CN115952892A - Branch iteration method and system for defective plate stock layout - Google Patents
Branch iteration method and system for defective plate stock layout Download PDFInfo
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Abstract
A branch iteration method and a branch iteration system for stock layout of plates with defects are disclosed, wherein the method comprises the following steps: setting a maximum corner limit number K1, and storing an initial arrangement state into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are sequentially sorted downwards from large to small according to the value upper bound of the arrangement states; acquiring an arrangement state T1 of the top layer in an arrangement queue Q, sequentially putting target blocks to be cut at a certain angular point 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 greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2; the invention is based on the iterative solution algorithm of the branch, the algorithm can solve the optimal solution of the defected layout accurately and rapidly, and the evolution direction is clear, and the invention has the advantages of 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 branch iteration method and a branch iteration system for defective plate stock layout.
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 material into different types of parts for manufacturing production. Such as the cutting of wooden boards and glass, this problem is known as the two-dimensional layout optimization problem. 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 layout of defective roll profiles, 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 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 the 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
Aiming at the defects, the invention aims to provide a branch iteration method and a branch iteration system for stock layout of plates with the defects so as to improve the convergence speed of an algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme: a branch iteration method for defective plate stock layout comprises the following steps:
step S1: setting a maximum corner limit number K1, and storing an initial arrangement state into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are sequentially sorted downwards from large to small according to the value upper bound of the arrangement states;
step S2: acquiring an arrangement state T1 of the top layer in an arrangement queue Q, sequentially putting target blocks to be cut at a certain angular point under the arrangement state T1, and updating the obtained arrangement state T2;
and step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the upper value threshold of the arrangement state T2 is greater than the current best upper value threshold, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
and step S4: obtaining values S1 of all arrangement states T2 in an arrangement queue Q, comparing the values with the current optimal value S2, if the values are larger than the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and if the values are smaller than the current optimal value S2, discarding the arrangement states T2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the angular points of the arrangement state T1, repeating the steps S2-S4 until all the angular points of the arrangement state T1 are 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 limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps S2-S6 until all the target blocks are put in, and acquiring the arrangement scheme with the highest value upper bound as the final arrangement scheme.
Preferably, the value upper bound value is obtained by the following method:
dividing the arrangement state into a target block area and an idle area, acquiring the sum of the value of a target block in the target block area and the upper value bound of the target block in the idle area as the upper value bound,
the value upper bound obtaining formula of the target blocks capable of being distributed in the free area is as follows:
S lub ＝min{u(P),u(V),u(H)}；
and the u (P) is obtained by relaxing the value of the target blocks capable of being distributed in the free 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 Width and length of the target block, DL representing defect set in free area, w d And h d The width and length of the defect, SL represents the area of the free region;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (V);
the acquisition formula of u (V) is as follows:
wherein
z i Representing the number of target blocks, v i Represents the value of the target block, h is the available length of the stripe, w i And h i The width and length of the target block respectively;
the acquisition process of u (H) is to horizontally divide the free area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (H);
the formula for u (H) is obtained as follows:
wherein
z i Representing the number of target blocks, v i Representing the value of the target block, w being the available width of the bar, w i And h i Respectively the width and length of the target block.
A branch iteration system for layout of a plate with a defect uses the branch iteration method for layout of the plate with the defect, and comprises a setting module, an updating module, a selecting module, a comparing module, a first circulation module and a second circulation module;
the setting module is used for setting the maximum corner limit number K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring the arrangement state T1 of the top layer in the arrangement queue Q, under the arrangement state T1, target blocks needing to be cut are sequentially placed at a certain angular point, and the obtained arrangement state T2 is updated;
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 greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the upper value threshold of the arrangement state T2 is greater than the current best upper value threshold, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning 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 values S1 of all the arrangement states T2 in the arrangement queue Q, comparing the values with the current optimal value S2, calling a greedy heuristic algorithm if the values are larger than the current optimal value S2, accelerating the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and discarding the arrangement states T2 if the values are 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 angular points of the arrangement state T1, and calling the updating module, the selecting module and the comparing module again until the angular points of the arrangement state T1 are traversed, replacing the next arrangement state T1 of the arrangement queue Q, calling the updating module, the selecting module and the comparing module again until all the arrangement states in the arrangement queue Q are traversed, and calling the second circulation module;
the second circulation module is used for adding one to the maximum corner limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps of the updating module, the selecting module, the comparing module and the first circulation module until all the target blocks are put in, and acquiring the arrangement scheme with the highest value as the final arrangement scheme.
Preferably, the system also comprises a value upper bound value calculation module;
the value upper bound value calculation module is used for dividing the distribution state into a target block area and an idle area, and acquiring the sum of the value of the target block in the target block area and the value upper bound of the target block capable of being distributed in the idle area as the value upper bound value.
