A two-dimensional arrangement method for metal sheets

Abstract

The present invention discloses a two-dimensional arrangement method of metal sheets, comprising the following steps: step 1: establishing a sheet material cutting constraint model; step 2: designing a particle swarm algorithm and a variable neighborhood search hybrid algorithm; step 3: designing an arrangement plan in combination with the constraint model; step 4: outputting the arrangement plan. The present invention utilizes a particle swarm algorithm and a variable neighborhood search algorithm for fusion improvement, solves the two-dimensional arrangement problem of metal sheets, and has a good arrangement effect, greatly improves the utilization rate of metal sheets, reduces the production cost of enterprises, and saves social resources at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of metal plate arrangement, and in particular relates to a two-dimensional metal plate arrangement method. Background Art

[0002] The optimization problem of sheet metal cutting belongs to the two-dimensional rectangular cutting problem, which is a problem with high computational complexity. At present, many companies still use manual cutting for metal sheets when producing metal products, which often takes a long time and causes serious material waste. Some companies use optimization algorithms to cut sheets and improve the utilization rate of sheets. However, due to the limitations of the algorithm, the utilization rate of sheets is still not high. Due to the diversity of customer needs, it is necessary to arrange the cutting plan reasonably, make full use of raw material metal sheets, improve the economic benefits of enterprises and save social resources.

[0003] The present invention mainly aims at the problem of blanking of single-specification metal sheets. When the length and width of the metal sheet are greater than the length and width of the part, a particle swarm hybrid variable neighborhood search algorithm is used to solve the problem of blanking of single-specification metal sheets, thereby greatly improving the utilization rate of the metal sheets. Summary of the invention

[0004] The present invention aims at the deficiencies in the prior art and provides a two-dimensional arrangement method for metal plates.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A two-dimensional arrangement method for metal sheets comprises the following steps:

[0007] Step 1: Establish a plate cutting constraint model;

[0008] Step 2: Design a hybrid algorithm of particle swarm optimization and variable neighborhood search;

[0009] Step 3: Design a layout plan based on the constraint model;

[0010] Step 4: Output the layout plan.

[0011] Furthermore, in step 1, the mathematical model is obtained with the optimization purpose of minimizing the remaining waste as follows:

[0012] 0≤X k ≤L,(1≤k≤C j ,1≤j≤N) (1)

[0013] 0≤Y k ≤W,(1≤k≤C j ,1≤j≤N) (2)

[0014] X k +(l k Pk +w k (1-P k ))≤L,(1≤k≤C j ,1≤j≤N) (3)

[0015] Y k +(w k P k +l k (1-P k ))≤W,(1≤k≤C j ,1≤j≤N) (4)

[0016]

[0017]

[0018]

[0019] T j ≥1,(1≤j≤N) (8)

[0020]

[0021] Where: L and W are the length and width of the rectangular metal raw material plate, K is the number of all types of blank parts to be cut, n i is the required quantity of each part, i is the serial number of the part type, 1≤i≤K; l k and is the length and width of the blank part; N is the number of single plates in the final overall optimized blanking solution, T j C is the number of times the raw material plate needs to be cut repeatedly according to the optimization plan for cutting the jth single board, j is the serial number of the single board in the final overall optimization cutting plan, 1≤j≤N; j is the total number of parts placed on the j-th single board solution, k is the number of parts R k The serial number, R k Name the rectangles where the parts are located. For the kth part placed on the jth board, k j is the serial number of the kth part arranged on the jth board. The coordinate of the lower left corner of each rectangle is (X k ,Y k ); The blank parts to be cut can be placed horizontally or vertically on the plate. The corresponding placement method is when P k =1(1≤k≤C j ), it means horizontal placement; when P k =0, 1≤k≤C j , when it means vertical placement; A ijA represents the number of the i-th type of parts in the j-th single board solution, ij ≤n i , 1≤i≤K, 1≤j≤N; l i is the length w of the blank part i is the width of the blank part;

[0022] Formula (1) and formula (2) determine the placement interval of the blank parts;

[0023] Formula (3) and (4) ensure that the parts will not exceed the boundaries of the raw material sheet within the placement interval, limiting the length and width;

[0024] Formula (5) ensures that the blank parts will not overlap on the raw material plate;

[0025] Formula (6) and (7) satisfy the quantity and matching requirements of all blank parts;

[0026] Formula (9) is the objective function, which minimizes the area of ​​the wasted raw material sheet, that is, ensures that the utilization rate of the raw material sheet can be maximized.

