Rectangular layout optimization method considering excess material utilization optimization

Abstract

The invention relates to a rectangular layout optimization method considering excess material utilization optimization. The method mainly comprises the following steps: 1, establishing a mixed integer rectangular layout mathematical model; 2, coding the rectangular pieces to form a sequence in an arrangement order, obtaining a set of layout solutions of the rectangular pieces, and reading residual material library information; 3, determining the arrangement positions of the rectangular pieces in the layout solution set through an improved lowest horizontal line search algorithm, evaluating the arrangement result through a fitness function, optimizing the arrangement sequence of the rectangular pieces through an improved adaptive genetic algorithm, and iterating the layout sequence of the rectangular pieces; and 4, outputting an optimal stock layout scheme, storing the remaining materials, and updating the remaining material library. According to the method provided by the invention, the layout efficiency can be improved, and the excess materials are effectively utilized for layout, so that the material utilization rate of layout plates is improved.

Description

Technical Field

[0001] The invention relates to a rectangular layout method, more specifically to a rectangular layout optimization method considering the optimization of residual material utilization. Background Art

[0002] With the continuous rise of labor and environmental costs in my country, and the increasing individual needs of consumers, more and more custom furniture companies are investing more production costs in modern production lines and digital technologies to carry out digital design and flexible production in order to improve their market competitiveness. Therefore, it is of great significance for companies to control production costs under fierce market competition. Layout is the primary process of panel furniture production and processing. Reasonable layout results will increase the utilization rate of panels and reduce the cost of raw materials. In addition, the rational use of waste materials is also an important way to improve the utilization rate of panels.

[0003] Researchers have conducted a lot of research on the rectangular piece arrangement problem. At present, most of them divide the problem into two parts: the arrangement layout strategy and the arrangement order of rectangular pieces. At present, the arrangement layout strategy mostly uses heuristic algorithms; the rectangular piece arrangement order mostly uses some intelligent optimization algorithms that simulate evolutionary ideas, biological group behavior laws or natural phenomena to search and solve the arrangement order, such as genetic algorithms (GA), ant colony algorithms (ACO), simulated annealing algorithms (SA), etc. In summary, the solution method that combines intelligent optimization algorithms with heuristic algorithms is one of the popular research directions of rectangular piece arrangement.

[0004] At present, furniture companies have begun to pay attention to the utilization of waste materials, and have made certain progress in the information management and intelligent storage and retrieval technology of waste materials. However, there is still little research on the layout of panel furniture waste materials. The author conducted in-depth research on furniture companies and found that a large number of large-scale usable board waste materials are generated in the cutting process of panel furniture production. Most companies still use manual experience to layout the waste materials, resulting in a low utilization rate of waste materials.

[0005] In view of the above situation, this paper studies the layout problem of panel furniture considering surplus materials based on the surplus material utilization needs of a furniture company in Zhejiang Province, and studies the surplus material utilization strategy. When applying the improved adaptive genetic algorithm to optimize the layout sequence, the improved heuristic algorithm is used to decode the layout sequence to improve the utilization rate of materials. Summary of the invention

[0006] Purpose of the invention: In view of the fact that the existing technology cannot meet the requirements of waste material utilization in panel furniture layout under industrial mass production, a rectangular layout optimization method that takes waste material utilization into consideration is proposed through research on this problem. The placement order of rectangular parts is optimized by improving the adaptive genetic algorithm. At the same time, by improving the lowest horizontal line search algorithm, the lowest and highest double horizontal lines and the placement evaluation function are considered to more efficiently determine the placement positions of rectangular parts in the layout solution set. The waste material is effectively utilized in combination with the waste material utilization strategy, thereby improving the material utilization rate of the layout board material.

[0007] Technical solution: The rectangular layout optimization method considering the optimization of waste material utilization described in the present invention comprises the following steps:

[0008] Step 1: Establish a mixed integer rectangular pattern mathematical model;

[0009] Step 2: Encode the rectangular parts to form a sequence of arrangement order, obtain a set of rectangular parts arrangement solutions, and read the residual material library information;

[0010] Step 3: Determine the placement position of the rectangular pieces in the packing solution set by improving the lowest horizontal line search algorithm, evaluate the placement result by the fitness function, and optimize the placement order of the rectangular pieces by improving the adaptive genetic algorithm, and iterate the packing order of the rectangular pieces;

[0011] Step 4: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

[0012] Furthermore, the specific method of mathematical modeling in step 1 is:

