CN115952892B - Branch iteration method and system for layout of plate with defects - Google Patents
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Abstract
A branch iteration method and system for a defective board stock layout, wherein the method comprises the following steps: setting a maximum corner limiting number K1, and storing initial arrangement states into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are orderly ordered downwards from big to small according to the upper value limit value of the arrangement states; acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2; acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper limit value of the arrangement state T2; the iterative solution algorithm based on the branches can accurately and rapidly solve the optimal solution of the layout with the defects, has definite evolution direction, and has the advantages of high evolution efficiency, high convergence speed and the like.
Description
Technical Field
The invention relates to the technical field of plate layout, in particular to a branch iteration method and a system for plate layout with defects.
Background
In the twenty-first century, as economy rapidly developed, the production scale of enterprises gradually increased, and more resources were consumed. The problem of the layout is closely related to daily life, and the effect of the layout directly influences the utilization rate of raw materials, and the environment is polluted while the waste is caused by insufficient utilization of resources. As a manufacturing country, a large amount of raw materials are required for manufacturing various products each year. Wherein a significant portion of the material needs to be cut, and the economic benefit is significant if the utilization of the material can be increased by one percentage.
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 type of problem is known as two-dimensional layout 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 in glass during processing, contaminated areas contained in steel, holes present in natural leather. Therefore, in the raw material cutting, it is necessary to avoid these regions and to make the utilization ratio of the raw material as large as possible. In addition, there are several constraints that need to be met, such as "one-shot" and "non-one-shot", whether the maximum number of goods is limited, whether the direction of the goods cut is rotatable, etc. Although the layouts in different industries have various limiting constraints, their common fundamental problem is to find an effective layout of the required components on the raw material, so that the area utilization of the planar area on the raw material is high, in order to save raw material as much as possible.
At present, the prior art is mainly aimed at defect-free layout problems, and the main methods can be divided into an accurate solving algorithm, an intelligent optimizing algorithm and a heuristic algorithm. However, the problem of coil profile layout with defects is rarely studied at present, and a heuristic algorithm and an intelligent optimization algorithm are mainly applied. 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 obtained feasible solution is unstable each time and cannot be judged whether to be the optimal solution or not. The intelligent optimization algorithm is generally 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 makes it possible to obtain a globally optimal solution to the optimization problem, and has gradually become a general, versatile method for optimizing problem solving, but this is at the cost of extremely lengthy annealing processes, i.e., problem solving processes, with low solving efficiency. The genetic algorithm has good global searching capability, but has the defects of long searching time, low evolution efficiency, low convergence speed and easiness in sinking into a 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 needed.
Disclosure of Invention
Aiming at the defects, the invention aims to provide a branch iteration method and a system for the layout of the plate with the defects so as to improve the convergence rate of an algorithm.
To achieve the purpose, the invention adopts the following technical scheme: a branch iteration method for a defective board stock layout comprises the following steps:
step S1: setting a maximum corner limiting number K1, and storing initial arrangement states into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are orderly ordered downwards from large to small according to the upper value limit value of the arrangement states;
step S2: acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper limit value of the arrangement state T2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
step S4: acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, calculating the value S1 of the complete state T2 if the value S1 is smaller than the current optimal value S2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the corner of the arrangement state T1, repeating the steps S2-S4 until the corner of the arrangement state T1 is traversed, changing the next arrangement state T1 of the arrangement queue Q, and repeating the steps S2-S5 until all the arrangement states in the arrangement queue Q are traversed;
step S6: and adding one to the maximum corner limiting quantity K1, updating the arrangement state T2 in the arrangement queue Q into the arrangement state T1, and repeating the steps S2-S6 until all target blocks are put in, and obtaining the arrangement scheme with the highest value upper limit value as a final arrangement scheme.
Preferably, the value upper limit value is obtained by the following method:
dividing the arrangement state into a target block area and a free area, obtaining the sum of the value of the target block in the target block area and the upper value limit of the target block capable of being arranged in the free area as the upper value limit value,
the value upper bound acquisition formula of the target block capable of being arranged in the idle area is as follows:
S lub ＝min{u(P)，u(V)，u(H)}；
the acquisition process of u (P) is to relax the value of the arrangeable target blocks in the idle area into an optimal value for calculating the knapsack problem, wherein the calculation formula of u (P) is as follows:
wherein z is i Representing the number of target blocks, z i ∈{0，1，2····，n}，v i Representing the value of the target block, w i And h i The width and length of the target block, respectively, DL represents the defect set, w in the free area d And h d The width and length of the defect, SL representing the area of the free area;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (V);
the acquisition formula of u (V) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, h is the available length of the strip, w i And h i The width and the length of the target block are respectively;
the acquisition process of u (H) is to horizontally divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (H);
the acquisition formula of u (H) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, w is the available width of the stripe, w i And h i The width and length of the target block, respectively.