[0027] Furthermore, the particle swarm hybrid variable neighborhood search algorithm in step 2 is as follows:

[0028] Step 2.1, initialize the particle swarm, including the particle population size N, the position x of each particle i , speed v i and the maximum number of iterations T max , where the particle position information is obtained by using the blank part coordinates (X k ,Y k ) is determined by the error of the iteration process, where the blank part coordinates (X k ,Y k ) First, the placement interval is determined by equations (1) and (2), and then equations (3) and (4) are used to ensure that the parts will not exceed the boundary of the raw material plate within the placement interval; finally, equation (5) is used to ensure that the parts will not overlap;

[0029] Step 2.2, using formula (9) in step 1 to calculate the utilization rate Fit[i] of this layout as the optimization target, and taking the area of ​​the raw material plate wasted in formula (9) as the optimization target so that the iteration direction is progressively toward the layout mode with the most material saving;

[0030] Step 2.3, for each particle, use its utilization value Fit[i] and individual extreme value p best (i) Compare and update the individual extreme values ​​of particles;

[0031] Step 2.4: For each particle, use its utilization value Fit[i] and the global extreme value g best(i) Compare and update the global extreme value of the entire population;

[0032] Step 2.5, update the velocity and position of the particle;

[0033] Step 2.6: Check whether the termination condition is met, that is, whether the maximum number of iterations T is reached max If it is not satisfied, jump to step 2.2. If it is satisfied, stop searching and take the updated global extreme value as the initial solution of variable neighborhood search. Let x best =g best ;

[0034] Step 2.7, call variable neighborhood search for particles. The main search strategy is: define a series of neighborhood structures N K ,K=1,2,…,K max , so that the search density and search range of each neighborhood structure are different, and each module is executed sequentially. Once an intermediate solution that is better than the current one appears, the intermediate solution is used to replace the current solution, and this module is called to search again until a worse intermediate solution appears; otherwise, the next module is executed until the end;

[0035] Step 2.8: Determine whether the end condition K is met according to step 2.7 <K max , that is, whether all neighborhood structures have been searched. If the termination condition is met, the algorithm terminates and outputs the optimal result; if the termination condition is not met, then go back to step 2.6;

[0036] Step 2.9 outputs the global optimal value and the algorithm ends.

[0037] Further, step 3: combining the constraint model with the particle swarm algorithm to design a layout scheme;

[0038] Step 3.1, design particle position information: the position x of each particle in step 2 i Contains the lower left corner coordinates (X k ,Y k ), speed v i Determined by the error of the iterative process, the number of iterations T max Determined by the user, the individual extreme value p in step 2 best (i) is the optimal particle position information of the particle that has been iterated, which is determined by the arrangement method with the smallest utilization rate Fit[i] value in the population of this iteration. The individual extreme value g in step 2 best (i) is the optimal particle position information of all particles after iteration, which is determined by the arrangement method with the smallest utilization rate Fit[i] value in the iterated population.

[0039] Step 3.2, particle position constraint design: Each particle x in step 2i The coordinates (X k ,Y k ),

[0040] Determine the blank placement interval by equations (1) and (2) in step 1;

[0041] Formula (3) and (4) in step 1 ensure that the part will not exceed the boundary of the raw material plate within the placement interval;

[0042] Step 1 (5) ensures that parts do not overlap;

[0043] Step 3.3, particle fitness function design: The optimization target Fit[i] in step 2 is taken as the objective function by equation (9) in step 1, that is, the utilization rate of the material sheet.