[0013] Step 1.1: Assume that the length of the original sheet is L, the width of the original sheet is W, and n rectangular pieces {p1, p2, ···, p i ,···,p n}, the length of the i-th rectangular piece is represented by l i , the width of the i-th rectangular piece is denoted as w i , whether the i-th rectangular piece is rotatable is represented by r i , N represents the total number of original pieces required, the number of types of rectangular pieces to be arranged is t, and the number of i-type rectangular pieces arranged by the rectangular original pieces is represented by n i ;

[0014]

[0015] Step 1.2: The length and width of the rotated rectangle are represented as l i ',w i ';

[0016]

[0017] Step 1.3: Establish a two-dimensional rectangular coordinate system with the lower left corner of the original sheet as the origin, the width direction as the x-axis, and the width direction as the y-axis. Each rectangular piece to be arranged takes the lower left corner as the initial point;

[0018] Step 1.4: Establish a mixed integer programming model with the maximum plate utilization as the objective function. The objective function is:

[0019]

[0020] Step 1.5: The constraints of the mathematical model are expressed as:

[0021]

[0022] Among them, formula (5-1) means that each rectangular piece is placed orthogonally to the plate; formula (5-2) means that there is no overlap between the rectangular pieces; formulas (5-3) and (5-4) mean that the length and width of the rectangular pieces do not exceed the length and width of the plate.

[0023] Furthermore, the step 2 is specifically as follows:

[0024] Step 2.1: First, number all rectangular pieces. The sequence of numbers of all rectangular pieces is a feasible solution for the arrangement. Each number id corresponds to a unique rectangular piece. The numbering order of the sequence represents the arrangement order of the rectangular pieces. Using decimal coding, the number of rectangular pieces n, and then assigning positive and negative signs to each rectangular piece. The positive sign indicates direct placement, and the negative sign indicates placement after rotating 90°. Then the overall coding method is: S = {p1, p2, ... p i ,...,p n}, where p i ∈(-n,n),i∈(1,n);

[0025] Step 2.2: Refer to step 2.1 to encode the remaining materials in the remaining material library, and generate the corresponding variable code S'={xp1, xp2, ... xp i ,...,xp n}, xp i =0 or 1.

[0026] Step 2.3: Initialize the population G, population size P num , Max number of evolutionary iterations g ; Set the evolution end condition.

[0027] Furthermore, the specific method of step 3 is:

[0028] Step 3.1: Initialize the horizontal line set L, which has only one horizontal contour line with a height of 0, which is the bottom boundary of the plate;

[0029] Step 3.2: Place the rectangular pieces one by one according to the coding sequence. If the current rectangular piece needs to be rotated during the placement process, swap the width and height information of the rectangular piece for placement;

[0030] Step 3.3: Discharge the plate p each time i Get the lowest horizontal line l from the horizontal line set min The width and height of the area to be placed. If there are multiple segments, select the leftmost horizontal line, and then determine whether the width of the placement area on the horizontal line is greater than or equal to the width of the rectangular piece to be placed:

[0031] Case 1) If the width of the area on the horizontal line is greater than the width of the rectangular piece to be arranged, the rectangular piece is placed in this area and the highest horizontal line l in the horizontal line set after arrangement is updated. max If l max If the height W of the original sheet increases or exceeds it, find a rectangular piece with a width that matches the horizontal line from the previously placed rectangular pieces. If there is no rectangular piece that meets the conditions, place them in the order of the original sequence, update the horizontal line set and go to step 3.3; if there are multiple rectangular pieces that meet the conditions, select rectangular pieces from the leftmost side, exchange their positions, and compare the l before and after the exchange. max and place P score , and then select other rectangular pieces in turn to perform the same steps. max To lower, press (l max Minimum>P score The highest priority is selected for exchange, and the horizontal line set L and the arrangement sequence are updated. The order of other arranged rectangular pieces remains unchanged. If the exchange before and after l max If unchanged, place them in the original sequence. score Value selection rules (a. If h i <h l ∨h i <h r ∨w i <w c , P score +=0; b. If h i >h l ∨h i >h r , P score +=1; c. If h i =h l ∨h i =h r ∨w i =w c , P score + = 2);

[0032] Case 2) If the width of the area on the horizontal line is less than the width of the rectangular piece to be arranged, search for a rectangular piece that meets the placement conditions after the rectangular piece in the encoding sequence S. If there is a rectangular piece whose width is equal to the width of the area on the horizontal line, prioritize the placement of the rectangular piece and update the horizontal line set L; if there is no rectangular piece with the same width, search for a rectangular piece that meets the placement conditions from the position after the rectangular piece in the sequence S, and select P score The highest rectangular piece is placed at this position, and the arrangement sequence and the horizontal line set L are updated; if no rectangular piece satisfies the placement of the area on the horizontal line, the horizontal line is raised to the height of the lower horizontal lines on both sides, and the horizontal line set L is updated;

[0033] Step 3.4 repeats step 3.2 and step 3.3 until all the rectangular pieces to be placed meet the end condition and are arranged. One chromosome carries one arrangement plan for the batch of orders.

