CN111985012A - Two-dimensional irregular part layout method based on optimal foraging algorithm - Google Patents
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Abstract
The invention relates to a two-dimensional irregular part layout method based on an optimal foraging algorithm. The method comprises the following steps: step S1: performing mathematical description on the layout problem of the two-dimensional irregular parts; step S2: establishing constraint conditions to be met in the stock layout optimization process; step S3: determining a target to be optimized, and establishing a corresponding two-dimensional irregular part layout target optimization function; step S4: and performing global optimization search on the discharge sequence and the rotation angle of the parts based on an optimal foraging algorithm, determining the optimal discharge sequence and the rotation angle of the parts, and outputting the optimal layout result. The invention provides a two-dimensional irregular part layout method based on an optimal foraging algorithm, which is suitable for layout of convex and concave polygonal parts and complex parts with holes; compared with a two-dimensional irregular stock layout problem solving method based on a traditional heuristic algorithm, the stock layout method is high in stock layout efficiency, good in robustness and high in material utilization rate.
Description
Technical Field
The invention relates to the technical field of computer-aided layout, in particular to a two-dimensional irregular part layout method based on an optimal foraging algorithm.
Background
1. The layout problem refers to that the parts to participate in layout are reasonably distributed according to the processing requirements on the given space of the raw material plate, so that the utilization rate of the raw material is maximized while the production requirement of the product is ensured. At present, stock layout problems are involved in many manufacturing industries. Along with the rapid development of society, the demand of human resources is increasing, resources are saved, and resource waste is reduced as much as possible, so that the method becomes an important support for the sustainable development of the current society.
2. For the problem of two-dimensional irregular part layout, the manual method is mainly used in the early stage, and the method cannot save raw materials and is high in time cost. Later, with the continuous development of information technology, computer-aided layout technology began to be applied. Compared with an artificial stock layout method, the method has the advantages of high stock layout efficiency and good stock layout effect, and gradually becomes the mainstream of industrial production. In the aspect of heuristic algorithm application of the two-dimensional irregular part layout problem, the currently widely applied intelligent algorithms comprise a genetic algorithm, a particle swarm algorithm, a simulated annealing algorithm and the like, but are basically applied to small-scale layout. In actual production, due to the large production scale, even if the method takes a long search time, the method is easy to generate poor layout results, has poor robustness and is difficult to be widely used.
3. The optimal foraging algorithm is a meta-heuristic algorithm provided based on a modern optimal foraging theory. The algorithm has better global search capability on the whole and better local search capability on the details, and the needed parameters are less, so that the global search capability and the local search capability of the algorithm are balanced without adjusting the parameters too much. The advantage ensures that the method has strong applicability when being applied to the two-dimensional irregular part stock layout problems of convex and concave parts, complex parts with holes and the like, and has high stock layout efficiency, good robustness and excellent stock layout results.
Disclosure of Invention
The invention aims to solve the defects of low stock layout efficiency and poor robustness when the conventional heuristic stock layout algorithm is applied to the stock layout problem of two-dimensional irregular parts, and provides a two-dimensional irregular part stock layout method based on an optimal foraging algorithm.
In order to achieve the purpose, the technical scheme of the invention is as follows: a two-dimensional irregular part layout method based on an optimal foraging algorithm comprises the following steps:
step S1, performing mathematical description on the layout problem of the two-dimensional irregular parts;
step S2: establishing constraint conditions required to be met in the stock layout optimization process;
step S3: determining a target to be optimized, and establishing a corresponding two-dimensional irregular part layout target optimization function;
step S4: and performing global optimization search on the discharge sequence and the rotation angle of the parts based on an optimal foraging algorithm, determining the optimal discharge sequence and the rotation angle of the parts, and outputting the optimal layout result.
In an embodiment of the present invention, in step S1, the two-dimensional irregular part layout problem is mathematically described as follows:
first, the variables are defined: given that the number of the parts participating in stock layout is n, the number of allowed rotation angles of each part is m, and the arrangement sequence { x ] of the parts is randomly generated1,…,xi,…,xn},xiE {1,2, …, n }, and the rotation angle number of each part { y1,y2,…,yn},yi∈{1,2,…,m}，yiCorresponding to a rotation angle of
The corresponding layout scheme is { (x)1,y1),…,(xi,yi),…,(xn,yn)}；
Then, defining the layout problem of the two-dimensional irregular parts: on the given raw and other materials panel, according to the processing requirement, rationally discharge the part, when satisfying the production demand, make raw and other materials utilization maximize.
