Heuristic algorithm for one-dimensional blanking problem

Abstract

The invention provides a heuristic algorithm for a one-dimensional blanking problem, relates to the technical field of one-dimensional blanking, and aims to optimize a cutting scheme through an algorithm under the condition that a certain number of raw materials with a certain specification are given so as to minimize the consumption and waste of the raw materials and reduce the processing time at the same time. The invention aims to provide a new heuristic algorithm to solve the problem of one-dimensional blanking, and the algorithm avoids a local optimal solution and searches a global optimal solution by solving in turns, that is, material waste is reduced through reasonable cutting planning on the premise of meeting the requirement for the number of all parts. The method is different from traditional random combination, a violent exhaustion method, a genetic algorithm, an ant colony algorithm and other methods. According to the one-dimensional blanking method, in the process of the combined cutting mode, the determined direction is provided, namely the large-specification machining requirement of parts is preferentially met, but under some special conditions, only part of machining requirements are met, and all the requirements are gradually met through round iteration.

Description

Technical Field

[0001] The present invention relates to the technical field of one-dimensional cutting stock, and particularly to a heuristic algorithm for one-dimensional cutting stock problems. Background Art

[0002] The one-dimensional cutting stock problem, as a core challenge commonly existing in industrial production, material management, and resource allocation, involves how to maximize the material utilization rate, reduce waste and processing time through delicate cutting strategies under the given quantity and specifications of raw materials. The importance of this problem is self-evident, as it directly relates to the production cost and efficiency of enterprises.

[0003] In the actual production process, the solution to the one-dimensional cutting stock problem requires precise planning in advance. During the planning process, not only the different specifications and quantity requirements of parts need to be considered, but also a high material utilization rate should be achieved through a delicate cutting plan. This requires that each cutting plan must include a combination of various efficient and high material utilization rate cutting methods to ensure the maximization of the overall material utilization rate.

[0004] However, the solution to the one-dimensional cutting stock problem is not simple. Although the traditional linear programming algorithm can theoretically calculate all possible cutting methods and obtain the optimal solution through combinatorial operations, this method faces huge challenges in practical applications. With the increase in the quantity of raw materials, the variety of part specifications, and the demand, the time and computing resources required by the linear programming algorithm will show an explosive growth, which places extremely high requirements on the performance of the computer and is often unbearable in actual operations.

[0005] To overcome this problem, people have begun to try to use heuristic algorithms such as genetic algorithms, ant colony algorithms, and neural network algorithms. These algorithms attempt to find an approximate optimal solution to the problem within an acceptable time by simulating certain phenomena or processes in nature. However, these algorithms also face some problems, such as long computing time and the need to adjust model parameters multiple times, which to a certain extent limits their application in actual production. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a heuristic algorithm for one-dimensional cutting stock problems, achieving the purpose of short computing time and few adjustments of model parameters.

[0007] To solve the above technical problems, the technical solution of the present invention is: a heuristic algorithm for one-dimensional cutting stock problems, characterized by including the following steps:

[0008] S1. Import the required part specifications P i , quantity N i , raw material length, and the number of iterations C;

[0009] S2. Generate all cutting methods for a single piece of material, and record the quantity of each part required and the material utilization rate in the cutting methods;

[0010] S3. According to all cutting plans, sort and select the cutting methods according to the material utilization rate and part specification P i , where the sorting rules include: sort all the generated cutting methods according to the part specification size and material utilization rate; select the cutting methods for the first solution according to the sorting, and select this cutting method. The number of generated parts n i is less than or equal to the imported part quantity N i , and record the combination of cutting methods;

[0011] S4. Repeat S3. When the number of generated parts n i is less than or equal to the imported part quantity N i , finally obtain the solution to the one-dimensional blanking problem, and record the combination of the corresponding quantities of the cutting methods in S3 and S4;

[0012] S5. Repeat S3 and S4, and gradually reduce the material utilization rate or part specification P in S3 i , and first reduce the material utilization rate and then reduce the part specification P i , that is, perform iteration from top to bottom according to the sorting rules in S3;

[0013] S6. According to all the generated cutting plans, record the situation with the least amount of raw material used and generate a plan.