[0034] Step 3.5: Taking the maximum utilization of the plate as the goal, the fitness function is:

[0035]

[0036] where n p is the number of plates, ReLU is a nonlinear activation function;

[0037] Step 3.6: According to the placement results of steps 3.1-3.4, evaluate the individuals and calculate the fitness of the individuals in the current generation population G;

[0038] Step 3.7: Perform a selection operation on the current generation population G, and then output the obtained population;

[0039] Step 3.8: Perform crossover operation on individuals in the population using formula (7);

[0040]

[0041] Among them, f c is the larger fitness value of the two individuals to be crossed, 0<k1<k2<1 is the value range of the crossover probability parameter, f avg is the average fitness of the population, f max is the maximum fitness;

[0042] Step 3.9: Perform mutation operation on individuals in the population using formula (8);

[0043]

[0044] Among them, f m is the larger fitness value of the two individuals to be mutated, 0<k3<k4<1 is the value range of the mutation probability parameter, favg is the average fitness of the population, f max is the maximum fitness;

[0045] Step 3.10: Repeat the above steps until the termination condition is met.

[0046] Furthermore, the step 4 is specifically as follows:

[0047] Step 4.1: Select a set of 0-1 logical variables {z1,z2,...,z n} represents an n-bit binary string. If z i =1 means the i-th piece of leftover material is selected; if z i =0 means that the i-th piece of leftover material is not selected and continues to exist in the leftover material library. The mathematical model of the leftover material combination is:

[0048]

[0049] Where: z i Is a logical variable, taking the value 0 or 1; A i represents the available area of ​​the i-th piece of waste material; S i represents the maximum enveloping rectangular area of ​​the layout parts; k is the coefficient of the surplus material utilization rate, formula (9) is the layout target, striving to maximize the utilization of surplus materials, and formula (10) is the search condition that constrains the combination utilization of surplus materials, while limiting the utilization rate of surplus materials;

[0050] Step 4.2: Conduct a trial layout of the parts to be arranged, roughly calculate the plate area required to complete the layout, and then find suitable plates in the surplus stock in a targeted manner based on the constraints of the mathematical model in step 4.1 above and step 3;

[0051] Step 4.3: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

[0052] In summary, the present invention proposes a rectangular layout optimization method that takes into account the optimization of waste material utilization, and the beneficial effects achieved are:

[0053] (1) The present invention proposes an improvement on the placement method based on the lowest horizontal line search algorithm, taking into account the lowest and highest double horizontal lines and the placement evaluation function, and more efficiently determining the placement positions of rectangular pieces in the arrangement solution set; in addition, by improving the adaptive genetic algorithm to optimize the placement order of rectangular pieces and introducing a two-stage crossover mutation probability, the algorithm's optimization efficiency is improved while protecting population diversity.

[0054] (2) A set of waste material utilization strategies specifically for the layout of rectangular parts of panel furniture was established, which achieved the goal of replacing original panels with waste panels as much as possible in panel production. Through the dynamic inventory of waste materials, waste materials were utilized at a faster speed and efficiency, achieving the goal of reducing raw material costs and increasing profits.

[0055] (3) The present invention can be applied to the layout process of rectangular pieces of panel furniture of different specifications. The lower limit of the size of the surplus material can be set in advance and it can be close to the actual furniture production to complete the cutting work of standard batch panel orders. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 : A flow chart of a rectangular layout optimization method considering the optimization of surplus material utilization according to the present invention;

[0057] Figure 2 : An overall block diagram of a specific embodiment of a rectangular layout optimization method considering the optimization of waste material utilization according to the present invention;

[0058] Figure 3 : A schematic diagram of the placement steps in a specific embodiment of a rectangular layout optimization method considering the optimization of waste material utilization according to the present invention;

[0059] Figure 4 : A flowchart of the algorithm steps for supplementing and utilizing surplus materials in a specific embodiment of a rectangular layout optimization method considering the optimization of surplus material utilization according to the present invention;

[0060] Figure 5 : A partial result diagram of sample data arrangement of a specific embodiment of a rectangular arrangement optimization method considering the optimization of surplus material utilization according to the present invention;

[0061] Figure 6 : A partial result diagram of rectangular layout using residual material in a specific embodiment of a rectangular layout optimization method taking residual material utilization optimization into consideration in the present invention. DETAILED DESCRIPTION

[0062] The technical solutions and advantages of this invention are further described in detail below in conjunction with the accompanying drawings and embodiments. The embodiments of the present invention are not limited thereto.

