A circular parts arrangement method based on sequence perturbation operator

Abstract

A circular parts layout method based on a sequence perturbation operator is mainly used to solve the circular parts layout problem of sheet metal materials. The method executes a search loop in a multi-starting manner. In each loop, based on the current number of circular parts, the algorithm first randomly generates an initial solution and performs local optimization on it; then, a dynamic threshold search method is executed to optimize the mathematical optimization model; when the dynamic threshold search method obtains a legal solution, the number of circular parts is increased by 1, and then the next cycle is re-executed; when the dynamic threshold search algorithm fails to find a legal solution under known conditions, an initial solution is randomly generated and the next cycle is entered. The present invention can obtain a high-quality circular parts layout within an acceptable time range, so that the utilization rate of sheet metal materials can be maximized as much as possible, reducing material waste, thereby generating certain economic benefits.

Description

Technical Field

[0001] The invention relates to the field of industrial circular layout, and in particular to a circular parts layout method based on a sequence perturbation operator. Background Art

[0002] With the rapid development of the economy, in the process of industrial production, it is very common to cut the required plates on the basis of large raw materials. A large part of the raw materials will be wasted due to unscientific cutting methods, which will relatively increase unnecessary costs and reduce economic benefits. At this time, the strategy of cutting came into being - nesting technology, and circular nesting technology occupies an important part of the nesting technology. The nesting problem refers to placing the graphics to be nested in a suitable way under given nesting boundaries and constraints, with compactness as the optimization goal. The practical application of the nesting problem is very wide. The raw materials and objects to be arranged in this problem are only abstract concepts. The raw materials can be plates, ground space, layouts, glass, etc., and the objects to be arranged can be parts cut from the plates, article fonts on the layout, glass plates in specific applications, etc. Therefore, the nesting problem is widely present in production activities such as sheet metal cutting, clothing cutting, newspaper layout, and cargo packing. The circular parts nesting problem is widely used in real life, so the circular parts nesting problem is also the basis of the nesting problem. Therefore, solving the problem of circular parts arrangement brings certain benefits to industrial production and people's daily life.

[0003] The circular parts nesting problem is a classic NP-hard problem with high complexity. There is no recognized optimal solution algorithm at present. The current solution idea is to use a heuristic algorithm to find the optimal solution or an approximate optimal solution, and hope that the approximate optimal solution is infinitely close to the optimal solution. The circular parts nesting problem is divided into equal circle nesting problem and unequal circle nesting problem. Many scholars have proposed a large number of methods to solve such problems, and have achieved certain results with the help of computer technology. Regarding the cutting problem of sheet metal, the traditional method of relying on engineers to manually operate the nesting on CAD software cannot reasonably plan the sheet metal materials, the nesting efficiency is low and the effect is not good, and as the number of circular parts to be nested increases, the time consumed increases accordingly, and it cannot adapt to the requirements of real-time product updates in a timely manner.

[0004] In daily life, some materials used for sheet metal cutting are not regular. Regarding the problem of equal-circle patterning of convex polygonal sheet metal materials, how to reasonably cut these sheet metal materials to maximize the utilization of materials and avoid unnecessary material waste is an optimization problem that needs to be solved. Summary of the invention

[0005] The purpose of the present invention is to propose a circular parts layout method based on an intelligent perturbation operator, which is used to solve the circular parts layout problem of sheet metal materials in industry, improve the utilization rate of materials and avoid waste.