One of the above technical solutions has the following advantages or beneficial effects: the invention is based on the iterative solution algorithm of the branch, the algorithm can solve the optimal solution of the defected layout accurately and rapidly, and the evolution direction is clear, and the invention has the advantages of high evolution efficiency, high convergence rate and the like. The method can easily design the visual interface of the operation and provide an efficient guidance 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 block diagram of one embodiment of the system of the present invention;
FIG. 3 is a schematic diagram of an initial state of alignment in one embodiment of the present invention;
FIG. 4 is a schematic diagram of a different arrangement state T2 in one embodiment of the present invention;
FIG. 5 is a schematic diagram of different tiling states resulting from the accelerated tiling of the A target blocks of FIG. 4;
fig. 6 is a schematic diagram of different placement order arrangement states T2 in one embodiment of the 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 or similar reference numerals refer to the same or similar elements or elements having the same or similar function 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" and "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 specific cases to those skilled in the art.
As shown in fig. 1 to 6, a branch iteration method for stock layout of a defective plate includes the following steps:
step S1: setting a maximum corner limit number K1, and storing an initial arrangement state into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are sequentially sorted downwards from large to small according to the value upper bound of the arrangement states;
the maximum corner limit number K1 is associated with the initial arrangement state, when only one corner exists in the initial arrangement state (i.e., no target block is placed), if the target block is rectangular, the maximum corner limit number K1 is 3, and when two corners exist in the initial arrangement state, the maximum corner limit number K1 is 4, that is, in cutting the rectangular target block, the maximum corner limit number K may be 2 added to the number of corners in the initial arrangement state, 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 an arrangement queue Q, sequentially putting target blocks to be cut at a certain angular point under the arrangement state T1, and updating the obtained arrangement state T2;
and step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limiting number K1 is greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the upper value threshold of the arrangement state T2 is greater than the current best upper value threshold, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning 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 put in, the different arrangement state T1 is changed to the same arrangement state T2 after the target block is put in, as shown in fig. 6, the numbers in the target block indicate the order of putting in. In order to avoid that the repeated arrangement state T2 remains in the arrangement queue Q, repeated calculation is performed, which affects the overall calculation speed. It is necessary to further determine whether or not the state T2 is duplicated with the state held in the queue Q before the state T2 is held.
And step S4: obtaining values S1 of all arrangement states T2 in an arrangement queue Q, comparing the values with the current optimal value S2, if the values are larger than the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and if the values are smaller than the current optimal value S2, discarding the arrangement states T2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the angular points of the arrangement state T1, repeating the steps S2-S4 until all the angular points of the arrangement state T1 are 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 limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps S2-S6 until all the target blocks are put in, and acquiring the arrangement scheme with the highest value upper bound as the final arrangement scheme.
Has the beneficial effects 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 stepped line is called an angular point.
In one embodiment, the black point 1 corner point shown in fig. 3 is set according to an initial arrangement state when the maximum corner point limit number K1 is set, for example, the target block is not put in the initial arrangement state, and the maximum corner point limit number K1 is set to 3.
Then, iteration processing is started, because no target block is placed in the initial arrangement state, only one arrangement state is in the arrangement queue Q at this time, and sequencing of upper value limit values is not needed, the initial arrangement state is used as the arrangement state T1, target blocks are sequentially placed at any corner of the arrangement state T1, and the obtained arrangement state T2 is updated, for example, in one embodiment, three target blocks need to be cut, at this time, three target blocks are placed at the origin respectively, three arrangement states T2 are obtained, as shown in fig. 4, at this time, three arrangement states T2 are obtained respectively, and the number of corners K2 obtaining the arrangement state T2 is 2, at this time, the number of corners K2 is smaller than the maximum limit number of corners K1, and the upper value 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 upper bound value of the optimal value is 0, so that all three arrangement states T2 can be retained, 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 by multiple aspects such as sale price, production deadline, and the like) and the area of the target block in production. When the importance of the target block is uniform, the larger the area of the target block is, the higher the value thereof is. Since the target block is not placed in the initial arrangement state in the current optimum value S2, the current optimum value S2 is 0 at this time. If the importance of all the target blocks is consistent in this embodiment, the three arrangement states T2 are accelerated by using a greedy heuristic algorithm to obtain three complete states T2, where 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 point limits K1, as shown in fig. 5, after the first arrangement state T2 is accelerated, 4 states are obtained, but the 4 states do not meet the requirement of the corner point limits, and all need to be discarded, so the complete state T2 of the first arrangement state T2 is the original state. The other two routing states T2 are analogized to obtain the corresponding full state T2. At this time, since the importance of the target block is uniform, the area of the target block a is maximized in the first complete state T2, and the value S1 of the target block is updated to the current optimum value S2. Then step S5 is executed, since there is only one corner point in the initial arrangement state in this embodiment, the corner points in step S5 have been traversed. Then, the next arrangement state T1 of the arrangement queue Q is further changed, and at this time, only 1 initial arrangement state is needed, so that the next arrangement state T1 does not need to be changed, then step S6 is executed, at this time, the maximum corner point limit number K1 is added by 1, the maximum corner point limit number K1 is 4, and steps S2 to S6 are executed here until all target blocks are put in. And obtaining a plurality of arrangement schemes, and calculating the arrangement scheme with the highest value as a final arrangement scheme in the arrangement schemes.
