CN113780651B - Two-dimensional irregular layout method based on improved mixed BL strategy - Google Patents
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Abstract
The invention relates to a two-dimensional irregular layout method based on an improved mixed BL strategy, which comprises the following steps: s1, constructing a two-dimensional irregular part layout problem model; s2, constructing an initial layout scheme and calculating an initial objective function; and S3, selecting a position to be moved by a constructive method according to a layout scheme, moving the part at the position to be arranged by using a leftmost and bottommost positioning strategy, and determining an optimal placement position according to the fit degree, wherein the step S4 is to optimize the discharge sequence and the rotation angle of the part by adopting an optimal foraging algorithm and output the optimal layout scheme. The invention can quickly and accurately obtain the optimal discharge position, effectively improves the manufacturing efficiency and has stronger universality.
Description
Technical Field
The invention relates to the technical field of two-dimensional irregular part layout, in particular to a two-dimensional irregular layout method based on an improved mixed BL strategy.
Background
The problem of layout optimization is a key link of design and manufacturing processes of clothes, leather, glass, paper products and the like, the quality of the layout directly influences the utilization rate of raw materials, the production cost and the economic benefits of enterprises, the early layout adopts a traditional manual mode, the layout is inefficient and unstable depending on the proficiency and experience summary of technical workers, along with the progress of science and technology, the demand of human on resources is continuously increased, and in order to reduce the resource waste as much as possible, the automatic layout technology is paid more attention to and developed.
The two-dimensional layout problem is most common in practical application, has wide application range and high complexity, is proved to be a typical NP complete combination problem in mathematics, is difficult to solve by adopting a traditional algorithm due to the large number and variety of layout parts, and is difficult to find out the optimal solution of the problem within an acceptable time range even if a high-performance computer is used by adopting an exhaustive method. How to shorten the layout time and improve the utilization rate of plate parts is always the key point and the difficulty of research in the layout problem.
Disclosure of Invention
In view of the above, the invention aims to provide a two-dimensional irregular layout method based on an improved mixed BL strategy, which solves the defects of overhigh layout complexity, lower layout quality and the like when the existing polygonal part positioning strategy is applied to the two-dimensional irregular part layout problem.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a two-dimensional irregular layout method based on an improved mixed BL strategy comprises the following steps:
s1, constructing a two-dimensional irregular part layout problem model;
s2, constructing an initial layout scheme and calculating an initial objective function;
step S3, selecting a position to be moved through a constructive method according to a layout scheme, moving a part at the position to be arranged by using a leftmost and bottommost positioning strategy, and determining an optimal placement position according to the fit degree;
and S4, optimizing the discharging sequence and the rotating angle of the parts by adopting an optimal foraging algorithm, and outputting an optimal layout scheme.
Further, the step S1 specifically includes:
defining a two-dimensional irregular part layout problem: on a given raw material plate, reasonably discharging parts according to processing requirements, and maximizing the utilization rate of raw materials while meeting production requirements;
according to the maximum width of the raw material plate discharged and the area of each part, in order to maximize the raw material utilization, an objective function is defined as follows:
in the formula (1),W max maximum width of part discharge, L max Maximum length of part discharge S i The area of the ith part is represented by n, the total number of the parts is represented by delta, and the material utilization rate is represented by delta;
and setting a preset geometric constraint condition in the stock layout optimization process.
Further, the preset geometric constraint condition includes:
(1) The parts to be arranged and the arranged parts cannot be overlapped, intersected or contained;
(2) The parts participating in the layout are all placed in the raw material plate;
(3) Technological constraint conditions required to be met in the stock layout optimization process.