[0063] Figure 1 This is a flowchart of a rectangular layout optimization method considering the optimization of waste material utilization provided by the embodiment of this invention. The operation steps described in the embodiment or flowchart in this specification do not represent the only execution order. In actual execution, the method sequence or parallel execution can be performed according to the embodiment or the method shown in the figure. Figure 1 As shown, the method comprises the following steps:

[0064] Step 1: Establish a mathematical model for mixed integer rectangular packing.

[0065] The rectangular arrangement problem of panel furniture is generally described as arranging a set of strongly heterogeneous rectangles of known different sizes into the minimum number of original sheet materials. In this process, the following constraints need to be met: 1) Each rectangular arrangement must be orthogonal to the original sheet material, that is, the edge of the rectangular piece is parallel to the edge of the sheet material; 2) There must be no overlap between all rectangular pieces; 3) The combination of rectangular pieces cannot exceed the original size of the sheet material. In addition, the constraints of the use of residual materials should also be considered (that is, in the arrangement scheme with higher utilization rate, the amount of available residual materials generated should be considered to comprehensively judge the better scheme).

[0066] Furthermore, step 1 includes the following sub-steps:

[0067] Step 1.1: Assume that the length of the original sheet is L, the width of the original sheet is W, and n rectangular pieces {p1, p2, ···, p i ,···,p n}, the length of the i-th rectangular piece is represented by l i , the width of the i-th rectangular piece is denoted as w i , whether the i-th rectangular piece is rotatable is represented by r i , N represents the total number of original pieces required, the number of types of rectangular pieces to be arranged is t, and the number of i-type rectangular pieces arranged by the rectangular original pieces is represented by n i ;

[0068]

[0069] Step 1.2: The length and width of the rotated rectangle are represented as l i ',w i ';

[0070]

[0071]

[0072] Step 1.3: Establish a two-dimensional rectangular coordinate system with the lower left corner of the original sheet as the origin, the width direction as the x-axis, and the width direction as the y-axis. Each rectangular piece to be arranged takes the lower left corner as the initial point;

[0073] Step 1.4: Establish a mixed integer programming model with the maximum plate utilization as the objective function. The objective function is:

[0074]

[0075] Step 1.5: The constraints of the mathematical model are expressed as:

[0076]

[0077] Among them, formula (5-1) means that each rectangular piece is placed orthogonally to the plate; formula (5-2) means that there is no overlap between the rectangular pieces; formulas (5-3) and (5-4) mean that the length and width of the rectangular pieces do not exceed the length and width of the plate.

[0078] Step 2: Encode the rectangular parts to form a sequence of arrangement order, obtain a set of rectangular parts arrangement solutions, and read the residual material library information.

[0079] Furthermore, the step 2 includes the following sub-steps:

[0080] Step 2.1: First, number all rectangular pieces. The sequence of numbers of all rectangular pieces is a feasible solution for the arrangement. Each number id corresponds to a unique rectangular piece. The numbering order of the sequence represents the arrangement order of the rectangular pieces. Using decimal coding, the number of rectangular pieces n, and then assigning positive and negative signs to each rectangular piece. The positive sign indicates direct placement, and the negative sign indicates placement after rotating 90°. Then the overall coding method is: S = {p1, p2, ... p i ,...,p n}, where p i ∈(-n,n),i∈(1,n);

[0081] Step 2.2: Initialize population G, population size P num , Max number of evolutionary iterations g ; Set the iteration end condition.

[0082] The initial population G is generated in a ratio of 5:2:2:1 according to (a) random generation, (b) sorting by length in descending order, (c) sorting by width in descending order, and (d) sorting by area in descending order. The evolutionary generation counter g is defined and initialized to g = 1.

[0083] Step 3: Determine the placement position of the rectangular pieces in the arrangement solution set by improving the lowest horizontal line search algorithm, evaluate the placement result by the fitness function, and optimize the placement order of the rectangular pieces by improving the adaptive genetic algorithm, and iterate the arrangement order of the rectangular pieces.