The invention is based on the iterative solution algorithm of the branch, the algorithm can solve the optimal solution of the defected layout accurately and rapidly, and the evolution direction is clear, and the invention has the advantages of high evolution efficiency, high convergence rate and the like. The method can easily design the visual interface of the operation and provide an efficient guidance scheme for enterprise production.
Preferably, the value upper bound value is obtained by the following method:
dividing the arrangement state into a target block area and an idle area, acquiring the sum of the value of a target block in the target block area and the upper value bound of the target block in the idle area as the upper value bound,
the value upper bound obtaining formula of the target blocks capable of being distributed in the free area is as follows:
S lub ＝min{u(P),u(V),u(H)}；
and the u (P) is obtained by relaxing the value of the target blocks capable of being distributed in the free 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 Respectively the width and length of the target block, DL representing the defect set in the free area, w d And h d The width and length of the defect, SL represents the area of the free region;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (V);
the formula for u (V) is obtained as follows:
wherein
z i Representing the number of target blocks, v i Representing the value of the target block, h being the usable length of the bar, w i And h i The width and length of the target block respectively;
the acquisition process of u (H) is to horizontally divide the free area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (H);
the formula for u (H) is obtained as follows:
wherein
z i Representing the number of target blocks, v i Representing the value of the target block, w being the available width of the stripe, w i And h i The width and length of the target block, respectively.
The calculation using the length h is specifically equal to the length of the strip minus the length of the defect on the strip.
In the invention, the algorithm is based on the step line placement strategy, and the arrangement state is divided into a target block area and an idle area. The value upper bound value is equal to the value of a target block area (which can be the comprehensive area of the target block) and the value upper bound of the target blocks in the free area, and in order to calculate the value upper bound of the target blocks in the free area, the invention is provided with three methods for calculating the value upper bound of the target blocks in the free area, and then the minimum value of the three is selected as the value upper bound of the target blocks in the free area. Wherein the formula (2) is used to constrain the total arrangeable area to be smaller than the available area of the free area.
A branch iteration system for stock layout of plates with defects is used, and comprises a setting module, an updating module, a selecting module, a comparing module, a first cycle module and a second cycle module;
the setting module is used for setting the maximum corner limit number K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring the arrangement state T1 of the top layer in the arrangement queue Q, sequentially placing target blocks to be cut at a certain angular point 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 greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the value upper bound of the arrangement state T2 is greater than the current optimal value upper bound, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning 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 values S1 of all the arrangement states T2 in the arrangement queue Q, comparing the values with the current optimal value S2, calling a greedy heuristic algorithm if the values are larger than the current optimal value S2, accelerating the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and discarding the arrangement states T2 if the values are 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 angular points of the arrangement state T1, and calling the updating module, the selecting module and the comparing module again until the angular points of the arrangement state T1 are traversed, replacing the next arrangement state T1 of the arrangement queue Q, calling the updating module, the selecting module and the comparing module again until all the arrangement states in the arrangement queue Q are traversed, and calling the second circulation module;
the second circulation module is used for adding one to the maximum corner limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps of the updating module, the selecting module, the comparing module and the first circulation module until all the target blocks are put in, and acquiring the arrangement scheme with the highest value as the final arrangement scheme.
Preferably, the system also comprises a value upper bound value calculation module;
the value upper bound value calculation module is used for dividing the arrangement state into a target block area and an idle area, and acquiring the sum of the value of a target block in the target block area and the value upper bound of the target block in the idle area as the value upper bound value.