[0006] A circular parts arrangement method based on a sequence perturbation operator comprises the following steps:

[0007] Step 1, input the shape parameters of the sheet metal material and the number N and radius r of the circular parts;

[0008] Step 2, randomly generating an initial layout based on the number of circular pieces and the shape of the material plate;

[0009] Step 3, perform a local search procedure on the initial layout, obtain the local optimal solution and use it as the current solution S0;

[0010] Step 4: Set the calculation deadline to T max , when the running time does not reach T max When the running time reaches T max When , go to step 7;

[0011] Step 5, executing a dynamic threshold search algorithm on the current solution S0, the steps of the dynamic threshold search algorithm are as follows;

[0012] Step 5.1, input the current solution S0, set the value of the maximum number of iterations MaxIter, set the value of the current disturbance intensity K and the value of the receiving threshold Th, and set the value of the current number of iterations Iter to 0;

[0013] Step 5.2, compare the values ​​of Iter and MaxIter. If Iter is less than the value of MaxIter, go to step 5.3; if Iter is greater than the value of MaxIter, go to step 5.6;

[0014] Step 5.3, execute the sequence perturbation program, perturb the current solution S0 with the perturbation intensity K, and obtain the perturbation solution S1;

[0015] Step 5.4, use the local search procedure in step 3 to perform local search on the perturbation solution S1 to obtain the local optimal solution S2;

[0016] Step 5.5, calculate the potential energy function value F0 of solution S0 and the potential energy function value F2 of solution S2, calculate the difference ΔF between F2 and F0, that is, ΔF = F2-F0. If the value of ΔF is less than the receiving threshold Th, then accept solution S2, that is, replace the current solution S0 with solution S2, and go to step 5.2, and increase the value of the number of reception times N_accept by 1, that is, N_accept←N_accept+1; if the value of ΔF is greater than the receiving threshold Th, refuse to accept the perturbation solution S2, indicating that the current solution has not been improved, and go to step 5. .2, and increase the number of rejections N_reject by 1, that is, N_reject←N_reject+1; if the number of acceptances N_accept is greater than the number of rejections p*N_reject, where p is the acceptance parameter, then reduce the acceptance threshold Th, that is, Th←Th*θ; if the number of acceptances N_accept is less than the number of rejections p*N_reject, then increase the acceptance threshold Th, that is, Th←Th / θ, where θ∈(0,1), and finally, increase the value of the current iteration number Iter by 1;

[0017] Step 5.6, the dynamic threshold search procedure ends, and the best solution obtained is recorded as S*;

[0018] Step 6, determine whether the solution S* is a legal solution. If the potential energy function value F(S*)=0, it means it is a legal solution, increase the number of circular pieces by 1, and go to step 2; otherwise, it means the optimal solution S* is not a legal solution, and go to step 2;

[0019] Step 7, running time reaches T max , the process ends and the optimal solution is output.

[0020] Furthermore, the local search procedure described in step 3 adopts a quasi-Newton algorithm, which is a continuous optimization algorithm whose goal is to find the nearest local optimal solution for the input solution.

[0021] Furthermore, the sequence perturbation operator described in step 5.3 is an iterative perturbation process, and its specific steps are as follows:

[0022] Step 5.3.1: Input the current solution S0 and perturbation intensity K, and set the maximum perturbation depth It max , set the value of the disturbance intensity scaling factor α, and set the current disturbance depth It to 0;

[0023] Step 5.3.2: Perform a perturbation operation with strength K on the current solution S0, and perform a perturbation operation on the solution X = (x 1 ,y 2 ,…,x i ,y i ,…x N ,y N) is uniformly randomly perturbed in a certain interval (-K, K), that is, X[l]←X[l]+rand(-K, K)(1≤l≤2N), and the perturbation solution S0′ is obtained, where (x i ,y i ) is the center coordinate of unit circle i, rand(-K,K) represents a random number in the interval (-K,K);

[0024] Step 5.3.3: Perform m-step local search operations on the perturbed solution S0′, where each local search operation moves the step size along the negative gradient direction of the objective function g is the gradient of the objective function, and the perturbation solution S0″ is obtained. Let K = K*α, and the value of the variable It is increased by 1;

[0025] Step 5.3.4: Compare It and It max If <It max , go to step 5.3.2; if It≥It max , the perturbation procedure ends and the perturbation solution S1 is output.