Further, the step S2 specifically includes: calculating external critical polygons between all the parts to be discharged and the next part to be discharged and internal critical polygons between the parts to be discharged and the raw material plate by using a Minkowski summation method, and obtaining the optimal dischargeable position of the parts to be discharged by combining all the critical polygons;
according to the layout characteristics, the n parts to be discharged are numbered according to the discharge sequence, and a discharge sequence { x ] of the parts is randomly generated 1 ,…,x i ,…,x n },x i ∈{1,2,…,n}，x i Randomly generating a corresponding polygon with a rotation angle y for the ith polygon part number of the plate i The corresponding pattern scheme is { (x) 1 ,y 1 ),…,(x i ,y i ),…,(x n ,y n )}。
Further, the step S3 specifically includes:
step S31, according to the layout scheme, placing a first part at the leftmost and bottommost position of the plate;
step S32, selecting three positions to be moved according to the generated critical polygon by a CA method, wherein the three positions are respectively the rightmost uppermost point of the critical polygonThe rightmost side of the uppermost->And leftmost side of the uppermost +.>
Step S33, traversing all possible placement positions according to the selected movement positions in the step S32 through the lowest left principle of the lowest left strategy;
and S34, calculating the overlapping area between the parts to be arranged and the enveloping rectangle of the parts to be arranged according to the positions to be arranged obtained in the step S34, taking the overlapping part as the fitting degree, calculating the fitting degree of all possible placement positions, and selecting the placement position with the maximum fitting degree as the optimal placement position.
Further, the step S4 specifically includes:
step S41, defining the fitness F (x) of the individual as follows:
the smaller the value of F (x), i.e., the higher the material utilization, the better the individual drainage results. Calculating F (x) values of all individuals in the population, arranging the individuals in descending order, wherein the better the individuals are, the more front the positions of the individuals are; calculating fitness values of all individuals in the initial population, and storing the optimal individuals as global optimal individuals;
step S42: updating the population, and calculating the fitness value of all individuals in the new population;
step S43: updating the global optimal individual;
step S44: and (3) iteratively updating, if the termination condition is met, outputting an optimal layout result, otherwise, turning to step S43.
Further, the updating mode in the optimal foraging algorithm is as follows:
setting an initial iteration number to t=1, and setting a maximum iteration number to t max Define a range factor k, and for globally optimal individuals when the number of iterations is t, < ->J e {1,2, …, n } for the j-th individual in the population; the updating mode of the population individual positions is as follows:
in the method, in the process of the invention,when the iteration number is t, the ith dimension element of the individual b is any one of the individuals in the population, which is better than the individual j, and the individual b is +.>Is a random number between 0 and 1 and independent of each other, j is {1,2, …, n };
for minimizing problems, next generation individuals are judgedThe model of whether accepted is:
in the method, in the process of the invention,is a random number between 0 and 1, < >>And->Respectively representing individual j in the population when the iteration times are t and t+1Fitness value.
Compared with the prior art, the invention has the following beneficial effects:
the invention can quickly and accurately obtain the optimal discharge position, effectively improves the manufacturing efficiency and has stronger universality.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram showing the layout effect of certain parts according to the present invention;
FIG. 3 illustrates three positions to be moved selected by the CA method according to an embodiment of the invention;
FIG. 4 shows the fit between the parts to be arranged and the parts to be arranged according to an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides a two-dimensional irregular layout method based on an improved hybrid BL strategy, comprising the following steps:
s1, constructing a two-dimensional irregular part layout problem model;
s2, constructing an initial layout scheme and calculating an initial objective function;
step S3, selecting a position to be moved through a constructive method according to a layout scheme, moving a part at the position to be arranged by using a leftmost and bottommost positioning strategy, and determining an optimal placement position according to the fit degree;
and S4, optimizing the discharging sequence and the rotating angle of the parts by adopting an optimal foraging algorithm, and outputting an optimal layout scheme.
In this embodiment, preferably, the step S1 specifically includes:
defining a two-dimensional irregular part layout problem: on a given raw material plate, reasonably discharging parts according to processing requirements, and maximizing the utilization rate of raw materials while meeting production requirements;
according to the maximum width of the raw material plate discharged and the area of each part, in order to maximize the raw material utilization, an objective function is defined as follows:
in the formula (1), W max Maximum width of part discharge, L max Maximum length of part discharge S i The area of the ith part is represented by n, the total number of the parts is represented by delta, and the material utilization rate is represented by delta;
and setting a preset geometric constraint condition in the stock layout optimization process.
In this embodiment, preferably, the preset geometric constraint condition includes:
(1) The parts to be arranged and the arranged parts cannot be overlapped, intersected or contained;
(2) The parts participating in the layout are all placed in the raw material plate;
(3) Technological constraint conditions required to be met in the stock layout optimization process.