[0014] As a preferred embodiment of the invention, the generation and optimization of the cutting method in S2 further include the following steps:

[0015] Randomly generate the cutting methods of a single piece of material according to the part specification P i and the raw material length;

[0016] Record the material utilization rate and specific cutting method of each cutting method.

[0017] As a preferred embodiment of the invention, the sorting and selection in S3 further include:

[0018] The sorting and selection in S3 further include:

[0019] Sort in descending order of part specification P i as the main condition and in descending order of material utilization rate as the secondary condition;

[0020] Prioritize the combination of cutting methods with high material utilization rate and meeting the part quantity requirements.

[0021] In summary, the present invention has the following beneficial effects:

[0022] (1) In the present invention, through fine cutting plan planning and combined with an efficient cutting method combination, the present invention can significantly improve the utilization rate of raw materials, which means that enterprises can produce more products with the same amount of raw materials, thereby reducing production costs and improving economic benefits. Through fine cutting plan planning and combined with an efficient cutting method combination, the present invention can significantly improve the utilization rate of raw materials, which means that enterprises can produce more products with the same amount of raw materials, thereby reducing production costs and improving economic benefits;

[0023] (2) In the present invention, due to the improvement of material utilization rate, waste in the production process is effectively controlled. This not only saves raw material resources but also reduces the additional processing costs caused by waste, further enhancing the competitiveness of enterprises. Due to the improvement of material utilization rate, waste in the production process is effectively controlled. This not only saves raw material resources but also reduces the additional processing costs caused by waste, further enhancing the competitiveness of enterprises;

[0024] (3) In the present invention, the optimized algorithm adopted can generate high-quality cutting plans in a short time, improving the response speed and flexibility of the production line. This enables enterprises to respond more quickly to market changes and customer demands, enhancing market competitiveness;

[0025] (4) In the present invention, compared with traditional algorithms such as linear programming and brute-force exhaustive solution, the heuristic algorithm adopted in the present invention can significantly reduce the requirements for computer computing power on the premise of ensuring the solution quality. This enables users to deploy and apply optimization solutions at a lower cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for description in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0027] Figure 1 It is a schematic flowchart of a heuristic algorithm for a one-dimensional cutting problem provided by an embodiment of the present invention;

[0028] Figure 2 It is a schematic flowchart of a specific solution generated in the application of a heuristic algorithm for a one-dimensional cutting problem provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0029] The following will describe the technical solutions in the present invention with reference to the drawings.

[0030] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as an "example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of the word "example" is intended to present concepts in a specific manner. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two.

[0031] To make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0032] Since the computers used for human-computer interaction in the actual production process are often embedded touchscreens, in addition to human-computer interaction, they also need to perform motion control of the lower computer board cards. They do not have excellent computing performance and the operators often do not have enough patience. The present invention proposes a new algorithm that combines randomness and heuristics, which requires very little time and can obtain the optimal solution or an approximate optimal solution.

[0033] The main core idea of the present invention is to propose an optimal or sub-optimal solution mathematical model. By randomly generating and having a certain evolutionary ability of single-piece material cutting methods, and continuously trying to combine these single-piece material cutting methods according to human thinking to obtain the optimal or sub-optimal solution. However, when manually combining these cutting methods, there will be a situation where the quantity requirement of one type of part is satisfied first, and then the requirement of another type of part is satisfied. At the beginning, it may cause over-satisfaction of the part quantity, resulting in material waste.

[0034] If we do not start with the thinking of satisfying the quantity requirement of one type of part and try to combine the cutting methods, and each time we select a cutting method to satisfy a part of the part quantity requirement and try to combine, we can often just satisfy all the part quantity requirements after several times. And the optimal cutting plan is often composed of a certain number of combinations of many cutting methods with relatively high material utilization rate. The material utilization rate is often not the highest but relatively high, and the number is often not large or even only 1. Based on this thinking, it is easy to avoid the dilemma that various heuristic algorithms are prone to falling into local optimal solutions, thus obtaining the optimal solution.