[0026] The beneficial effects of the present invention are as follows: the circular parts layout method based on the sequence perturbation operator proposed by the present invention improves the utilization rate of raw materials and avoids waste by continuously iterating to find the optimal circular layout state. In the process of finding the optimal layout, the method can easily jump out of the local optimal trap on the one hand; on the other hand, it increases the adaptability of the algorithm and can adapt to the circular layout problems of sheet metal materials of different specifications, and has a wider range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of problem modeling based on pentagonal sheet metal material in an embodiment of the present invention.

[0028] Figure 2 It is an overall flow chart of the circular parts arrangement method in an embodiment of the present invention.

[0029] Figure 3 is a flow chart of a dynamic threshold search algorithm in an embodiment of the present invention.

[0030] Figure 4 4 is a flow chart of a sequence perturbation operator method in an embodiment of the present invention.

[0031] Figure 5 This is the optimal arrangement diagram of circular parts in the test example of the embodiment of the present invention. DETAILED DESCRIPTION

[0032] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0033] Figure 1This is a schematic diagram of modeling the circular parts arrangement problem according to an embodiment of the present invention, and its implementation process is as follows:

[0034] First, the sheet metal material to be cut is converted into a simple convex polygon area. The shape to be cut is a circular part. The following takes a regular pentagon area as an example, and then a mathematical model is established for it: the information of the regular pentagon area is converted into Figure 1 The regular pentagon formed by the five points A, B, C, D, and E in the figure is a regular pentagon. The center of the regular pentagon is placed at the origin (0,0), the horizontal direction is the x-axis, and a Cartesian coordinate system is established with the center of the circle as (x i ,y i ), N small circles (i=1, 2, ..., N) with a radius of r are used to fill the regular pentagonal area.

[0035] The mathematical model can be written as follows:

[0036]

[0037]

[0038]

[0039] Among them, F(x) represents the potential energy function, N represents the number of small circles, i and j (i≠j) represent two different small circles, (x i ,y i ),(x j ,y j ) are the center coordinates of small circle i and small circle j, M is the number of vertices in the convex polygon area, that is, the number of edges in the convex polygon area, d ij represents the overlapping depth between small circle i and small circle j, d ij = 0 means that there is no overlap between small circle i and small circle j, d ik represents the overlapping depth between small circle i and the kth edge, d ik =0 means there is no overlapping part between small circle i and the kth edge, where a, b, c are the parameters corresponding to the equation of each edge.

[0040] This method proposes a circular parts layout method based on a sequence perturbation operator to solve the problem of circular parts layout of sheet metal materials in industry. Figure 2 As shown, the method mainly comprises the following steps:

[0041] Step 1, input the shape parameters of the sheet metal material (the shape parameters specifically refer to the number of vertices M of the convex polygon area in the above mathematical model and the coordinate information of the vertices and the center origin after the Cartesian coordinate system is established) and the number N and radius r of the circular parts;

[0042] Step 2: randomly generate an initial layout based on the number of circular pieces and the shape of the material plate.

[0043] Step 3: Perform a local search procedure on the initial layout to obtain the local optimal solution and use it as the current solution S0.

[0044] Wherein, in step 3, a local search procedure is executed, and the local search procedure adopts a quasi-Newton algorithm, wherein the quasi-Newton algorithm is a continuous optimization algorithm, and the goal is to find the nearest local optimal solution for the input solution. The algorithm is an efficient local search method and has been widely used in the optimization of differentiable functions.

[0045] Step 4: Set the calculation deadline T max The value is 120 minutes. When the running time does not reach T max When the running time reaches T max , go to step 7.

[0046] Step 5: Execute the dynamic threshold search algorithm on the current solution S0, such as Figure 3 As shown, the specific steps of the dynamic threshold search algorithm are as follows:

[0047] Step 5.1, input the current solution S0, set the maximum number of iterations MaxIter to 10000, set the current disturbance intensity K to 0.8, set the receiving threshold Th to 0.1, and set the current number of iterations Iter to 0.