The branch iteration system with the defective board stock layout uses the branch iteration method with the defective board stock layout, and comprises a setting module, an updating module, a selecting module, a comparing module, a first circulating module and a second circulating module;
the setting module is used for setting the maximum corner limiting quantity K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
the selection module is used for acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, discarding the arrangement state T2 if the maximum corner limit number K1 is smaller than the corner number K2, and calculating the value upper limit value of the arrangement state T2 if the maximum corner limit number K1 is larger than or equal to the corner limit number K2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
the comparison module is used for acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, wherein the complete state is a state that all the corner points cannot be placed into a target block, calculating the value S1 of the complete state T2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 of the complete state T2 as the current optimal value S2;
the first circulation module is used for replacing the corner points of the arrangement state T1, and recalling the updating module, the selecting module and the comparing module until the corner points of the arrangement state T1 are all traversed, replacing the next arrangement state T1 of the arrangement queue Q, recalling the updating module, the selecting module and the comparing module until all the arrangement states in the arrangement queue Q are traversed, and recalling the second circulation module;
the second circulation module is used for adding one to the maximum corner limiting number K1, updating the arrangement state T2 in the arrangement queue Q into the arrangement state T1, and repeating the step of updating the module, the selecting module, the comparing module and the first circulation module until all target blocks are put in, so that the arrangement scheme with the highest value upper limit value is obtained as the final arrangement scheme.
Preferably, the system further comprises a value upper limit value calculation module;
the value upper limit value calculation module is used for dividing the arrangement state into a target block area and an idle area, and obtaining the sum of the value of the target block in the target block area and the value upper limit of the target block capable of being arranged in the idle area as the value upper limit value.
One of the above technical solutions has the following advantages or beneficial effects: the iterative solution algorithm based on the branches can accurately and rapidly solve the optimal solution of the layout with the defects, has definite evolution direction, and has the advantages of high evolution efficiency, high convergence speed and the like. The method can easily design a visual interface of operation and provides an efficient guiding scheme for enterprise production.
Drawings
FIG. 1 is a flow chart of one embodiment of the method of the present invention;
FIG. 2 is a schematic diagram of one embodiment of a system of the present invention;
FIG. 3 is a schematic illustration of an initial arrangement in one embodiment of the invention;
FIG. 4 is a schematic diagram of a different arrangement T2 according to an embodiment of the invention;
FIG. 5 is a schematic diagram of different arrangement states generated by the accelerated arrangement process of the target blocks in FIG. 4A;
fig. 6 is a schematic diagram of a different placement order arrangement T2 in an embodiment of the invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.
In the description of embodiments of the present invention, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more of the described features. In the description of the embodiments of the present invention, the meaning of "plurality" is two or more, unless explicitly defined otherwise.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
As shown in fig. 1 to 6, a branching iteration method for a defective sheet stock, comprising the steps of:
step S1: setting a maximum corner limiting number K1, and storing initial arrangement states into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are orderly ordered downwards from large to small according to the upper value limit value of the arrangement states;
when the initial arrangement state only has one corner (i.e. no target block is placed), if the shape of the target block is rectangular, the maximum corner limit number K1 is 3, and when the initial arrangement state has two corners, the maximum corner limit number K1 is 4, i.e. in the cutting of the target block of the rectangular, the maximum corner limit number K can be the number of the corners of the initial arrangement state plus 2, but the specific maximum corner limit number K still needs to be set according to the shape of the specific target block.
Step S2: acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper limit value of the arrangement state T2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
since the positions of the corner points are random when the target block is placed, the different arrangement states T1 are changed to the same arrangement state T2 after the target block is placed, and the numbers in the target block indicate the placement order as shown in fig. 6. In order to avoid that the repeated arrangement state T2 remains in the arrangement queue Q, repeated calculation is performed, and the overall operation speed is affected. Therefore, before the arrangement state T2 is reserved, it is further necessary to determine whether the arrangement state T2 is repeated with the arrangement state reserved in the arrangement queue Q.