In an embodiment of the present invention, in step S2, the constraint conditions that need to be satisfied in the layout optimization process are: (1) the discharge positions of the parts participating in stock layout are not overlapped; (2) the parts participating in stock layout are all placed inside the raw material plate.
In an embodiment of the present invention, in step S3, the raw material utilization rate, which is the target to be optimized, is maximized; defining the area of the ith part participating in stock layout as s (i), i belongs to {1,2, …, n }, and then the utilization rate of raw materials is as follows:
wherein, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction;
then the two-dimensional irregular part layout objective optimization function is described as follows:
in an embodiment of the present invention, in step S4, the optimal foraging algorithm includes the following steps:
step S41, initializing algorithm parameters and population;
step S42, evaluating population fitness; calculating the fitness values of all individuals in the initial population, arranging the fitness values in a descending order, and storing the optimal individual as a global optimal individual;
step S43, updating the population, calculating the fitness values of all individuals in the new population, arranging the fitness values in a descending order, and storing the optimal individuals;
step S44, updating the global optimal individual;
and S45, performing iterative updating, outputting an optimal stock layout result if a termination condition is met, and otherwise, turning to the step S43.
In an embodiment of the present invention, the step S41 specifically includes:
initializing algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t;
the population initializing method comprises the following steps: according to the initialized population size popsize, adopting an integer coding form, wherein
The population individuals are generated in a random generation mode, and the rest is
The population individuals are generated in a descending order according to the area size.
In an embodiment of the present invention, the population fitness evaluation function in step S42 is:
the smaller the value of F (x), i.e. the higher the material utilization, the better the result of the layout of the individuals in the population.
In an embodiment of the present invention, the manner of updating the population in step S43 is as follows:
define a range factor k, and
for a globally optimal individual when the number of iterations is t,
j is the j-th individual in the population, and j belongs to {1,2, …, n }; the updating mode of the population individual position is as follows:
in the formula (I), the compound is shown in the specification,
is an individual
The ith dimension element of (1), r1ji、r2jiIs a random number which is uniformly distributed between 0 and 1, and b belongs to {1,2, …, n };
is the worst individual in the population
The ith element of (1), N ═ N;
the optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, so that the algorithm is helped to jump out of the constraint of the local optimal solution; for minimization problems, next generation individuals are judged
The accepted model is:
in the formula (I), the compound is shown in the specification,
is random numbers uniformly distributed between 0 and 1,
and
the fitness values of the individuals j in the population are respectively shown when the iteration times are t and t 1.
In an embodiment of the present invention, the manner of updating the global optimal individuals in step S44 is an elite reservation policy.
In an embodiment of the present invention, the termination condition in step S45 is a preset maximum iteration number maxter.
Compared with the traditional heuristic two-dimensional irregular part layout technology, the method has the following beneficial effects:
1. the invention adopts integer coding mode to the arrangement sequence of the parts and the corresponding rotation angle, reduces the solving complexity, combines two modes of random generation and sequential arrangement generation according to the area size to construct the initial population, has good population diversity, ensures the quality of individuals in the initial population, and has faster convergence rate and high solving efficiency of the algorithm.
2. Compared with a two-dimensional irregular problem layout method based on a traditional intelligent heuristic algorithm, the layout method needs less adjustment parameters and is wide in application range, and the method has good applicability to the layout problem of two-dimensional irregular parts such as convex and concave polygonal parts and complex parts with holes. And the stock layout effect is good, the utilization rate of the plate is high, and the robustness is good.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a diagram of the layout effect of an exemplary part of the present invention based on the method of the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a two-dimensional irregular part layout method based on an optimal foraging algorithm, which comprises the following steps:
step S1, performing mathematical description on the layout problem of the two-dimensional irregular parts;
step S2: establishing constraint conditions required to be met in the stock layout optimization process;
step S3: determining a target to be optimized, and establishing a corresponding two-dimensional irregular part layout target optimization function;
step S4: and performing global optimization search on the discharge sequence and the rotation angle of the parts based on an optimal foraging algorithm, determining the optimal discharge sequence and the rotation angle of the parts, and outputting the optimal layout result.