[0044] The beneficial effects of the present invention are as follows: the present invention utilizes the particle swarm algorithm and the variable neighborhood search algorithm for fusion improvement, solves the two-dimensional layout problem of metal sheets, and has good layout effect, greatly improves the utilization rate of metal sheets, reduces the production cost of enterprises, and saves social resources at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the present invention;

[0046] Figure 2 It is a flow chart of the particle swarm variable neighborhood search hybrid algorithm of the present invention;

[0047] Figure 3 (a) is the particle swarm algorithm sorting scheme, Figure 3 (b) is the sampling scheme of the variable neighborhood search algorithm, Figure 3 (c) is the variable neighborhood sorting scheme for particle swarm. DETAILED DESCRIPTION

[0048] The present invention will now be described in further detail with reference to the accompanying drawings.

[0049] like Figure 1 , Figure 2 As shown, the two-dimensional arrangement method of metal sheets of the present invention comprises the following steps:

[0050] Step 1: Establish a plate cutting constraint model;

[0051] Step 2: Design a hybrid algorithm of particle swarm optimization and variable neighborhood search;

[0052] Step 3: Design a layout plan based on the constraint model;

[0053] Step 4: Output the layout plan.

[0054] In step 1, the present invention aims at the metal sheet layout optimization problem, and under the premise of fully considering various factors and constraints, selects the minimum remaining waste as the optimization purpose to obtain the following mathematical model:

[0055] 0≤X k ≤L,(1≤k≤C j ,1≤j≤N) (1)

[0056] 0≤Y k ≤W,(1≤k≤C j ,1≤j≤N) (2)

[0057] X k +(l k P k +w k (1-P k ))≤L,(1≤k≤C j ,1≤j≤N) (3)

[0058] Y k +(w k P k +l k (1-P k ))≤W,(1≤k≤C j ,1≤j≤N) (4)

[0059]

[0060]

[0061]

[0062] T j ≥1,(1≤j≤N) (8)

[0063]

[0064] Where: L and W are the length and width of the rectangular metal raw material plate, K is the number of all types of blank parts to be cut, n i is the required quantity of each part, i is the serial number of the part type, 1≤i≤K; l k and is the length and width of the blank part; N is the number of single plates in the final overall optimized blanking solution, T j C is the number of times the raw material plate needs to be cut repeatedly according to the optimization plan for cutting the jth single board, j is the serial number of the single board in the final overall optimization cutting plan, 1≤j≤N; j is the total number of parts placed on the j-th single board solution, k is the number of parts R k The serial number, Rk Name the rectangles where the parts are located. For the kth part placed on the jth board, k j is the serial number of the kth part arranged on the jth board, and the coordinate of the lower left corner of each rectangle is (X k ,Y k ); The blank parts to be cut can be placed horizontally or vertically on the plate. The corresponding placement method is when P k =1(1≤k≤C j ), it means horizontal placement; when P k =0, 1≤k≤C j , when it means vertical placement; A ij A represents the number of the i-th type of parts in the j-th single board solution, ij ≤n i , 1≤i≤K, 1≤j≤N; l i is the length w of the blank part i is the width of the blank part;

[0065] Formula (1) and formula (2) determine the placement interval of the blank parts;

[0066] Formula (3) and (4) ensure that the parts will not exceed the boundaries of the raw material sheet within the placement interval, limiting the length and width;

[0067] Formula (5) ensures that the blank parts will not overlap on the raw material plate;

[0068] Formula (6) and (7) satisfy the quantity and matching requirements of all blank parts;

[0069] Formula (9) is the objective function, which minimizes the area of ​​the wasted raw material sheet, that is, ensures that the utilization rate of the raw material sheet can be maximized.

[0070] Step 2, the particle swarm hybrid variable neighborhood search algorithm is as follows:

[0071] Step 2.1, initialize the particle swarm, including the particle population size N, the position x of each particle i , speed v i and the maximum number of iterations T max , where the particle position information is obtained by using the blank part coordinates (X k ,Y k ), the speed information is determined by the error of the iterative process, and the number of iterations T max Determined by the user; the blank part coordinates (X k ,Y k) First, the placement interval is determined by equations (1) and (2), and then equations (3) and (4) are used to ensure that the parts will not exceed the boundary of the raw material plate within the placement interval; finally, equation (5) is used to ensure that the parts will not overlap;

[0072] Step 2.2, using formula (9) in step 1 to calculate the utilization rate Fit[i] of this layout as the optimization target, and taking the area of ​​the raw material plate wasted in formula (9) as the optimization target so that the iteration direction is progressively toward the layout mode with the most material saving;