Step S4: acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, calculating the value S1 of the complete state T2 if the value S1 is smaller than the current optimal value S2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the corner of the arrangement state T1, repeating the steps S2-S4 until the corner of the arrangement state T1 is traversed, changing the next arrangement state T1 of the arrangement queue Q, and repeating the steps S2-S5 until all the arrangement states in the arrangement queue Q are traversed;
step S6: and adding one to the maximum corner limiting quantity K1, updating the arrangement state T2 in the arrangement queue Q into the arrangement state T1, and repeating the steps S2-S6 until all target blocks are put in, and obtaining the arrangement scheme with the highest value upper limit value as a final arrangement scheme.
The beneficial effects are that: the target block is in the shape of an object to be cut, and the left end point of each horizontal line segment of the ladder line is called a corner point.
In one embodiment, as shown in fig. 3, the black point 1 corner point is set according to an initial arrangement state when the maximum corner limiting number K1 is set, for example, when the target block is not placed in the initial arrangement state, and the maximum corner limiting number K1 is set to 3.
Then, starting iterative processing, wherein no target block is placed in the initial arrangement state, only one arrangement state is in the arrangement queue Q at this time, and no ordering of the value upper limit value is required, the initial arrangement state is used as the arrangement state T1, the target blocks are sequentially placed in any corner of the arrangement state T1, the obtained arrangement state T2 is updated, for example, three target blocks are needed to be cut in one embodiment, at this time, the three target blocks are placed in the origin, three arrangement states T2 are obtained, at this time, three arrangement states T2 are obtained respectively, and the number K2 of corners of the arrangement state T2 is 2, at this time, the number K2 of corners is smaller than the maximum corner limit number K1, and the value upper limit values of the three arrangement states T2 are calculated respectively. Since the target block is not placed in the arrangement state T1, the current optimal value upper bound value is 0 at this time, all three arrangement states T2 can be reserved, and then the values S1 of the three arrangement states T2 are calculated again, wherein the calculation of the values depends on the target block and is determined together with the importance (determined together by multiple aspects such as sales price and production period) and the area of the target block in production. When the importance of the target blocks is consistent, the larger the area of the target block is, the higher the value thereof is. And the current optimal value S2 is 0 at the moment because the target block is not put in the initial arrangement state. If the importance of all the target blocks is consistent in the embodiment, the three arrangement states T2 are all accelerated by using a greedy heuristic algorithm to obtain three complete states T2, wherein the complete states T2 also need to satisfy the limitation that the number of corner points K2 is smaller than the maximum number of corner points K1, as shown in fig. 5, after the first arrangement state T2 is accelerated, 4 states are obtained, but all the 4 states do not meet the requirement of the corner point limitation, and all the 4 states need to be discarded, so the complete state T2 of the first arrangement state T2 is the original state. The other two arrangement states T2 are all similarly to obtain the corresponding complete state T2. At this time, since the importance of the target blocks is consistent, the area of the target block a in the first full state T2 is the largest, and the value S1 of the target block is updated to the current optimal value S2. Then step S5 is performed, and since there is only one corner in the initial arrangement state in this embodiment, the corner has been traversed in step S5. Then, the next arrangement state T1 of the queue Q is further arranged, and only 1 initial arrangement state is needed, so that the next arrangement state T1 does not need to be replaced, then step S6 is executed, and at this time, the maximum corner limiting number K1 is added with 1, the maximum corner limiting number K1 is 4, and steps S2 to S6 are executed here until all the target blocks are put in. At this time, a plurality of arrangement schemes are obtained, and the arrangement scheme with the highest value upper limit value is calculated in the arrangement schemes to be used as the final arrangement scheme.
The iterative solution algorithm based on the branches can accurately and rapidly solve the optimal solution of the layout with the defects, has definite evolution direction, and has the advantages of high evolution efficiency, high convergence speed and the like. The method can easily design a visual interface of operation and provides an efficient guiding scheme for enterprise production.