[0035] Taking the processing of aluminum alloy profiles as an example, the mathematical model used in the present invention is as follows: Let the length of a single aluminum alloy profile be L, the upper limit of the number of sub-profiles be n, and now the number d i (i = 1, 2,..., n) of sub-profiles with a length of l i (i = 1, 2,..., n). Where L > max(l i ), i = 1, 2,..., n, x j$n_j$ is the number of repetitions of the $j$-th cutting method, where the upper limit of the number of repetitions is $p$, $j = 1, 2, \ldots, p$. Each cutting method represents the cutting situation of a piece of material, $A$ ij $x_{ij}$ is the number of the $i$-th part cut by the $j$-th cutting method, and $q$ represents the material consumption caused by each sawing machine cutting:

[0036]

[0037] The mathematical model proposed in the embodiment of the present invention allows small-scale multi-cutting. Most of the obtained sets of solutions are combinations of cutting methods with high utilization rates. Moreover, for the second formula of this mathematical model, that is, in the case of a large variety of specifications, large quantities, and uneven levels, there may be a situation where the cutting method of a randomly generated piece of material is incomplete. In this case, the mathematical model of the optimal solution will be enabled in the algorithm, resulting in slightly different selected symbols.

[0038] Refer to the attached Figure 1 illustrates a schematic flowchart of a heuristic algorithm for a one-dimensional material cutting problem provided by an embodiment of the present invention.

[0039] The embodiment of the present invention provides a heuristic algorithm for a one-dimensional material cutting problem, including the following steps:

[0040] Input the length of the raw material of one specification, the parts of different specifications and quantities.

[0041] For the cutting method of a piece of material, assign a quantity range to each part of different specifications, from 0 to the maximum value that can be cut by a single piece.

[0042] Generate the cutting method of a piece of material. Randomly select a specification and randomly assign a value within its quantity range. Repeat the above operation until the generation of the cutting method of a piece of material is completed. During the generation process of the intermediate cutting method, if it exceeds the length range of a single piece of material, decrease the quantity of the parts of this specification, so as to ensure that the cutting plan generated each time has a high material utilization rate. It is necessary to record the quantity of several parts finally generated by a piece of material and the overall material utilization rate. Repeat the above operation $N$ times, which is recorded as the total number of iterations $N$ at this stage.

[0043] Subsequently, obtain the optimal solution for generating all cutting methods by manually simulating and combining various cutting methods. Imagine an ordinary worker facing several cutting methods of a single piece of material. First, he will select the cutting methods with high material utilization rates for continuous attempts, which should not only just meet the processing requirements but also have a high material utilization rate. During the continuous attempts of the ordinary worker, it will be found that the optimal solution often consists of a combination of several cutting methods with high material utilization rates. And if the condition of just meeting the processing requirements is slightly broken, the global optimal solution can be quickly obtained. The combination method algorithm is described below:

[0044] Step 1: Confirm the maximum required part specification (i.e., the target part), sort the cutting methods according to the main condition as this part specification and the secondary condition as the part utilization rate, and continuously try this combination of cutting methods from top to bottom. During the combination of cutting methods, it must be ensured that the requirements less than this part specification can also be more satisfied, but not exceeded at this stage. At this time, the inequality sign in the second formula of the mathematical model proposed in the embodiment of the present invention must take the less than or equal to case.

[0045] Step 2: Meet the integer cutting method for parts with a secondary part specification and that can meet other parts with a specification smaller than this part. This method requires giving priority to using the cutting method that consumes the largest quantity of this part specification, and secondly, the cutting method with the highest material utilization rate. This cutting method must satisfy that there is no excessive cutting during the previous cutting. The quantity of parts with a larger specification can be incompletely cut (i.e., the required quantity of parts d i can be greater than 0), and the requirements of other parts with a specification different from this part specification should be more satisfied. In Step 2, try to find a way that can be completely cut as much as possible, that is, the parts with a smaller specification can just meet the cutting requirements, and exit when just satisfied. The maximum number of iterations is the sum of the number of cutting methods with a positive quantity of the largest part specification among all the generated cutting methods.