[0073] Step 2.3, for each particle, use its utilization value Fit[i] and individual extreme value p best (i) Compare and update the individual extreme values ​​of particles;

[0074] Step 2.4: For each particle, use its utilization value Fit[i] and the global extreme value g best (i) Compare and update the global extreme value of the entire population;

[0075] Step 2.5, update the velocity and position of the particle;

[0076] Step 2.6: Check whether the termination condition is met, that is, whether the maximum number of iterations T is reached max If it is not satisfied, jump to step 2.2. If it is satisfied, stop searching and take the updated global extreme value as the initial solution of variable neighborhood search. Let x best =g best ;

[0077] Step 2.7, call variable neighborhood search for particles. The main search strategy is: define a series of neighborhood structures N K ,K=1,2,…,K max , so that the search density and search range of each neighborhood structure are different, and each module is executed sequentially. Once an intermediate solution that is better than the current one appears, the intermediate solution is used to replace the current solution, and this module is called to search again until a worse intermediate solution appears; otherwise, the next module is executed until the end;

[0078] Step 2.8: Determine whether the end condition K is met according to step 2.7 <K max , that is, whether all neighborhood structures have been searched. If the termination condition is met, the algorithm terminates and outputs the optimal result; if the termination condition is not met, then go back to step 2.6;

[0079] Step 2.9, output the global optimal value and the algorithm ends.

[0080] like Figure 3 (a) Figure 3 (b) Figure 3As shown in (c), step 3: combining the constraint model with the particle swarm algorithm to design a sample arrangement scheme;

[0081] Step 3.1, design particle position information: the position x of each particle in step 2 i Contains the lower left corner coordinates (X k ,Y k ), speed v i Determined by the error of the iterative process, the number of iterations T max Determined by the user, the individual extreme value p in step 2 best (i) is the optimal particle position information of the particle that has been iterated, which is determined by the arrangement method with the smallest utilization rate Fit[i] value in the population of this iteration. The individual extreme value g in step 2 best (i) is the optimal particle position information of all particles after iteration, which is determined by the arrangement method with the smallest utilization rate Fit[i] value in the iterated population.

[0082] Step 3.2, particle position constraint design: Each particle x in step 2 i The coordinates (X k ,Y k ),

[0083] Determine the blank placement interval by equations (1) and (2) in step 1;

[0084] Formula (3) and (4) in step 1 ensure that the part will not exceed the boundary of the raw material plate within the placement interval;

[0085] Step 1 (5) ensures that parts do not overlap;

[0086] Step 3.3, particle fitness function design: The optimization target Fit[i] in step 2 is taken as the objective function by equation (9) in step 1, that is, the utilization rate of the material sheet.

[0087] Step 4: Output the layout plan.

[0088] Determine whether the solution meets the material utilization requirements of the metal sheet. If not, return to modify the mathematical model and repeat steps 2, 3, and 4 until the requirements are met.

[0089] Input of raw material plate size and required information for cutting. The raw material plate size mainly includes the length and width of the plate, and the required size of the plate to be cut mainly includes the length, width and quantity of various required plates. Fast plate layout based on particle swarm algorithm, variable neighborhood search algorithm and improved particle swarm hybrid optimization algorithm. Query the utilization rate of layout results and browse, edit and print layout example pictures.