Preferably, the value upper limit value is obtained by the following method:
dividing the arrangement state into a target block area and a free area, obtaining the sum of the value of the target block in the target block area and the upper value limit of the target block capable of being arranged in the free area as the upper value limit value,
the value upper bound acquisition formula of the target block capable of being arranged in the idle area is as follows:
S lub ＝min{u(P)，u(V)，u(H)}；
the acquisition process of u (P) is to relax the value of the arrangeable target blocks in the idle area into an optimal value for calculating the knapsack problem, wherein the calculation formula of u (P) is as follows:
wherein z is i Representing the number of target blocks, z i ∈{0，1，2····，n}，v i Representing the value of the target block, w i And h i The width and length of the target block, respectively, DL represents the defect set, w in the free area d And h d The width and length of the defect, SL representing the area of the free area;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (V);
the acquisition formula of u (V) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, h is the available length of the strip, w i And h i The width and the length of the target block are respectively;
the acquisition process of u (H) is to horizontally divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (H);
the acquisition formula of u (H) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, w is the available width of the stripe, w i And h i The width and length of the target block, respectively.
The calculation using length h is specifically equal to the length of the strip minus the length of the defect on the strip.
In the invention, the arrangement state is divided into a target block area and an idle area based on the arrangement strategy of the step line. The value upper bound value is calculated together with the value of the target block area (the comprehensive area of the target block) and the value upper bound value of the target block capable of being arranged in the idle area, and meanwhile, in order to calculate the value upper bound value of the target block capable of being arranged in the idle area, the method for calculating the value upper bound value of the target block capable of being arranged in the idle area is provided, and then the minimum value in the three values is selected as the value upper bound value of the target block capable of being arranged in the idle area. Wherein the formula (2) is used to restrict the total area available for arrangement to be smaller than the available area of the free area.
The branch iteration system with the defective board stock layout uses the branch iteration method with the defective board stock layout, and comprises a setting module, an updating module, a selecting module, a comparing module, a first circulating module and a second circulating module;
the setting module is used for setting the maximum corner limiting quantity K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
the selection module is used for acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, discarding the arrangement state T2 if the maximum corner limit number K1 is smaller than the corner number K2, and calculating the value upper limit value of the arrangement state T2 if the maximum corner limit number K1 is larger than or equal to the corner limit number K2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
the comparison module is used for acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, wherein the complete state is a state that all the corner points cannot be placed into a target block, calculating the value S1 of the complete state T2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 of the complete state T2 as the current optimal value S2;
the first circulation module is used for replacing the corner points of the arrangement state T1, and recalling the updating module, the selecting module and the comparing module until the corner points of the arrangement state T1 are all traversed, replacing the next arrangement state T1 of the arrangement queue Q, recalling the updating module, the selecting module and the comparing module until all the arrangement states in the arrangement queue Q are traversed, and recalling the second circulation module;
the second circulation module is used for adding one to the maximum corner limiting number K1, updating the arrangement state T2 in the arrangement queue Q into the arrangement state T1, and repeating the step of updating the module, the selecting module, the comparing module and the first circulation module until all target blocks are put in, so that the arrangement scheme with the highest value upper limit value is obtained as the final arrangement scheme.
Preferably, the system further comprises a value upper limit value calculation module;
the value upper limit value calculation module is used for dividing the arrangement state into a target block area and an idle area, and obtaining the sum of the value of the target block in the target block area and the value upper limit of the target block capable of being arranged in the idle area as the value upper limit value.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means 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, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations of the above embodiments may be made by those of ordinary skill in the art within the scope of the invention.
Claims (3)
1. The branching iteration method for the defective board stock is characterized by comprising the following steps of:
step S1: setting a maximum corner limiting number K1, and storing initial arrangement states into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are orderly ordered downwards from large to small according to the upper value limit value of the arrangement states;
step S2: acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper limit value of the arrangement state T2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
step S4: acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, calculating the value S1 of the complete state T2 if the value S1 is smaller than the current optimal value S2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the corner of the arrangement state T1, repeating the steps S2-S4 until the corner of the arrangement state T1 is traversed, changing the next arrangement state T1 of the arrangement queue Q, and repeating the steps S2-S5 until all the arrangement states in the arrangement queue Q are traversed;
step S6: adding one to the maximum corner limiting number K1, updating the arrangement state T2 in the arrangement queue Q to be the arrangement state T1, and repeating the steps S2-S6 until all target blocks are put in, and obtaining an arrangement scheme with the highest value upper limit value as a final arrangement scheme;
the method for acquiring the value upper bound value comprises the following steps:
dividing the arrangement state into a target block area and a free area, obtaining the sum of the value of the target block in the target block area and the upper value limit of the target block capable of being arranged in the free area as the upper value limit value,
the value upper bound acquisition formula of the target block capable of being arranged in the idle area is as follows:
S lub ＝min{u(P)，u(V)，u(H)}；
the acquisition process of u (P) is to relax the value of the arrangeable target blocks in the idle area into an optimal value for calculating the knapsack problem, wherein the calculation formula of u (P) is as follows:
wherein z is i Representing the number of target blocks, z i ∈{0，1，2…·，n}，v i Representing the value of the target block, w i And h i The width and length of the target block, respectively, DL represents the defect set, w in the free area d And h d The width and length of the defect, SL representing the area of the free area;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (V);
the acquisition formula of u (V) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, h is the available length of the strip, w i And h i The width and the length of the target block are respectively;
the acquisition process of u (H) is to horizontally divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (H);
the acquisition formula of u (H) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing target blocksW is the available width of the strip, w i And h i The width and length of the target block, respectively.