[0048] Step 5.2, compare the values ​​of Iter and MaxIter. If Iter is less than the value of MaxIter, go to step 5.3; if Iter is greater than the value of MaxIter, go to step 5.7.

[0049] Step 5.3, execute the sequence perturbation operator program, perturb the current solution S0 with the perturbation intensity K, and obtain the perturbation solution S1.

[0050] Among them, the intelligent perturbation operator process described in step 5.3 is as follows Figure 4 As shown, the following steps are included:

[0051] Step 5.3.1: Input the current solution S0 and perturbation intensity K, and set the maximum perturbation depth It max The value of is 20000, the value of the disturbance intensity scaling factor parameter α is set to 0.9, and the current disturbance depth It is set to 0.

[0052] Step 5.3.2: Perform a perturbation operation with strength K on the current solution S0, and perform a perturbation operation on the solution X = (x 1 ,y 2 ,…,x i ,yi ,…x N ,y N ) is uniformly randomly perturbed in a certain interval (-K, K), that is, X[l]←X[l]+rand(-K, K)(1≤l≤2N), and the perturbation solution S0′ is obtained, where (x i ,y i ) is the center coordinate of the unit circle i, and rand(-K,K) represents a random number in the interval (-K,K).

[0053] Step 5.3.3: Perform m-step local search operations on the perturbed solution S0′, where m is set to 4 and each local search operation moves the step length along the negative gradient direction of the objective function. g is the gradient of the objective function, and the perturbation solution S0″ is obtained. Let K = K*α, and the value of the variable It increases by 1.

[0054] Step 5.3.4: Compare It and It max If <It max , go to step 5.3.2; if It≥It max , the perturbation procedure ends and the perturbation solution S1 is output.

[0055] Step 5.4, use the local search procedure in step 3 to perform local search on the perturbation solution S1 to obtain the local optimal solution S2.

[0056] Step 5.5, calculate the potential energy function value F0 of solution S0 and the potential energy function value F2 of solution S2, calculate the difference ΔF between F2 and F0, that is, ΔF=F2-F0. If the value of ΔF is less than an acceptance threshold Th, then accept solution S2, that is, replace the current solution S0 with solution S2, and go to step 5.2, and increase the value of the number of acceptance times N_accept by 1, that is, N_accept←N_accept+1. Otherwise, refuse to accept the perturbation solution S2, indicating that the current solution has not been improved, and go to step 5.2; and increase the number of rejections N_reject by 1, that is, N_reject←N_reject+1. If the number of acceptance times N_accept is greater than the number of rejections p*N_reject, p is a reception parameter, then reduce the acceptance threshold Th, that is, Th←Th*θ. Otherwise, increase the acceptance threshold Th, that is, Th←Th / θ, where θ∈(0,1). Finally, increase the value of the current number of iterations Iter by 1.

[0057] Step 5.6, the dynamic threshold search procedure ends, and the best solution obtained is recorded as S*.

[0058] Step 6, determine whether the solution S* is a legal solution. If the potential energy function value F(S*) = 0, it means it is a legal solution. Increase the number of circular parts by 1 and go to step 2; otherwise, it means that the optimal solution S* is not a legal solution and go to step 2.

[0059] Step 7: The algorithm running time reaches T max When , the algorithm ends and outputs the optimal solution.

[0060] The optimal arrangement diagram of circular parts in the test example of the embodiment of the present invention is as follows Figure 5 shown.