[0084] Furthermore, the step 3 specifically includes the following steps:

[0085] Step 3.1: Initialize the horizontal line set L, which has only one horizontal contour line with a height of 0, which is the bottom boundary of the plate;

[0086] Step 3.2: Place the rectangular pieces one by one according to the coding sequence. If the current rectangular piece needs to be rotated during the placement process, swap the width and height information of the rectangular piece for placement;

[0087] Step 3.3: Discharge the plate p each time iGet the lowest horizontal line l from the horizontal line set min The width and height of the area to be placed. If there are multiple segments, select the leftmost horizontal line, and then determine whether the width of the placement area on the horizontal line is greater than or equal to the width of the rectangular piece to be placed:

[0088] Case 1) If the width of the area on the horizontal line is greater than the width of the rectangular piece to be arranged, the rectangular piece is placed in this area and the highest horizontal line l in the horizontal line set after arrangement is updated. max If l max If the height W of the original sheet increases or exceeds it, find a rectangular piece with a width that matches the horizontal line from the previously placed rectangular pieces. If there is no rectangular piece that meets the conditions, place them in the order of the original sequence, update the horizontal line set and go to step 3.3; if there are multiple rectangular pieces that meet the conditions, select rectangular pieces from the leftmost side, exchange their positions, and compare the l before and after the exchange. max And the evaluation function P score , l during placement min and placement area, l max , P score Rating judgment Figure 2 As shown, place and then select other rectangular pieces in turn to perform the same steps. max To lower, press (l max Minimum>P score The highest priority is selected for exchange, and the horizontal line set L and the arrangement sequence are updated. The order of other arranged rectangular pieces remains unchanged. If the exchange before and after l max If unchanged, place them in the original sequence.

[0089] P score Evaluation value rules:

[0090] a. If h i <h l ∨h i <h r ∨w i <w c , P score +=0;

[0091] b. If h i >h l ∨h i >h r , P score +=1;

[0092] c. If h i =h l ∨h i =h r ∨w i =w c , Pscore + = 2);

[0093] Case 2) If the width of the area on the horizontal line is less than the width of the rectangular piece to be arranged, search for a rectangular piece that meets the placement conditions after the rectangular piece in the encoding sequence S. If there is a rectangular piece whose width is equal to the width of the area on the horizontal line, prioritize the placement of the rectangular piece and update the horizontal line set L; if there is no rectangular piece with the same width, search for a rectangular piece that meets the placement conditions from the position after the rectangular piece in the sequence S, and select P score The highest rectangular piece is placed at this position, and the arrangement sequence and the horizontal line set L are updated; if no rectangular piece satisfies the placement of the area on the horizontal line, the horizontal line is raised to the height of the lower horizontal lines on both sides, and the horizontal line set L is updated;

[0094] Step 3.4 repeats step 3.2 and step 3.3 until all the rectangular pieces to be placed meet the end condition and are arranged. One chromosome carries one arrangement plan for the batch of orders.

[0095] For details of steps 3.1-3.4 above, please refer to Figure 3 , Figure 3 is a schematic diagram of the placement process of the improved lowest horizontal line search solution provided by an embodiment of the present invention,

[0096] against Figure 3 The improved arrangement process is as follows: after placing the No. 1 and No. 2 panels, the overall arrangement height is increased, but there are no parts with suitable width to replace, so the arrangement position remains unchanged. When arranging the third panel, the width of the No. 3 panel is larger than the lowest horizontal line l min The width of the board is 1, so we search backwards for boards 4 to 7 and find that all of these 4 boards meet the entry conditions, but the width of board 7 is exactly equal to l. min Width, so place plate 7 first, update the highest horizontal line of the part l max ; Update l max After min The horizontal line is the leftmost, and then the No. 3 plate is placed, which can be placed normally, so update l max ; Then place plate 4, and place plate 4 after the conditions are met, and update the part's l max ; Then place plate No. 5 and find that the conditions are met, place part 5 in, and update part l max ; Finally, place plate No. 6 and find the highest horizontal line l max The height is increased. If you search forward for a suitable replacement plate, the widths of plate No. 4 and plate No. 5 are suitable and can be replaced. However, after replacing plate No. 5, the highest horizontal line l max The height has not changed, but replacing the No. 4 plate can just lower lmax Therefore, the positions of plate No. 6 and plate No. 4 are swapped to obtain the final layout diagram.

