CN111368421B - Grouping heuristic method for stacking and blanking furniture boards - Google Patents
Grouping heuristic method for stacking and blanking furniture boards Download PDFInfo
- Publication number
- CN111368421B CN111368421B CN202010136723.XA CN202010136723A CN111368421B CN 111368421 B CN111368421 B CN 111368421B CN 202010136723 A CN202010136723 A CN 202010136723A CN 111368421 B CN111368421 B CN 111368421B
- Authority
- CN
- China
- Prior art keywords
- blank
- blanking
- current
- layout
- grouping
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- General Factory Administration (AREA)
Abstract
The invention belongs to the technical field of plate stacking cutting and blanking, and discloses a grouping heuristic method for furniture plate stacking blanking, which comprises the following steps: generating a candidate blank set by adopting a whole stacking rule in the grouping process; selecting blanks from the candidate blank sets to generate a current layout, adding the current layout into a current blanking scheme, and repeating until the requirements of all the blanks are met; and after obtaining a blanking scheme, correcting the blank value by adopting a value correction algorithm, continuing iteration to obtain a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost. Compared with a heuristic algorithm without grouping, the method is more suitable for solving the stacking blanking problem, and a group of same finished products are obtained by one-time cutting, so that the cutting efficiency is greatly improved, and the method has obvious advantages in the aspects of reducing the stacking number of raw materials and reducing the total cost.
Description
Technical Field
The invention belongs to the technical field of cutting and blanking of boards according to stacking, and particularly relates to a grouping heuristic method for blanking furniture boards according to stacking.
Background
Currently, blanking problems occur in a number of areas, such as shearing metal logs and strips, sawing wood boards, cutting flat glass, etc. In actual production, the raw materials can be stacked and cut by the blanking of the artificial wood board, the paper and the plastic cloth, and the advantage is that a group of same finished products can be obtained by one-time cutting, so that the cutting efficiency can be improved to a great extent. The problem of cutting and blanking plates according to the stack is widely applied to the production process of paper products, wood products and the like with high production yield and lower material unit price. The method is characterized in that one or more plates can be stacked together during plate blanking, and the stacked plates are cut by a machine at the same time, so that a plurality of finished products with the same shape and size can be obtained at one time. The heuristic grouping algorithm is advantageous in reducing the number of stacks of sheet material that are blanked in stacks, thereby reducing the overall cutting costs. The reduction of the cutting costs is of great importance for reducing the overall cost of production.
There are several documents currently dealing with the blanking of groups. In the prior art, a grouping dimension reduction rule is designed aiming at the optimized layout of large-scale rectangular parts, the whole requirement is divided into a plurality of groups, and the problems of optimized layout and combination of no more than 3 rectangular parts in each group are solved by combining a genetic algorithm and a punishment function. In the second prior art, a rectangular piece optimizing blanking method for machinability is provided, and a cutting machining path can be shortened, so that cutting cost is reduced. In the third prior art, a part grouping rule is provided, the size collocation of parts in a group is fully considered, and the time efficiency of an algorithm can be improved. In the optimization of adjacent groups, a compensation strategy is adopted to dynamically correct the distribution of parts among the groups, and finally, the optimization results of all groups are combined to obtain the solution of the original problem. In the fifth prior art, aiming at the problem of small batch round piece blanking under the special application background, a blanking scheme is generated by combining a sequential grouping heuristic algorithm with a recursive algorithm. The grouping heuristic method in the sixth prior art takes the reduction of the variety number of the raw materials as a main target, takes the reduction of the consumption of the raw materials as a secondary target, and limits the variety number of blanks in the group and the total area of the blanks in the group during grouping.
The prior art researches mainly utilize grouping to achieve the purpose of dimension reduction, so that complexity of a layout algorithm is reduced, and a solution with higher material utilization rate can be obtained in a reasonable time. However, these algorithms do not realize grouping of the sheets by stacking, and therefore, the total number of sheets to be cut cannot be reduced in the production of the sheets by stacking, and thus, the total production cost including the cutting cost cannot be effectively reduced. However, in the actual production of enterprises, the generated blanking scheme is not only considered to reduce the material cost, but also considered to reduce the cutting cost, improve the production efficiency and the like.