2. A branch iteration system with defective board stock, which uses the branch iteration method with defective board stock of claim 1, and is characterized by comprising a setting module, an updating module, a selecting module, a comparing module, a first circulating module and a second circulating module;
the setting module is used for setting the maximum corner limiting quantity K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring an arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut into a certain corner under the arrangement state T1, and updating the obtained arrangement state T2;
the selection module is used for acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is larger than the corner number K2, discarding the arrangement state T2 if the maximum corner limit number K1 is smaller than the corner number K2, and calculating the value upper limit value of the arrangement state T2 if the maximum corner limit number K1 is larger than or equal to the corner limit number K2;
judging whether the upper value limit value of the arrangement state T2 is larger than the current optimal value limit value, if not, discarding the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q are repeated, if so, discarding the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
the comparison module is used for acquiring the value S1 of all the arrangement states T2 in the arrangement queue Q, comparing the value S1 with the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2 if the value S1 is larger than the current optimal value S2, wherein the complete state is a state that all the corner points cannot be placed into a target block, calculating the value S1 of the complete state T2, and discarding the arrangement states T2 if the value S1 is smaller than the current optimal value S2;
updating the highest value S1 of the complete state T2 as the current optimal value S2;
the first circulation module is used for replacing the corner points of the arrangement state T1, and recalling the updating module, the selecting module and the comparing module until the corner points of the arrangement state T1 are all traversed, replacing the next arrangement state T1 of the arrangement queue Q, recalling the updating module, the selecting module and the comparing module until all the arrangement states in the arrangement queue Q are traversed, and recalling the second circulation module;
the second circulation module is used for adding one to the maximum corner limiting number K1, updating the arrangement state T2 in the arrangement queue Q into the arrangement state T1, and repeating the steps of the updating module, the selecting module, the comparing module and the first circulation module until all target blocks are put in, so as to obtain an arrangement scheme with the highest value upper limit value as a final arrangement scheme;
the method for acquiring the value upper bound value comprises the following steps:
dividing the arrangement state into a target block area and a free area, obtaining the sum of the value of the target block in the target block area and the upper value limit of the target block capable of being arranged in the free area as the upper value limit value,
the value upper bound acquisition formula of the target block capable of being arranged in the idle area is as follows:
S lub ＝min{u(P)，u(V)，u(H)}；
the acquisition process of u (P) is to relax the value of the arrangeable target blocks in the idle area into an optimal value for calculating the knapsack problem, wherein the calculation formula of u (P) is as follows:
wherein z is i Representing the number of target blocks, z i ∈{0，1，2…·，n}，v i Representing the value of the target block, w i And h i The width and length of the target block, respectively, and DL represents the free areaDefect collection in domain, w d And h d The width and length of the defect, SL representing the area of the free area;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (V);
the acquisition formula of u (V) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, h is the available length of the strip, w i And h i The width and the length of the target block are respectively;
the acquisition process of u (H) is to horizontally divide the idle area into m long strips with unit widths, and accumulate the sum of the maximum value of each long strip as u (H);
the acquisition formula of u (H) is as follows:
wherein the method comprises the steps ofz i Representing the number of target blocks, v i Representing the value of the target block, w is the available width of the stripe, w i And h i The width and length of the target block, respectively.
3. The branching iteration system for defective board stock according to claim 2, further comprising an upper value limit calculation module;
the value upper limit value calculation module is used for dividing the arrangement state into a target block area and an idle area, and obtaining the sum of the value of the target block in the target block area and the value upper limit of the target block capable of being arranged in the idle area as the value upper limit value.
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