[0097] Step 3.5: Taking the maximum utilization of the plate as the goal, the fitness function is:

[0098]

[0099] where n p is the number of plates, ReLU is a nonlinear activation function;

[0100] Step 3.6: According to the placement results of steps 3.1-3.4, evaluate the individuals and calculate the fitness of the individuals in the current generation population G;

[0101] Step 3.7: Perform a selection operation on the current generation population G. The selection operator combines the roulette selection and binary tournament selection strategies. The roulette selection is performed twice, and the probability of being selected is Select the one with higher fitness from the two selected individuals as the offspring individual, and then output the resulting population;

[0102] Among them, f i is the fitness of individual i, N is the population size;

[0103] Step 3.8: Perform crossover operation on individuals in the population using formula (7);

[0104]

[0105] Among them, f c is the larger fitness value of the two individuals to be crossed, 0<k1<k2<1 is the value range of the crossover probability parameter, f avg is the average fitness of the population, f max is the maximum fitness;

[0106] Step 3.9: Perform mutation operation on individuals in the population using formula (8);

[0107]

[0108] Among them, f m is the larger fitness value of the two individuals to be mutated, 0<k3<k4<1 is the value range of the mutation probability parameter, f avg is the average fitness of the population, f max is the maximum fitness;

[0109] The specific process of the crossover operation is as follows: A ={6, 5 ,3,9,7, 1 ,2,8,4} and individual pB ={3, 7 ,5,9,4, 6 ,1,2,8,} perform a crossover operation, randomly generate two crossover positions in [0,n], and generate offspring individuals p A '={ 7,5,9,4,6, 3,1,2,8} and p B '={ 5,3,9,7,1, 4,6,2,8,};

[0110] Step 3.10: Repeat the above steps until the termination condition is met. Figure 4 As shown, Figure 4 This is the overall flow chart of the improved adaptive genetic algorithm in a specific embodiment of the rectangular layout optimization method considering the optimization of waste material utilization of the present invention.

[0111] Step 4: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

[0112] This paper proposes an optimization method for the utilization of surplus materials. It performs an initial layout of the rectangular parts to be arranged, and preliminarily estimates the maximum enveloping rectangular area of ​​the plate area required to complete the layout. Then, according to the constraints of the above-mentioned mathematical model, the improved adaptive genetic algorithm is used to find suitable plates in the surplus material inventory in a targeted manner. The embodiment is a specific workflow diagram as shown in the figure. Figure 5 shown.

[0113] Furthermore, the step 4 is specifically as follows:

[0114] Step 4.1: Select a set of 0-1 logical variables {z1,z2,...,z n} represents an n-bit binary string. If z i =1 means the i-th piece of leftover material is selected; if z i =0 means that the i-th piece of leftover material is not selected and continues to exist in the leftover material library. The mathematical model of the leftover material combination is:

[0115]

[0116] Where: z i Is a logical variable, taking the value 0 or 1; A i represents the available area of ​​the i-th piece of waste material; S i represents the maximum enveloping rectangular area of ​​the layout parts; k is the coefficient of the surplus material utilization rate, formula (9) is the layout target, striving to maximize the utilization of surplus materials, and formula (10) is the search condition that constrains the combination utilization of surplus materials, while limiting the utilization rate of surplus materials;

[0117] Step 4.2: Refer to step 2.1 to encode the remaining materials in the remaining material library, and generate the corresponding variable code S'={xp1, xp2, ... xp i ,...,xp n}, xp i =0 or 1.

[0118] Step 4.3: During decoding, the additional code p i Indicates the i-th piece of leftover material. The variable code value of 0 indicates that the leftover material is not selected, and the variable code value of 1 indicates that the leftover material is selected.

[0119] Step 4.4: Perform a trial layout of the parts to be arranged, roughly calculate the plate area required to complete the layout, and then find suitable plates in the surplus stock in a targeted manner based on the constraints of the mathematical model in step 4.1 above and step 3;

[0120] Step 4.5: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

[0121] This article selects 4 different batches of production orders from a customized panel furniture enterprise factory as the data sample source. The specifications and quantities of rectangular panels in the third group of orders are shown in the following table:

[0122]

[0123] The final layout result of the algorithm in this paper is taken as an example. The third group of orders uses a total of 52 raw material boards, and the utilization rate reaches 90.97%. Figure 5 Shown is an example of the layout plan diagram for the original plates of the 2nd and 45th plates.