In summary, the problems of the prior art are: the existing blanking problem solving algorithm cannot effectively reduce the total cost of blanking by stack; meanwhile, the production efficiency is low.
The difficulty of solving the technical problems is as follows: the method is mainly characterized in that in the production of stacking and blanking of the plates, the purpose of dimension reduction is realized by grouping, and meanwhile, the layout of plate cutting is ensured to be generated in a stacking way as much as possible.
Meaning of solving the technical problems: the method is mainly characterized in that the total number of plate stacks required to be cut can be reduced by grouping and stacking blanking, so that the cutting cost is reduced, and the production blanking efficiency is improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a grouping heuristic method for stacking and blanking furniture boards.
The invention is realized in such a way that a furniture board material is stacked and blanked in a grouping heuristic method, and the furniture board material is stacked and blanked in a grouping heuristic method comprises the following steps: generating a candidate blank set by adopting a whole stacking rule in the grouping process; selecting blanks from the candidate blank sets to generate a current layout, adding the current layout into a current blanking scheme, and repeating until the requirements of all the blanks are met; and after obtaining a blanking scheme, correcting the blank value by adopting a value correction algorithm, continuing iteration to obtain a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
Further, the grouping heuristic method for stacking and blanking the furniture boards further comprises the following steps:
firstly, selecting blanks, namely rectangular pieces, according to the whole stacking rule of the plate blanking problem based on a heuristic algorithm grouped by stacking, and determining the blanks grouped to form a candidate set;
step two, grouping and layout are carried out by utilizing the demand blanks of the candidate set to generate a current layout, and the using times of the current layout are determined according to the stacking rule;
step three, repeating the step two until all blanks meet the requirements; determining a blanking scheme;
and fourthly, correcting the blank value by adopting a blank value correction algorithm, constructing an optimized model with a target structure with the minimum total cost of material cost and cutting cost, iterating for a plurality of times to generate a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
Further, the grouping heuristic method for the furniture boards according to the stacking blanking comprises the following steps:
g is the current iteration number, G max For maximum iteration number, b i The remaining demand for the ith blank, c i For the value of the ith blank, d i Initial demand for ith blank, y i For the number of i-th blanks in the current map (i=1,., m), f is the number of current map uses;
the method comprises the following steps:
(1) Inputting blank and raw material data, initializing the current blanking scheme to be empty, wherein G=1, and c i ＝l i w i ；
(2) If G > G max Turning to Step9, otherwise, let b i ＝d i ；
(3) Calling a GetGroup () function, and grouping by using the whole stacking rule;
(4) Calling a GetPattern () function to generate a current layout;
(5) Calculating the use times f and the stacking number omega of the current layout, and adding the current layout into the current blanking scheme;
(6) Let b i ＝b i -fy i The remaining requirements of the blank are updated, wherein i=1 and wherein, m; if b is present i > 0, step (3);
(7) Calculating the total cost of the current blanking scheme;
(8) Calling a CorrectValue () function to correct the value of the blank, enabling G=G+1, and turning to the step (2);
(9) And selecting the blanking scheme with the minimum total cost from all blanking schemes as an optimal scheme to output.
Further, in step (3), the GetGroup () function includes:
the GetGroup () function groups the rest blank according to the whole stacking rule, and obtains the current candidate blank set, namely the CI set after each grouping; sequentially inspecting all blank types during grouping, adding the blank types with larger demand into the CI set preferentially, selecting various blanks, and keeping the blank type diversity of the CI set; when the blank demand is large, the number of raw materials cut each time reaches the upper limit of the number of each stack.
Further, in step (4), the GetPattern () function includes:
the GetPattern () function determines the current layout by solving the bounded two-dimensional knapsack problem as follows:
generating a current layout by adopting a recurrence method;
v (y) and N (y, i) respectively represent the value of the blank and the number of the ith blank contained in the layout with the width of y; the recurrence formula is as follows:
and (3) a recursion formula represents a layout diagram with the width of y, and during recursion, judging whether the ith blank can be placed on the raw material according to the total value v (y) of the blanks arranged on the raw material: if the total value v (y) of the blank on the raw material after being placed is greater than the total value v (y-w) of the blank before being placed i ) And placing the current blank, or else, not placing the current blank.