Further, in step S1, the mathematical description of the two-dimensional irregular part layout problem is as follows:
first, the variables are defined: given that the number of the parts participating in stock layout is n, the number of allowed rotation angles of each part is m, and the arrangement sequence { x ] of the parts is randomly generated1,…,xi,…,xn},xiE {1,2, …, n }, each partRotational angle number of { y1,y2,…,yn},yi∈{1,2,…,m}，yiCorresponding to a rotation angle of
The corresponding layout scheme is { (x)1,y1),…,(xi,yi),…,(xn,yn)}；
Then, defining the layout problem of the two-dimensional irregular parts: on the given raw and other materials panel, according to the processing requirement, rationally discharge the part, when satisfying the production demand, make raw and other materials utilization maximize.
Further, in step S2, the constraint conditions that need to be satisfied in the stock layout optimization process are: (1) the discharge positions of the parts participating in stock layout are not overlapped; (2) the parts participating in stock layout are all placed inside the raw material plate.
Further, in step S3, the raw material utilization rate, which is the target to be optimized, is maximized; defining the area of the ith part participating in stock layout as s (i), i belongs to {1,2, …, n }, and then the utilization rate of raw materials is as follows:
wherein, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction;
then the two-dimensional irregular part layout objective optimization function is described as follows:
further, in step S4, the optimal foraging algorithm includes the following steps:
step S41, initializing algorithm parameters and population;
step S42, evaluating population fitness; calculating the fitness values of all individuals in the initial population, arranging the fitness values in a descending order, and storing the optimal individual as a global optimal individual;
step S43, updating the population, calculating the fitness values of all individuals in the new population, arranging the fitness values in a descending order, and storing the optimal individuals;
step S44, updating the global optimal individual;
and S45, performing iterative updating, outputting an optimal stock layout result if a termination condition is met, and otherwise, turning to the step S43.
Further, the step S41 is specifically:
initializing algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t;
the population initialization method generally comprises the following steps: (1) randomly generating; (2) arranging and generating according to the size of the area in a descending order; when the stock layout scale is large, the diversity of the randomly generated initial population is good, but the quality of the population is not high, the convergence speed of the algorithm is low, and the stock layout efficiency is low; generally, more gaps are generated after parts with larger areas are discharged, and the parts with smaller areas can be utilized without occupying more space, so that the initial population generated by descending order according to the sizes of the areas has better quality, the convergence speed of the algorithm is high, and the stock layout efficiency is high.
Therefore, the population initializing method of the invention comprises the following steps: according to the initialized population size popsize, adopting an integer coding form, wherein
The population individuals are generated in a random generation mode, and the rest is
The population individuals are generated in a descending order according to the area size.
Further, the population fitness evaluation function in step S42 is:
the smaller the value of F (x), i.e. the higher the material utilization, the better the result of the layout of the individuals in the population. Arranging parts based on a left lower gravity center critical polygon positioning strategy, calculating F (x) values of all individuals in a population after all the parts are arranged, and arranging the F (x) values in a descending order, wherein the more excellent the individuals are, the more forward the positions of the individuals are; the lower left gravity center critical polygon positioning strategy is that when the feasible layout position of the part to be arranged is selected, the feasible point with the lowest gravity center position is always selected, and if a plurality of feasible lowest gravity center layout positions exist, the leftmost feasible lowest gravity center layout position is selected.
Further, the manner of updating the population in step S43 is as follows:
define a range factor k, and
for a globally optimal individual when the number of iterations is t,
j is the j-th individual in the population, and j belongs to {1,2, …, n }; the updating mode of the population individual position is as follows:
in the formula (I), the compound is shown in the specification,
is an individual
The ith dimension element of (1), r1ji、r2jiIs a random number which is uniformly distributed between 0 and 1, and b belongs to {1,2, …, n };
is the worst individual in the population
The ith dimension ofElement, N ═ N;
the optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, so that the algorithm is helped to jump out of the constraint of the local optimal solution; for minimization problems, next generation individuals are judged
The accepted model is:
in the formula (I), the compound is shown in the specification,
is random numbers uniformly distributed between 0 and 1,
and
the fitness values of the individuals j in the population are respectively shown when the iteration times are t and t 1.