[0124] To further verify the performance of the proposed algorithm in the actual use of residual materials in panel furniture layout, assume an empty residual material warehouse and run the algorithm twice. The first time, since the residual material warehouse is empty and there is no available residual material, only new residual materials are generated after the layout is completed; during the second layout, the residual material warehouse has the residual materials generated in the first time. Comparing the results of the two operations, the algorithm's utilization of residual materials is verified. The experimental samples still use the above 4 groups of production orders, and the lower limit of the residual materials is preset to 300mm*150mm. Figure 6 The figure shows the partial waste material utilization results. The following conclusions can be drawn: In orders with different numbers of rectangular pieces, the proposed algorithm can use waste materials to reduce the usage of the corresponding board originals for layout. As the size of the board in the order increases, the usage of waste materials will also increase; the proposed algorithm has a good waste material utilization rate, thereby improving the material utilization rate of panel furniture layout.

[0125] As mentioned above, the above description describes the embodiments of the present invention in conjunction with the accompanying drawings, and the present invention has been represented and described with reference to specific preferred embodiments, but the present invention is not limited to the above specific implementation methods and shall not be interpreted as limiting the present invention. Various changes in form and details may be made without departing from the purpose and scope of the present invention defined in the attached claims.

Claims

1. A rectangular layout optimization method considering the optimization of waste material utilization, characterized in that: The steps include: Step 1: Establish a mixed integer rectangular pattern mathematical model; Step 2: Encode the rectangular parts to form a sequence of arrangement order, obtain a set of rectangular parts arrangement solutions, and read the residual material library information; Step 3: Determine the placement position of the rectangular pieces in the packing solution set by improving the lowest horizontal line search algorithm, evaluate the placement result by the fitness function, and optimize the placement order of the rectangular pieces by improving the adaptive genetic algorithm, and iterate the packing order of the rectangular pieces; Step 4: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

2. A rectangular layout optimization method considering waste material utilization optimization according to claim 1, characterized in that: The specific method of mathematical modeling in step 1 is: Step 1.1: Assume that the length of the original sheet is L, the width of the original sheet is W, and n rectangular pieces {p1, p2, ···, p i ,···,p n }, the length of the i-th rectangular piece is represented by l i , the width of the i-th rectangular piece is denoted as w i , whether the i-th rectangular piece is rotatable is represented by r i , N represents the total number of original pieces required, the number of types of rectangular pieces to be arranged is t, and the number of i-type rectangular pieces arranged by the rectangular original pieces is represented by n i ; Step 1.2: The length and width of the rotated rectangle are represented as l i ',w i '; Step 1.3: Establish a two-dimensional rectangular coordinate system with the lower left corner of the original sheet as the origin, the width direction as the x-axis, and the width direction as the y-axis. Each rectangular piece to be arranged takes the lower left corner as the initial point; Step 1.4: Establish a mixed integer programming model with the maximum plate utilization as the objective function. The objective function is: Step 1.5: The constraints of the mathematical model are expressed as: Among them, formula (5-1) means that each rectangular piece is placed orthogonally to the plate; formula (5-2) means that there is no overlap between the rectangular pieces; formulas (5-3) and (5-4) mean that the length and width of the rectangular pieces do not exceed the length and width of the plate.

3. The rectangular layout optimization method considering the optimization of waste material utilization according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: First, number all rectangular pieces. The sequence of numbers of all rectangular pieces is a feasible solution for the arrangement. Each number id corresponds to a unique rectangular piece. The numbering order of the sequence represents the arrangement order of the rectangular pieces. Using decimal coding, the number of rectangular pieces n, and then assigning positive and negative signs to each rectangular piece. The positive sign indicates direct placement, and the negative sign indicates placement after rotating 90°. Then the overall coding method is: S = {p1, p2, ... p i ,...,p n }, where p i ∈(-n,n),i∈(1,n); Step 2.2: Refer to step 2.1 to encode the remaining materials in the remaining material library, and generate the corresponding variable code S'={xp1, xp2, ... xp i ,...,xp n }, xp i =0 or 1. Step 2.3: Initialize the population G, population size P num , Max number of evolutionary iterations g ; Set the evolution end condition.