In this embodiment, preferably, the step S2 specifically includes: calculating external critical polygons between all the parts to be discharged and the next part to be discharged and internal critical polygons between the parts to be discharged and the raw material plate by using a Minkowski summation method, and obtaining the optimal dischargeable position of the parts to be discharged by combining all the critical polygons;
according to the layout characteristics, the n parts to be discharged are numbered according to the discharge sequence, and a discharge sequence { x ] of the parts is randomly generated 1 ,…,x i ,…,x n },x i ∈{1,2,…,n}，x i Randomly generating a corresponding polygon with a rotation angle y for the ith polygon part number of the plate i The corresponding pattern scheme is { (x) 1 ,y 1 ),…,(x i ,y i ),…,(x n ,y n )}。
In this embodiment, preferably, the step S3 specifically includes:
step S31, according to the layout scheme, placing a first part at the leftmost and bottommost position of the plate;
step S32, according to the generated critical polygon, passing through CA methodThree positions to be moved are selected, namely the rightmost uppermost point of the critical polygonThe rightmost side of the uppermost->And leftmost side of the uppermost +.>
Step S33, traversing all possible placement positions according to the selected movement positions in the step S32 through the lowest left principle of the lowest left strategy;
step S34, according to the position to be arranged obtained in the step S33, calculating the overlapping area between the arranged parts and the part enveloping rectangle to be arranged, taking the overlapping part as the fitting degree, as shown in fig. 4, taking the A frame as the part enveloping rectangle to be arranged, the B frame as the part enveloping rectangle to be arranged, taking the area of the overlapping part C as the fitting degree, calculating the fitting degree of all possible placement positions, and selecting the placement position with the largest fitting degree as the optimal placement position.
In this embodiment, the step S4 specifically includes:
step S41: evaluating population fitness; according to step S31, a certain layout scheme is taken as an individual, and the fitness evaluation method comprises the following steps: the fitness F (x) of an individual is defined as:
the smaller the value of F (x), i.e., the higher the material utilization, the better the individual drainage results. Calculating F (x) values of all individuals in the population, arranging the individuals in descending order, wherein the better the individuals are, the more front the positions of the individuals are; calculating fitness values of all individuals in the initial population, and storing the optimal individuals as global optimal individuals;
step S42: updating the population, and calculating the fitness value of all individuals in the new population;
step S43: updating the global optimal individual;
step S44: and (3) iteratively updating, if the termination condition is met, outputting an optimal layout result, otherwise, turning to step S43.
In this embodiment, the update manner in the optimal foraging algorithm is as follows:
setting an initial iteration number to t=1, and setting a maximum iteration number to t max Define a range factor k, and for globally optimal individuals when the number of iterations is t, < ->J e {1,2, …, n } for the j-th individual in the population; the updating mode of the population individual positions is as follows:
in the method, in the process of the invention,when the iteration number is t, the ith dimension element of the individual b is any one of the individuals in the population, which is better than the individual j, and the individual b is +.>Is a random number between 0 and 1 and independent of each other, j is {1,2, …, n };
the optimal foraging algorithm has a small probability of accepting some worse individuals in the iterative process, so that the algorithm is helped to jump out of the constraint of the local optimal solution; for minimizing problems, next generation individuals are judgedThe model of whether accepted is:
in the method, in the process of the invention,random numbers obeying uniform distribution between 0 and 1, ">And->The fitness value of the individual j in the population is respectively represented when the iteration times are t and t+1;
referring to FIG. 2, the pattern layout effect of the present invention on some irregular parts (raw material plate height: 80cm, number of parts: 71, raw material plate width H:50cm, material utilization: 80.06%).