Further, the manner of updating the globally optimal individuals in step S44 is an elite reservation policy.
Further, the termination condition in step S45 is a preset maximum iteration time maxter, and it is determined whether the evolution iteration time t reaches the maximum iteration time; if so, the optimal solution is output, otherwise, go to step S43.
Referring to fig. 2, the layout effect of the present invention for some irregular parts (material height: 1000mm, number of sample pieces: 28, layout width H: 5200mm, material utilization: 78.6%), initial algorithm parameters are set to 20 for population size popsize and 500 for maximum number of iterations maxIter.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (10)
1. A two-dimensional irregular part layout method based on an optimal foraging algorithm is characterized by comprising the following steps:
step S1, performing mathematical description on the layout problem of the two-dimensional irregular parts;
step S2: establishing constraint conditions required to be met in the stock layout optimization process;
step S3: determining a target to be optimized, and establishing a corresponding two-dimensional irregular part layout target optimization function;
step S4: and performing global optimization search on the discharge sequence and the rotation angle of the parts based on an optimal foraging algorithm, determining the optimal discharge sequence and the rotation angle of the parts, and outputting the optimal layout result.
2. The optimal foraging algorithm-based two-dimensional irregular part layout method according to claim 1, wherein in the step S1, the mathematical description of the two-dimensional irregular part layout problem is as follows:
first, the variables are defined: given that the number of the parts participating in stock layout is n, the number of allowed rotation angles of each part is m, and the arrangement sequence { x ] of the parts is randomly generated1,…,xi,…,xn},xiE {1,2, …, n }, and the rotation angle number of each part { y1,y2,…,yn},yi∈{1,2,…,m}，yiCorresponding to a rotation angle of
The corresponding layout scheme is { (x)1,y1),…,(xi,yi),…,(xn,yn)}；
Then, defining the layout problem of the two-dimensional irregular parts: on the given raw and other materials panel, according to the processing requirement, rationally discharge the part, when satisfying the production demand, make raw and other materials utilization maximize.
3. The optimal foraging algorithm-based two-dimensional irregular part layout method according to claim 1, wherein in step S2, the constraint conditions required to be met in the layout optimization process are as follows: (1) the discharge positions of the parts participating in stock layout are not overlapped; (2) the parts participating in stock layout are all placed inside the raw material plate.
4. The optimal foraging algorithm-based two-dimensional irregular part layout method according to claim 1, wherein in step S3, the target to be optimized, namely raw material utilization rate, is maximized; defining the area of the ith part participating in stock layout as s (i), i belongs to {1,2, …, n }, and then the utilization rate of raw materials is as follows:
wherein, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction;
then the two-dimensional irregular part layout objective optimization function is described as follows:
5. the optimal-foraging-algorithm-based two-dimensional irregular part layout method according to claim 1, wherein in the step S4, the optimal-foraging algorithm comprises the following steps:
step S41, initializing algorithm parameters and population;
step S42, evaluating population fitness; calculating the fitness values of all individuals in the initial population, arranging the fitness values in a descending order, and storing the optimal individual as a global optimal individual;
step S43, updating the population, calculating the fitness values of all individuals in the new population, arranging the fitness values in a descending order, and storing the optimal individuals;
step S44, updating the global optimal individual;
and S45, performing iterative updating, outputting an optimal stock layout result if a termination condition is met, and otherwise, turning to the step S43.
6. The optimal-foraging-algorithm-based two-dimensional irregular part layout method according to claim 4, wherein the step S41 is specifically as follows:
initializing algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t;
the population initializing method comprises the following steps: according to the initialized population size popsize, adopting an integer coding form, wherein
The population individuals are generated in a random generation mode, and the rest is
The population individuals are generated in a descending order according to the area size.