Further, in the step (5), the method for calculating the number of times f and the number of stacks ω of the current layout includes:
determining the number of times f of use of the current layout and determining the log cutting stack number omega by using the following steps:
further, in step (8), the directvalue () function includes:
a value correction formula is adopted, the utilization rate of the current layout, the area of the blank and the value of the previous blank are integrated, and a new blank value is obtained after each iteration;
the value correction formula is as follows:
c i ＝g 1 c i +g 2 (l i w i ) ρ /u
g 2 ＝σfy i /d i
g 1 ＝1-g 2
wherein σ and ρ are control parameters; u is the utilization rate of the current layout, and f is the use times of the current layout; calculate g 2 The numerator is multiplied by f for increasing the value adjustment amplitude.
In summary, the invention has the advantages and positive effects that: compared with a heuristic algorithm without grouping, the method is more suitable for solving the stacking blanking problem, and a group of same finished products are obtained by one-time cutting, so that the cutting efficiency is greatly improved, and the method has obvious advantages in the aspects of reducing the stacking number of raw materials and reducing the total cost.
The invention adopts the homogeneous strip, and compared with the common strip and the uniform strip, the homogeneous strip can simplify the cutting process to the greatest extent. The sequential, stacked, and grouped heuristic of the present invention is effective in reducing the number of stacks and reducing the overall cost. The invention provides a heuristic algorithm grouped according to stacks, which determines that the blanks grouped form a candidate set according to the stacking rule of the plate blanking problem, and then utilizes the blank required by the candidate set to generate a current layout and the using times thereof. In determining the current layout, consider combining with a value correction strategy to construct an optimization model with the objective of minimizing the total cost of material cost and cut cost construction to determine the blanking scheme of the sheet material by fold blanking problem, reducing the material cost while also reducing the cut cost.
According to the invention, through grouping operation, a layout diagram with higher utilization rate is obtained when the blank of the CI set is subjected to layout, and meanwhile, the scale of the CI set can be controlled, so that the complexity of a layout algorithm is reduced. The grouping aims to reduce the total stack number of the cutting of the raw materials, thereby reducing the cutting cost of blanking; meanwhile, the method is beneficial to increasing the use times of the same layout, so that the preparation cost generated by replacing the layout when cutting the raw materials is reduced.
The layout diagram generated by the invention is more compact, so that the residual material blocks are relatively concentrated to form larger available residual materials, on one hand, the subsequent blanking can be facilitated, and on the other hand, the blank with other requirements can be arranged by allowing the spare raw materials.
Drawings
Fig. 1 is a flowchart of a grouping heuristic method for stacking and blanking furniture boards according to an embodiment of the invention.
FIG. 2 is a schematic diagram of the types of stripes provided by an embodiment of the present invention;
in the figure: (a) a common stripe Ordinary Strip; (b) Uniform stripe Strip; (c) homogenic strips.
FIG. 3 is a layout diagram of a prior art data acquisition system according to an embodiment of the present invention;
in the figure: (a) a First layout Pattern; (b) a Second layout Pattern.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems existing in the prior art, the invention provides a grouping heuristic method for stacking and blanking furniture boards, and the invention is described in detail below with reference to the accompanying drawings.
The grouping heuristic method for the furniture boards according to the stacking blanking provided by the embodiment of the invention comprises the following steps: generating a candidate blank set by adopting a whole stacking rule in the grouping process; selecting blanks from the candidate blank sets to generate a current layout, adding the current layout into a current blanking scheme, and repeating until the requirements of all the blanks are met; and after obtaining a blanking scheme, correcting the blank value by adopting a value correction algorithm, continuing iteration to obtain a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
As shown in fig. 1, the grouping heuristic method for stacking and blanking furniture boards provided by the embodiment of the invention further includes:
s101, selecting blanks, namely rectangular pieces, according to the whole stacking rule of the plate blanking problem based on a heuristic algorithm of stacking and grouping, and determining the blanks to be grouped to form a candidate set.
S102, generating a current layout by grouping and layout of the demand blanks of the candidate set, and determining the use times of the current layout according to the stacking rule.
S103, repeating the step S102 until all blanks meet the requirements; a blanking schedule is determined.