[0046] Step 3: Iterate Step 2 multiple times. Each iteration is carried out in rounds from the largest to the smallest according to the target part specification. When Step 2 iterates to the smallest specification part or all cutting requirements have been completed, the first round of iteration is completed. If the cutting target is completed at this time, record the material utilization rate and specific cutting method of each cutting method in this solution in detail.

[0047] Step 4: For the remaining uncompletely cut profiles, repeat Steps 2 and 3. Still, first meet the requirements of the large - specification parts. At this time, relax the iteration conditions for selecting the cutting method, and give priority to the case of complete cutting. If it cannot be satisfied, allow a minimum degree of excessive cutting of the parts, that is, when the larger parts must be completely cut, the smaller parts can have a small amount of excessive cutting. Record the material utilization rate and specific cutting method of each cutting method in this cutting solution. At this time, the inequality sign in the second formula of the mathematical model proposed in the embodiment of the present invention must take the greater than or equal to case.

[0048] Step 5: Reduce the number of repetitions in the cutting methods in Step 2, and repeat Steps 2 - 4.

[0049] Step 6: Select the cutting method with the lowest consumption quantity of sub - profiles and the lowest material utilization rate, and repeat Steps 2 - 5.

[0050] Step 7: Finally, select the optimal solution.

[0051] Since the embodiment of the present invention adopts a randomly generated cutting method in the first part of the specific algorithm, when there are many specifications and a large number of parts required, the set number of iterations N may not be able to generate all cutting solutions, which may ultimately result in the inability to obtain an optimal solution, and the emergence of a near-optimal solution, with some parts being cut multiple times. In this case, it is necessary to increase the number of iterations or re-enable the algorithm and make manual decisions based on actual conditions.

[0052] In order to more clearly express the technical solution of the present invention, a one-dimensional cutting problem will be answered in more detail below to more clearly illustrate the specific implementation process of the algorithm proposed in the present invention.

[0053] Example 1: Assuming the raw material length is L = 1000, the required part specifications and quantity are shown in the following table, the sawing loss q = 0, and the total number of iterations N is 5000:

[0054] i 1 2 3 4 5 <![CDATA[l i > 128 247 290 321 512 <![CDATA[d i > 8 22 6 12 5

[0055] 75 cutting methods are randomly generated before the combination algorithm:

[0056] In the present invention, any combination of cutting methods is performed from top to bottom in order. Before step 4 of the algorithm, the second formula in the mathematical model must be strictly satisfied to be less than or equal to 0, that is, the remaining parts requirement must be greater than or equal to 0. In this example:

[0057] According to step 1, sort by maximum specification as the primary condition and material utilization rate as the secondary condition, select the first cutting method from the generated cutting methods (if it does not meet the optimal solution, select the next one), and select this cutting method 5 times (if it does not meet the optimal solution, reduce the number of times).

[0058] According to step 2, the specifications mentioned in step 1 are the main conditions, and the material utilization rate is the secondary condition. The first cutting method is selected from the generated cutting methods (if it does not meet the optimal solution, select the next one), and this cutting method is selected twice (if it does not meet the optimal solution, reduce the number of times).

[0059] Step 3: Repeat step 2 multiple times until the remaining demand is 1 part with a specification of 321, 2 parts with a specification of 247, and 1 part with a specification of 128. At this time, the second formula in the mathematical model is still strictly satisfied, that is, the remaining part demand must be greater than or equal to 0. Select from top to bottom until the 36th cutting method is just satisfied, and the remaining required parts quantity is all 0. At this point, the solution of this example is completed.

[0060] The solution obtained by applying the heuristic algorithm proposed in the embodiment of the present invention is 15, and the overall material utilization rate is 97.4%. The solution is shown in the following table:

[0061]

[0062]

[0063] Refer to the attached instruction manual Figure 2 , which shows a specific process schematic diagram of the solution generated in the application of a heuristic algorithm for a one-dimensional blanking problem provided by an embodiment of the present invention.