4. The rectangular layout optimization method considering the optimization of waste material utilization according to claim 1 is characterized in that: The specific method of step 3 is: Step 3.1: Initialize the horizontal line set L, which has only one horizontal contour line with a height of 0, which is the bottom boundary of the plate; Step 3.2: Place the rectangular pieces one by one according to the coding sequence. If the current rectangular piece needs to be rotated during the placement process, swap the width and height information of the rectangular piece for placement; Step 3.3: Discharge the plate p each time i Get the lowest horizontal line l from the horizontal line set min The width and height of the area to be discharged. If there are multiple segments, select the leftmost horizontal line, and then determine whether the width of the placement area on the horizontal line is greater than or equal to the width of the rectangular piece to be arranged: Case 1) If the width of the area on the horizontal line is greater than the width of the rectangular piece to be arranged, the rectangular piece is placed in this area and the highest horizontal line l in the horizontal line set after arrangement is updated. max If l max If the height W of the original sheet increases or exceeds it, find a rectangular piece with a width that matches the horizontal line from the previously placed rectangular pieces. If there is no rectangular piece that meets the conditions, place them in the order of the original sequence, update the horizontal line set and go to step 3.3; if there are multiple rectangular pieces that meet the conditions, select rectangular pieces from the leftmost side, exchange their positions, and compare the l before and after the exchange. max and place P score , and then select other rectangular pieces in turn to perform the same steps. max To lower, press (l max Minimum>P score The highest priority is selected for exchange, and the horizontal line set L and the arrangement sequence are updated, and the order of other arranged rectangular pieces remains unchanged; If you swap the front and back l max If unchanged, place them in the original sequence. score Value selection rules (a. If h i <h l ∨h i <h r ∨w i <w c , P score +=0; b. If h i >h l ∨h i >h r , P score +=1; c. If h i =h l ∨h i =h r ∨w i =w c , P score + = 2); Case 2) If the width of the area on the horizontal line is less than the width of the rectangular piece to be arranged, search for a rectangular piece that meets the placement conditions after the rectangular piece in the encoding sequence S. If there is a rectangular piece whose width is equal to the width of the area on the horizontal line, prioritize the placement of the rectangular piece and update the horizontal line set L; if there is no rectangular piece with the same width, search for a rectangular piece that meets the placement conditions from the position after the rectangular piece in the sequence S, and select P score The highest rectangular piece is placed at this position, and the arrangement sequence and the horizontal line set L are updated; if no rectangular piece satisfies the placement of the area on the horizontal line, the horizontal line is raised to the height of the lower horizontal lines on both sides, and the horizontal line set L is updated; Step 3.4 repeats step 3.2 and step 3.3 until all the rectangular pieces to be placed meet the end condition and are arranged. One chromosome carries one arrangement plan for the batch of orders. Step 3.5: Taking the maximum utilization of the plate as the goal, the fitness function is: where n p is the number of plates, ReLU is a nonlinear activation function; Step 3.6: According to the placement results of steps 3.1-3.4, evaluate the individuals and calculate the fitness of the individuals in the current generation population G; Step 3.7: Perform a selection operation on the current generation population G, and then output the obtained population; Step 3.8: Perform crossover operation on individuals in the population using formula (7); Among them, f c is the larger fitness value of the two individuals to be crossed, 0<k1<k2<1 is the value range of the crossover probability parameter, f avg is the average fitness of the population, f max is the maximum fitness; Step 3.9: Perform mutation operation on individuals in the population using formula (8); Among them, f m is the larger fitness value of the two individuals to be mutated, 0<k3<k4<1 is the value range of the mutation probability parameter, f avg is the average fitness of the population, f max is the maximum fitness; Step 3.10: Repeat the above steps until the termination condition is met.

5. The rectangular layout optimization method considering the optimization of waste material utilization according to claim 1 is characterized in that: The step 4 is specifically as follows: Step 4.1: Select a set of 0-1 logical variables {z1,z2,...,z n } represents an n-bit binary string. If z i =1 means the i-th piece of leftover material is selected; if z i =0 means that the i-th piece of leftover material is not selected and continues to exist in the leftover material library. The mathematical model of the leftover material combination is: Where: z i Is a logical variable, taking the value 0 or 1; A i represents the available area of ​​the i-th piece of waste material; S i represents the maximum enveloping rectangular area of ​​the layout parts; k is the coefficient of the surplus material utilization rate, formula (9) is the layout target, striving to maximize the utilization of surplus materials, and formula (10) is the search condition that constrains the combination utilization of surplus materials, while limiting the utilization rate of surplus materials; Step 4.2: Conduct a trial layout of the parts to be arranged, roughly calculate the plate area required to complete the layout, and then find suitable plates in the surplus stock in a targeted manner based on the constraints of the mathematical model in step 4.1 above and step 3; Step 4.3: Output the optimal layout plan, save the remaining materials, and update the remaining material library.

Images