S104, correcting the blank value by adopting a blank value correction algorithm, constructing a target construction optimization model with the minimum total cost of material cost and cutting cost, iterating for a plurality of times, generating a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
The grouping heuristic method for the furniture boards according to the stacking blanking provided by the embodiment of the invention comprises the following steps:
g is the current iteration number, G max For maximum iteration number, b i The remaining demand for the ith blank, c i For the value of the ith blank, d i Initial demand for ith blank, y i For the number of i-th blanks in the current map (i=1, m), f is the number of current map uses.
The method comprises the following steps:
(1) Inputting blank and raw material data, initializing the current blanking scheme to be empty, wherein G=1, and c i ＝l i w i 。
(2) If G > G max Turning to Step9, otherwise, let b i ＝d i 。
(3) The GetGroup () function is called and the whole stack of rules is used for grouping.
(4) The GetPattern () function is called to generate the current layout.
(5) And calculating the using times f and the stacking number omega of the current layout, and adding the current layout into the current blanking scheme.
(6) Let b i ＝b i -fy i The remaining requirements of the blank are updated, wherein i=1 and wherein, m; if b is present i > 0, step (3).
(7) The total cost of the current blanking scheme is calculated.
(8) And (3) calling a CorrectValue () function to correct the blank value, and turning to the step (2) when G=G+1.
(9) And selecting the blanking scheme with the minimum total cost from all blanking schemes as an optimal scheme to output.
In step (3), the GetGroup () function provided by the embodiment of the present invention includes:
the GetGroup () function groups the rest blank according to the whole stacking rule, and obtains the current candidate blank set, namely the CI set after each grouping; sequentially inspecting all blank types during grouping, adding the blank types with larger demand into the CI set preferentially, selecting various blanks, and keeping the blank type diversity of the CI set; when the blank demand is large, the number of raw materials cut each time reaches the upper limit of the number of each stack.
In step (4), the GetPattern () function provided by the embodiment of the present invention includes:
the GetPattern () function determines the current layout by solving the bounded two-dimensional knapsack problem as follows:
and generating a current layout by adopting a recurrence method.
v (y) and N (y, i) respectively represent the value of the blank and the number of the ith blank contained in the layout with the width of y; the recurrence formula is as follows:
the recursion formula represents a layout diagram with the width of y, and during recursion, the ith wool is judged according to the total value v (y) of blanks arranged on the raw materialsWhether the blank can be placed on a log: if the total value v (y) of the blank on the raw material after being placed is greater than the total value v (y-w) of the blank before being placed i ) And placing the current blank, or else, not placing the current blank.
In step (5), the method for calculating the number of times f and the number of stacks ω of the current layout according to the embodiment of the present invention includes:
determining the number of times f of use of the current layout and determining the log cutting stack number omega by using the following steps:
in step (8), the coretvalue () function provided by the embodiment of the present invention includes:
and (3) integrating the utilization rate of the current layout, the area of the blank and the value of the previous blank by adopting a value correction formula, and obtaining a new blank value after each iteration.
The value correction formula is as follows:
c i ＝g 1 c i +g 2 (l i w i ) ρ /u
g 2 ＝σfy i /d i
g 1 ＝1-g 2
wherein σ and ρ are control parameters; u is the utilization rate of the current layout, and f is the use times of the current layout; calculate g 2 The numerator is multiplied by f for increasing the value adjustment amplitude.
The technical scheme of the invention is further described below with reference to specific embodiments.
Example 1:
1 related concepts and mathematical models
1.1 related concepts
(1) Stripe and layout diagram: a plurality of rectangular parts are continuously put together in a horizontal or vertical direction to form a strip. The three common types of strips are plain, uniform and homogenous, as shown in fig. 2. The homogeneous strips contain the same kind of blanks, and the layout directions of the blanks in the strips are the same. The invention adopts the homogeneous strip, and compared with the common strip and the uniform strip, the homogeneous strip can simplify the cutting process to the greatest extent. The layout refers to the arrangement of the strips on the log, the layout of the strips not exceeding the boundary constraints of the log.
(2) And (3) stacking and blanking: meaning that the logs can be stacked in a stack for cutting, the same stack having the same layout (the layout of the blanks on each log being identical).