[0064] The beneficial effects brought by the technical solution provided by the embodiment of the present invention at least include:

[0065] (1) In the present invention, through fine cutting plan planning and combined with an efficient cutting method combination, the present invention can significantly improve the utilization rate of raw materials, which means that enterprises can produce more products with the same amount of raw materials, thereby reducing production costs and improving economic benefits. Through fine cutting plan planning and combined with an efficient cutting method combination, the present invention can significantly improve the utilization rate of raw materials, which means that enterprises can produce more products with the same amount of raw materials, thereby reducing production costs and improving economic benefits;

[0066] (2) In the present invention, due to the improvement of material utilization rate, the waste phenomenon in the production process is effectively controlled. This not only saves raw material resources, but also reduces the additional processing costs caused by waste, further enhancing the competitiveness of enterprises. Due to the improvement of material utilization rate, the waste phenomenon in the production process is effectively controlled. This not only saves raw material resources, but also reduces the additional processing costs caused by waste, further enhancing the competitiveness of enterprises;

[0067] (3) In the present invention, the optimized algorithm adopted can generate high-quality cutting plans in a short time, improving the response speed and flexibility of the production line. This enables enterprises to respond more quickly to market changes and customer needs, enhancing market competitiveness;

[0068] (4) In the present invention, compared with traditional linear programming algorithms, brute-force enumeration solutions, genetic algorithms, etc., especially in the case of non-integer solutions that may occur in linear programming algorithms, the heuristic algorithm adopted by the present invention can significantly reduce the requirements for computer computing power on the premise of ensuring the solution quality. This enables enterprises to deploy and apply optimized solutions at a lower cost.

[0069] As mentioned above, the above are only the specific implementation manners of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claimed rights.

[0070] The following points need to be explained:

[0071] (1) The accompanying drawings of the embodiments of the present invention only relate to the structures involved in the embodiments of the present invention, and other structures can be referred to the general design.

[0072] (2) For clarity, in the accompanying drawings used to describe the embodiments of the present invention, the thickness of layers or regions is enlarged or reduced, that is, these drawings are not drawn to actual scale. It can be understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element can be "directly" on or under the other element or there can be intervening elements.

[0073] (3) Without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0074] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A heuristic algorithm for the one-dimensional cutting stock problem, characterized in that: The steps include: S1. Import the required parts specifications P i 、Number i , raw material length and number of iterations C; S2. Generate all cutting methods for a single material and record the quantity and material utilization rate of each part in the cutting method; S3. According to all cutting plans, according to material utilization and part specifications P i , sorting and selecting the cutting methods, the sorting rules include: sorting all the generated cutting methods according to the size of the parts and the material utilization rate; selecting the cutting method according to the sorting for the first solution, and selecting the cutting method, the number of parts generated n i Less than or equal to the number of imported parts N i , record the combination of cutting methods; S4, repeat S3, the number of parts generated is n i Less than or equal to the number of imported parts N i , and finally obtain the solution to the one-dimensional cutting problem, and record the combination of cutting method × corresponding quantity in S3 and S4; S5, repeat S3 and S4, gradually reduce the material utilization rate or part specifications P in S3 i , and first reduce material utilization and then reduce part specifications P i , that is, iterate from top to bottom according to the sorting rules in S3; S6. Based on all the generated cutting plans, record the situation where the least amount of raw materials is used and generate a plan.

2. A heuristic algorithm for a one-dimensional cutting stock problem according to claim 1, characterized in that: The generation and optimization of the cutting mode of S2 further comprises the following steps: According to part specification P i and raw material length, randomly generate cutting methods for single material; Record the material utilization and specific cutting methods for each cutting method.

3. A heuristic algorithm for a one-dimensional cutting stock problem according to claim 1, characterized in that: The sorting and selection in S3 further includes: According to part specification P i Sort by the main condition from large to small and the secondary condition from high to low material utilization rate; Prioritize the combination of cutting methods that have high material utilization and meet the number of parts required.

4. The heuristic algorithm for the one-dimensional cutting stock problem according to claim 1, characterized in that: Also includes: Set the repetition threshold to limit the number of repetitions for each cutting method.

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