7. The optimal foraging algorithm-based two-dimensional irregular part layout method according to claim 4, wherein the population fitness evaluation function in the step S42 is as follows:
the smaller the value of F (x), i.e. the higher the material utilization, the better the result of the layout of the individuals in the population.
8. The optimal foraging algorithm-based two-dimensional irregular part layout method according to claim 4, wherein the updating of the population in step S43 is performed by:
define a range factor k, and
for a globally optimal individual when the number of iterations is t,
j is the j-th individual in the population, and j belongs to {1,2, …, n }; the updating mode of the population individual position is as follows:
in the formula (I), the compound is shown in the specification,
is an individual
The ith dimension element of (1), r1ji、r2jiIs a random number which is uniformly distributed between 0 and 1, and b belongs to {1,2, …, n };
is the worst individual in the population
The ith element of (1), N ═ N;
the optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, so that the algorithm is helped to jump out of the constraint of the local optimal solution; for minimization problems, next generation individuals are judged
The accepted model is:
in the formula，
Is random numbers uniformly distributed between 0 and 1,
and
respectively representing the fitness value of an individual j in the population when the iteration times are t and t + 1.
9. The optimal-foraging-algorithm-based two-dimensional irregular part layout method according to claim 4, wherein the global optimal individual is updated in step S44 in a manner of an elite retention strategy.
10. The optimal-foraging-algorithm-based two-dimensional irregular part layout method according to claim 4, wherein the termination condition in the step S45 is a preset maximum iteration number maxIter.
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| CN112873855A (en) * | 2021-04-13 | 2021-06-01 | 河北工业大学 | STL model center layout method in 3DP process |
| CN113435094A (en) * | 2021-05-27 | 2021-09-24 | 中国地质大学（武汉） | Two-dimensional irregular part layout method based on genetic algorithm |
| CN113762380A (en) * | 2021-09-07 | 2021-12-07 | 成都理工大学 | Part layout optimization method based on self-adaptive grouping |
| CN114066099A (en) * | 2021-11-30 | 2022-02-18 | 郑州轻工业大学 | Round piece coiled material layout optimization method based on improved chicken flock algorithm |
| CN114611413A (en) * | 2022-05-09 | 2022-06-10 | 广东三维家信息科技有限公司 | Raw material stock layout method, device, electronic equipment and storage medium |
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| CN115759634A (en) * | 2022-11-18 | 2023-03-07 | 中南大学 | Efficient collaboration method for batch layout of rectangular plates |
| CN117131989A (en) * | 2023-09-04 | 2023-11-28 | 晞德求索(北京)科技有限公司 | Two-dimensional blanking method and system based on dynamic allocation |
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| CN112873855A (en) * | 2021-04-13 | 2021-06-01 | 河北工业大学 | STL model center layout method in 3DP process |
| CN113435094A (en) * | 2021-05-27 | 2021-09-24 | 中国地质大学（武汉） | Two-dimensional irregular part layout method based on genetic algorithm |
| CN113435094B (en) * | 2021-05-27 | 2022-07-05 | 中国地质大学（武汉） | Two-dimensional irregular part layout method based on genetic algorithm |
| CN113762380A (en) * | 2021-09-07 | 2021-12-07 | 成都理工大学 | Part layout optimization method based on self-adaptive grouping |
| CN114066099A (en) * | 2021-11-30 | 2022-02-18 | 郑州轻工业大学 | Round piece coiled material layout optimization method based on improved chicken flock algorithm |
| CN114611413A (en) * | 2022-05-09 | 2022-06-10 | 广东三维家信息科技有限公司 | Raw material stock layout method, device, electronic equipment and storage medium |
| CN114996781A (en) * | 2022-05-27 | 2022-09-02 | 华中科技大学 | Two-dimensional irregular part layout method and system based on actors-critics |
| CN115759634A (en) * | 2022-11-18 | 2023-03-07 | 中南大学 | Efficient collaboration method for batch layout of rectangular plates |
| CN115759634B (en) * | 2022-11-18 | 2024-04-26 | 中南大学 | Efficient cooperation method for rectangular plate batch layout |
| CN117131989A (en) * | 2023-09-04 | 2023-11-28 | 晞德求索(北京)科技有限公司 | Two-dimensional blanking method and system based on dynamic allocation |
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