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 (4)
1. A branch iteration method for stock layout of plates with defects is characterized by comprising the following steps:
step S1: setting a maximum corner limit number K1, and storing an initial arrangement state into an arrangement queue Q, wherein the arrangement states in the arrangement queue Q are sequentially sorted downwards from large to small according to the value upper bound of the arrangement states;
step S2: acquiring an arrangement state T1 of the top layer in an arrangement queue Q, sequentially putting target blocks to be cut at a certain angular point under the arrangement state T1, and updating the obtained arrangement state T2;
and step S3: acquiring the corner number K2 of the arrangement state T2, judging whether the maximum corner limit number K1 is greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the upper value threshold of the arrangement state T2 is greater than the current best upper value threshold, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning the arrangement state T2, and if not, keeping the arrangement state T2 in the arrangement queue Q;
and step S4: obtaining values S1 of all arrangement states T2 in an arrangement queue Q, comparing the values with the current optimal value S2, if the values are larger than the current optimal value S2, calling a greedy heuristic algorithm to accelerate the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and if the values are smaller than the current optimal value S2, discarding the arrangement states T2;
updating the highest value S1 in the complete state T2 as the current optimal value S2;
step S5: changing the angular points of the arrangement state T1, repeating the steps S2-S4 until all the angular points of the arrangement state T1 are 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 limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps S2-S6 until all the target blocks are put in, and acquiring the arrangement scheme with the highest value upper bound as the final arrangement scheme.
2. The branched iterative method for stock layout of plates with defects according to claim 1, wherein the value upper bound value is obtained by the following method:
dividing the arrangement state into a target block area and an idle area, acquiring the sum of the value of a target block in the target block area and the upper value bound of the target block in the idle area as the upper value bound,
the value upper bound obtaining formula of the target blocks capable of being distributed in the free area is as follows:
S lub ＝min{u(P),u(V),u(H)}；
and the u (P) is obtained by relaxing the value of the target blocks capable of being distributed in the free 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 Width and length of the target block, DL representing defect set in free area, w d And h d The width and length of the defect, SL represents the area of the free region;
the acquisition process of u (V) is to vertically divide the idle area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (V);
the formula for u (V) is obtained as follows:
wherein
z i Representing the number of target blocks, v i Representing the value of the target block, h being the usable length of the bar, w i And h i The width and length of the target block respectively;
the acquisition process of u (H) is to horizontally divide the free area into m long strips with unit width, and the sum of the maximum value of each long strip is accumulated to be used as u (H);
the formula for u (H) is obtained as follows:
wherein
z i Representing the number of target blocks, v i Representing the value of the target block, w being the available width of the bar, w i And h i The width and length of the target block, respectively.
3. A branch iteration system for stock layout of a defective plate, which uses the branch iteration method for stock layout of a defective plate according to any one of claims 1-2, is characterized by comprising a setting module, an updating module, a selecting module, a comparing module, a first circulation module and a second circulation module;
the setting module is used for setting the maximum corner limit number K1 and storing the initial arrangement state into an arrangement queue Q;
the updating module is used for acquiring the arrangement state T1 of the top layer in the arrangement queue Q, under the arrangement state T1, target blocks needing to be cut are sequentially placed at a certain angular point, and the obtained arrangement state T2 is updated;
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 greater than the corner number K2, if so, discarding the arrangement state T2, and if so, calculating the value upper bound of the arrangement state T2;
judging whether the upper value threshold of the arrangement state T2 is greater than the current best upper value threshold, if not, abandoning the arrangement state T2, if so, judging whether the arrangement state T2 and other arrangement states T2 in the arrangement queue Q have repetition, if so, abandoning 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 values S1 of all the arrangement states T2 in the arrangement queue Q, comparing the values with the current optimal value S2, calling a greedy heuristic algorithm if the values are larger than the current optimal value S2, accelerating the arrangement states T2 to a complete state T2, wherein the complete state is a state that all corner points cannot be put into a target block, calculating the values S1 of the complete state T2, and discarding the arrangement states T2 if the values are smaller than the current optimal value S2;
updating the value S1 with the highest complete state T2 as the current optimal value S2;
the first circulation module is used for replacing the angular points of the arrangement state T1, and calling the updating module, the selecting module and the comparing module again until the angular points of the arrangement state T1 are traversed, replacing the next arrangement state T1 of the arrangement queue Q, calling the updating module, the selecting module and the comparing module again until all the arrangement states in the arrangement queue Q are traversed, and calling the second circulation module;
the second circulation module is used for adding one to the maximum corner limit number K1, updating the arrangement state T2 in the arrangement queue Q to the arrangement state T1, repeating the steps of the updating module, the selecting module, the comparing module and the first circulation module until all the target blocks are put in, and acquiring the arrangement scheme with the highest value as the final arrangement scheme.
4. The branched iterative system for stock layout of defective boards as claimed in claim 3, further comprising a value upper bound value calculation module;
the value upper bound value calculation module is used for dividing the distribution state into a target block area and an idle area, and acquiring the sum of the value of the target block in the target block area and the value upper bound of the target block capable of being distributed in the idle area as the value upper bound value.
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