[0061] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A circular parts arrangement method based on a sequence perturbation operator, characterized in that: The method comprises the following steps: Step 1, input the shape parameters of the sheet metal material and the number N and radius r of the circular parts; Step 2, randomly generating an initial layout based on the number of circular pieces and the shape of the material plate; Step 3, perform a local search procedure on the initial layout, obtain the local optimal solution and use it as the current solution S0; Step 4: Set the calculation deadline to T max , when the running time does not reach T max When the running time reaches T max When , go to step 7; Step 5, executing a dynamic threshold search algorithm on the current solution S0, the steps of the dynamic threshold search algorithm are as follows; Step 5.1, input the current solution S0, set the value of the maximum number of iterations MaxIter, set the value of the current disturbance intensity K and the value of the receiving threshold Th, and set the value of the current number of iterations Iter to 0; Step 5.2, compare the values ​​of Iter and MaxIter. If Iter is less than the value of MaxIter, go to step 5.3; if Iter is greater than the value of MaxIter, go to step 5.6; Step 5.3, execute the sequence perturbation program, perturb the current solution S0 with the perturbation intensity K, and obtain the perturbation solution S1; the sequence perturbation program described in step 5.3 is an iterative perturbation process, and its specific steps are as follows: Step 5.3.1: Input the current solution S0 and perturbation intensity K, and set the maximum perturbation depth It max , set the value of the disturbance intensity scaling factor α, and set the current disturbance depth It to 0; Step 5.3.2: Perform a perturbation operation of strength K on the current solution S0, and perturb the solution X = (x1, y2, ..., x i ,y i ,…x N ,y N ) is uniformly randomly perturbed in a certain interval (-K, K), that is, X[l]←X[l]+rand(-K, K)(1≤l≤2N), and the perturbation solution S0′ is obtained, where (x i ,y i ) is the center coordinate of unit circle i, rand(-K,K) represents a random number in the interval (-K,K); Step 5.3.3: Perform m-step local search operations on the perturbed solution S0′, where each local search operation moves the step size along the negative gradient direction of the objective function g is the gradient of the objective function, and the perturbation solution S0″ is obtained. Let K = K*α, and the value of the variable It is increased by 1; Step 5.3.4: Compare It and It max If <It max , go to step 5.3.2; if It≥It max , the perturbation procedure ends and the perturbation solution S1 is output; Step 5.4, use the local search procedure in step 3 to perform local search on the perturbation solution S1 to obtain the local optimal solution S2; Step 5.5, calculate the potential energy function value F0 of solution S0 and the potential energy function value F2 of solution S2, calculate the difference ΔF between F2 and F0, that is, ΔF = F2-F0. If the value of ΔF is less than the receiving threshold Th, then accept solution S2, that is, replace the current solution S0 with solution S2, and go to step 5.2, and increase the value of the number of reception times N_accept by 1, that is, N_accept←N_accept+1; if the value of ΔF is greater than the receiving threshold Th, refuse to accept the perturbation solution S2, indicating that the current solution has not been improved, and go to step 5. .2, and increase the number of rejections N_reject by 1, that is, N_reject←N_reject+1; if the number of acceptances N_accept is greater than the number of rejections p*N_reject, where p is the acceptance parameter, then reduce the acceptance threshold Th, that is, Th←Th*θ; if the number of acceptances N_accept is less than the number of rejections p*N_reject, then increase the acceptance threshold Th, that is, Th←Th / θ, where θ∈(0,1), and finally, increase the value of the current iteration number Iter by 1; Step 5.6, the dynamic threshold search procedure ends, and the best solution obtained is recorded as S*; Step 6, determine whether the solution S* is a legal solution. If the potential energy function value F(S*)=0, it means it is a legal solution, increase the number of circular pieces by 1, and go to step 2; otherwise, it means the optimal solution S* is not a legal solution, and go to step 2; Step 7, running time reaches T max , the process ends and the optimal solution is output.

2. The circular parts arrangement method based on the sequence perturbation operator according to claim 1, characterized in that: The local search procedure described in step 3 adopts the quasi-Newton algorithm, which is a continuous optimization algorithm whose goal is to find the nearest local optimal solution for the input solution.

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