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (5)
1. The two-dimensional irregular layout method based on the improved mixed BL strategy is characterized by comprising the following steps of:
s1, constructing a two-dimensional irregular part layout problem model;
s2, constructing an initial layout scheme and calculating an initial objective function;
step S3, selecting a position to be moved through a constructive method according to a layout scheme, moving a part at the position to be arranged by using a leftmost and bottommost positioning strategy, and determining an optimal placement position according to the fit degree;
s4, optimizing the discharge sequence and the rotation angle of the parts by adopting an optimal foraging algorithm, and outputting an optimal layout scheme;
calculating external critical polygons between all the parts to be discharged and the next part to be discharged and internal critical polygons between the parts to be discharged and the raw material plate by using a Minkowski summation method, and obtaining the optimal dischargeable position of the parts to be discharged by combining all the critical polygons;
according to the layout characteristics, the n parts to be discharged are numbered according to the discharge sequence, and a discharge sequence { x ] of the parts is randomly generated 1 ,…,x i ,…,x n },x i ∈{1,2,…,n}，x i Randomly generating a corresponding polygon with a rotation angle y for the ith polygon part number of the plate i The corresponding pattern scheme is { (x) 1 ,y 1 ),…,(x i ,y i ),…,(x n ,y n )}；
The step S3 specifically comprises the following steps:
step S31, according to the layout scheme, placing a first part at the leftmost and bottommost position of the plate;
step S32, selecting three positions to be moved according to the generated critical polygon by a CA method, wherein the three positions are respectively the rightmost uppermost point of the critical polygonThe rightmost side of the uppermost->And leftmost side of the uppermost +.>
Step S33, traversing all possible placement positions according to the selected movement positions in the step S32 through the lowest left principle of the lowest left strategy;
and S34, calculating the overlapping area between the parts to be arranged and the enveloping rectangle of the parts to be arranged according to the positions to be arranged obtained in the step S33, taking the overlapping part as the fitting degree, calculating the fitting degree of all possible placement positions, and selecting the placement position with the maximum fitting degree as the optimal placement position.
2. The two-dimensional irregular layout method based on the improved hybrid BL strategy according to claim 1, wherein the step S1 is specifically:
defining a two-dimensional irregular part layout problem: on a given raw material plate, reasonably discharging parts according to processing requirements, and maximizing the utilization rate of raw materials while meeting production requirements;
according to the maximum width of the raw material plate discharged and the area of each part, in order to maximize the raw material utilization, an objective function is defined as follows:
in the formula (1), W max Maximum width of part discharge, L max Maximum length of part discharge S i The area of the ith part is represented by n, the total number of the parts is represented by delta, and the material utilization rate is represented by delta;
and setting a preset geometric constraint condition in the stock layout optimization process.
3. The two-dimensional irregular layout method based on the improved hybrid BL strategy according to claim 2, wherein the preset geometric constraint condition includes:
(1) The parts to be arranged and the arranged parts cannot be overlapped, intersected or contained;
(2) The parts participating in the layout are all placed in the raw material plate;
(3) Technological constraint conditions required to be met in the stock layout optimization process.
4. The two-dimensional irregular layout method based on the improved hybrid BL strategy according to claim 1, wherein the step S4 is specifically:
step S41, defining the fitness F (x) of the individual as follows:
the smaller the value of F (x), i.e. the higher the material utilization, the better the individual stock layout result; calculating F (x) values of all individuals in the population, arranging the individuals in descending order, wherein the better the individuals are, the more front the positions of the individuals are; calculating fitness values of all individuals in the initial population, and storing the optimal individuals as global optimal individuals;
step S42: updating the population, and calculating the fitness value of all individuals in the new population;
step S43: updating the global optimal individual;
step S44: and (3) iteratively updating, if the termination condition is met, outputting an optimal layout result, otherwise, turning to step S43.
5. The two-dimensional irregular layout method based on the improved hybrid BL strategy of claim 1 wherein the update in the optimal foraging algorithm is as follows:
setting an initial iteration number to t=1, and setting a maximum iteration number to t max Define a range factor k, andfor globally optimal individuals when the number of iterations is t, < ->J e {1,2, …, n } for the j-th individual in the population; the updating mode of the population individual positions is as follows:
in the method, in the process of the invention,when the iteration number is t, the ith dimension element of the individual b is any one of the individuals in the population, which is better than the individual j, and the individual b is +.>Is a random number between 0 and 1 and independent of each other, j is {1,2, …, n };
for minimizing problems, next generation individuals are judgedThe model of whether accepted is:
in the method, in the process of the invention,is a random number between 0 and 1, < >>And->And respectively representing the fitness value of the individual j in the population when the iteration times are t and t+1.
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