyline;
and accumulating the number of satisfied conditions, the fitness value being in direct proportion to the number of satisfied conditions.
4. The two-dimensional strip defect layout method for coil section bars according to claim 1, characterized in that the lower limit value Lh in the step S1 is obtained as follows:
the lower bound Lh is obtained by the following formula:
wherein Lh = min { L1, L2};
wherein the acquisition formula of L1 is as follows:
wherein w i And h i Width and length, w, of the target block i, respectively d And h d The width and the length of the defect d are respectively, and W is the width of the roll profile;
the acquisition model for L2 is as follows:
min h; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (1);
wherein r is xi Is a variable of 0 to 1 and representsWhether the lower left corner of the target block i is on the x-th target block, and if so, r xi =1, otherwise r xi ＝0，D q Denotes the total length of the q-th column defect, h i Denotes the length of the target block i, h denotes the total length of the coil used, X 0 Representing a discrete set of points.
5. The two-dimensional strip defect layout method for coil section bars according to claim 1, wherein the cutting position discrete point subtracting algorithm in the step S2 is specifically as follows:
obtaining the size information of the target block and the position information of the defect in the coil section bar, and calculating to obtain the wide linear combination value N of the target block v (w)；
Calculating a plurality of discrete point sets N which do not exceed the side length of the raw material by taking the right boundary of the defect as a reference v (x,y,w,h)；
Selecting an arbitrary positive integer t, wherein 0<t<W, respectively acquiring the calculation point sets on two sides of t
And the set of calculation points->
And a total set M w (t,x,y,w,h)，
Go through all t values and finally choose to make the total set M w (t, x, y, w, h) t with the least number of points;
wherein
N v (x,y,w,h)＝N v (w)∪{zz＝x j +w d +v,j∈D,v∈N v (w),0≤z≤W}；
The minimum cut position discrete point set is:
M w (x,y,w,h)＝{M w (t,x,y,w,h)t＝argmin{M w (t,x,y,w,h)}}；
middle w i And h i Width and length, w, of the target block i, respectively d And h d Width and length of defect d, W and h width and length of coil profile, x j And y j The left lower corner abscissa and ordinate of defect D, D defect set, I target block set, a i Is a variable from 0 to 1, z has no specific meaning but one symbol in the set;
t＝argmin{M w (t, x, y, w, h) } denotes that M is made w And (t, x, y, w, h) the value of t with the minimum value.
6. The two-dimensional strip defect layout method for coil section bars according to claim 1, wherein the one-dimensional continuous packing model in step S3 is as follows:
wherein r is yi Is a variable of 0-1, which indicates whether the lower left corner of the target block i is on the y-th long target block, and if so, r yi =1, otherwise r yi ＝0，W q Denotes the usable width of the q-th slice target block, Y 0 Representing a set of discrete points of a vertical cut line in the y-axis direction, w i And h i Width and length, w, of the target block i, respectively d And h d Width and length, x, of defect d, respectively d And y d The abscissa and ordinate of the lower left corner coordinate of the defect d are respectively indicated.
7. The two-dimensional strip defect layout method for coil section bars according to claim 1, wherein the check detection algorithm in step S4 is specifically as follows:
x i +(1-z ij )M≥x j +w j ,{i,j∈Iy i +w i ≥y i ∩y i +w i ≥y i -formula (9);
x i +(1-z ij )M≥x d +w d ,{i∈I,d∈Dy i +w i ≥y d ∩y d +w d ≥y i formula (10);
0≤x i ≤W-w i -formula (11);
wherein M represents a very large number, z ij ∈{0，1}，z ij Is a variable from 0 to 1, indicating whether the target block i is to the right of the target block j, if z ij =1, otherwise z ij ＝0,x i Are defined variables.
8. The method for two-dimensional strip defect layout facing roll section bar according to claim 1, wherein the method for adjusting the one-dimensional continuous packing model in step S4 is to add a constraint condition to the one-dimensional continuous packing model, wherein the constraint condition is:
9. A two-dimensional strip defect layout system for coil section bars, which uses the two-dimensional strip defect layout method for the coil section bars of any one of claims 1 to 8, is characterized by comprising a boundary value acquisition module, a point set acquisition module, a model construction module and a judgment module;
the threshold value acquisition module is used for acquiring an optimal solution of two-dimensional rectangular layout of a target block in a coil profile with defects, wherein the optimal solution comprises an upper threshold value Uh and a lower threshold value Lh;
the point set acquisition module is used for calling a cutting position discrete point subtraction algorithm and searching a minimum cutting position discrete point set without losing a stock layout optimal solution;
the model building module is used for converting the two-dimensional rectangular layout problem of the roll profile with the defects into the two-dimensional rectangular layout problem with the defects, the length of which is Lh and the width of which is W, loosening the two-dimensional rectangular layout problem into a one-dimensional continuous boxing problem, and building a one-dimensional continuous boxing model according to the one-dimensional continuous boxing problem and the discrete point set at the minimum cutting position;
the judging module is used for solving the one-dimensional continuous boxing model, if the one-dimensional continuous boxing model has a solution, a check detection algorithm is called to judge whether the solution meets the requirement for solving the two-dimensional rectangular layout problem, if so, the optimal solution Lh of the problem is output, and if not, the one-dimensional continuous boxing model is adjusted and the judging module is called again;
if the one-dimensional continuous boxing model has no solution, enabling Lh = Lh +1, judging whether the lower bound value Lh is smaller than the upper bound value Uh, if so, updating the lower bound value Lh and calling the bound value acquisition module again, and if so, outputting the lower bound value Lh as the solution of the two-dimensional rectangular layout.
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