[0090] It should be noted that the terms such as "upper", "lower", "left", "right", "front", "back", etc. cited in the invention are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments in their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0091] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A two-dimensional arrangement method for metal sheets, characterized in that: The steps include: Step 1: Establish a plate cutting constraint model; Step 2: Design a hybrid algorithm of particle swarm optimization and variable neighborhood search; Step 3: Design a layout plan based on the constraint model; Step 4: Output the layout plan; In step 1, the mathematical model is obtained with the optimization purpose of minimizing the remaining waste as follows: 0≤X k ≤L,(1≤k≤C j ,1≤j≤N) (1) 0≤Y k ≤W,(1≤k≤C j ,1≤j≤N) (2) X k +(l k P k +w k (1-P k ))≤L,(1≤k≤C j ,1≤j≤N) (3) Y k +(w k P k +l k (1-P k ))≤W,(1≤k≤C j ,1≤j≤N) (4) T j ≥1,(1≤j≤N) (8) Where: L and W are the length and width of the rectangular metal raw material plate, K is the number of all types of blank parts to be cut, n i is the required quantity of each part, i is the serial number of the part type, 1≤i≤K; l k and W k is the length and width of the blank part; N is the number of single plates in the final overall optimized blanking solution, T j C is the number of times the raw material plate needs to be cut repeatedly according to the optimization plan for cutting the jth single board, j is the serial number of the single board in the final overall optimization cutting plan, 1≤j≤N; j is the total number of parts placed on the j-th single board solution, k is the number of parts R k The serial number, R k Name the rectangles where the parts are located. For the kth part placed on the jth board, k j is the serial number of the kth part arranged on the jth board. The coordinate of the lower left corner of each rectangle is (X k ,Y k ); The blank parts to be cut can be placed horizontally or vertically on the plate. The corresponding placement method is when P k =1(1≤k≤C j ), it means horizontal placement; when P k =0, 1≤k≤C j , when it means vertical placement; A ij A represents the number of the i-th type of parts in the j-th single board solution, ij ≤n i , 1≤i≤K, 1≤j≤N; l i is the length w of the blank part i is the width of the blank part; Formula (1) and formula (2) determine the placement interval of the blank parts; Formula (3) and (4) ensure that the parts will not exceed the boundaries of the raw material sheet within the placement interval, limiting the length and width; Formula (5) ensures that the blank parts will not overlap on the raw material plate; Formula (6) and (7) satisfy the quantity and matching requirements of all blank parts; Formula (9) is the objective function, which minimizes the area of ​​the wasted raw material sheet, that is, ensures that the utilization rate of the raw material sheet can reach the highest; Step 2 The particle swarm hybrid variable neighborhood search algorithm is as follows: Step 2.1, initialize the particle swarm, including the particle population size N, the position x of each particle i , speed v i and the maximum number of iterations T max , where the particle position information is obtained by using the blank part coordinates (X k ,Y k ) is determined by the error of the iteration process, where the blank part coordinates (X k ,Y k ) First, the placement interval is determined by equations (1) and (2), and then equations (3) and (4) are used to ensure that the parts will not exceed the boundary of the raw material plate within the placement interval; finally, equation (5) is used to ensure that the parts will not overlap; Step 2.2, using formula (9) in step 1 to calculate the utilization rate Fit[i] of this layout as the optimization target, and taking the area of ​​the raw material plate wasted in formula (9) as the optimization target so that the iteration direction is progressively toward the layout mode with the most material saving; Step 2.3, for each particle, use its utilization value Fit[i] and individual extreme value p best (i) Compare and update the individual extreme values ​​of particles; Step 2.4: For each particle, use its utilization value Fit[i] and the global extreme value g best (i) Compare and update the global extreme value of the entire population; Step 2.5, update the velocity and position of the particle; Step 2.6: Check whether the termination condition is met, that is, whether the maximum number of iterations T is reached max If it is not satisfied, jump to step 2.2; if it is satisfied, stop searching and take the updated global extreme value as the initial solution of variable neighborhood search. Let x best =g best ; Step 2.7, call variable neighborhood search for particles. The main search strategy is: define a series of neighborhood structures N K ,K=1,2,…,K max , so that the search density and search range of each neighborhood structure are different, and each module is executed sequentially. Once an intermediate solution that is better than the current one appears, the intermediate solution is used to replace the current solution, and this module is called to search again until a worse intermediate solution appears; otherwise, the next module is executed until the end; Step 2.8: Determine whether the end condition K is met according to step 2.7 <K max , that is, whether all neighborhood structures have been searched. If the termination condition is met, the algorithm terminates and outputs the optimal result; if the termination condition is not met, then go back to step 2.6; Step 2.9 outputs the global optimal value and the algorithm ends.

2. A two-dimensional arrangement method of metal sheets according to claim 1, characterized in that: Step 3: Design a layout plan by combining the constraint model with the particle swarm algorithm; Step 3.1, design particle position information; Step 3.2, particle position constraint design; Step 3.3, particle fitness function design.

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