(3) Maximum number of sheets p per stack: because of plant equipment and process limitations, the maximum number of sheets per stack that can be cut is typically limited, typically with p ranging from [5,8]. In the stacking and blanking process with lower material unit price, the cutting cost occupies a larger proportion of the total production cost, and from the viewpoint of cost reduction, the cutting is required to be carried out according to the maximum number of sheets per stack of raw materials during blanking.
(4) Grouping and layout: during the layout, all blanks do not need to be considered at a time, but a part of the rest blanks are selected to generate a candidate blank set, and only the blanks in the candidate set are considered in the one-time layout process. Due to the fact that the number of the blank is reduced, the layout complexity can be reduced, and the cutting cost is reduced.
(5) The stacking rule: in order to cut according to the maximum number of sheets as much as possible during each blanking, and simultaneously in order to ensure that higher material utilization rate is obtained during the generation of a layout, the whole stacking rule of stacking blanking provided by the invention means that the number of blanks is selected to be integer times of p during grouping and layout; after each generation of the map, the number of uses of the map is determined to be an integer multiple of p.
1.2 description of the problem and its mathematical model
The problem of stacking and blanking of the two-dimensional rectangle refers to raw materialsAnd the desired blanks are all regular rectangles, i.e. m desired rectangular blanks are cut from a stock of size L x W (assuming the available number is not limited), of size L i ×w i The demand is d i I=1,..m, cutting in stacks.
Assuming that a blanking scheme has K layout diagrams, the number of times of using the K layout diagrams is x k (k=1,., K), the material cost per sheet is q 1 The cutting cost of each stack of raw materials is q 2 The maximum number of sheets of the cut raw materials in each stack is p, and the kth layout contains the ith blank with the number of a ik (i=1.,), m). The mathematical model of the press fit problem can be expressed as:
equation (1) represents that the model optimization objective is to minimize the total cost of the laydown problem, which is the sum of the material cost and the cutting cost. Wherein the material cost q of each sheet of raw material 1 In relation to the unit area of the log, the material cost of a blanking scheme is therefore proportional to the amount of log consumed;the total stack to be cut for the kth map is proportional to the total stack to be cut. The constraint of formula (2) indicates that all required blank requirements are satisfied. The formula (3) represents the number x of uses of the map k Must be a non-negative integer.
2. Algorithm design and implementation
The invention adopts a heuristic algorithm of sequential stacking grouping, and adopts a whole stacking rule to generate a candidate blank set (CI set) in the grouping process; and selecting blanks from the candidate blank sets to generate a current layout, adding the current layout into a current blanking scheme, and repeating until the requirements of all the blanks are met. And after obtaining a blanking scheme, correcting the blank value by adopting a value correction algorithm, continuing iteration to obtain a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
2.1 blanking scheme Generation Algorithm
Let G be the current iteration number, G max For maximum iteration number, b i The remaining demand for the ith blank, c i For the value of the ith blank, d i Initial demand for ith blank, y i For the number of i-th blanks in the current map (i=1, m), f is the number of current map uses. The sequence used by the present invention is as follows, with the GetGroup () function and GetPattern () function introduced in sections 2.2 and 2.3, respectively:
step1, inputting blank and raw material data, initializing the current blanking scheme to be empty, wherein G=1, and c i ＝l i w i ；
Step2: if G > G max Turning to Step9, otherwise, let b i ＝d i ；
Step3: calling a GetGroup () function, and grouping by using the whole stacking rule;
step4: calling a GetPattern () function to generate a current layout;
step5: calculating the use times f and the stacking number omega of the current layout, and adding the current layout into the current blanking scheme;
step6: let b i ＝b i -fy i The remaining requirements of the blank are updated, wherein i=1 and wherein, m; if b is present i > 0, step3;
step7: calculating the total cost of the current blanking scheme;
step8: calling a CorrectValue () function to correct the value of the blank, and turning G=G+1 to Step2;
step9: and selecting the blanking scheme with the minimum total cost from all blanking schemes as an optimal scheme to output.
Wherein Step5 determines the number of times f of use of the current layout and the number of log cutting stacks ω by equations (4) (5) and (6), respectively:
2.2 GetGroup () function
The basic idea of grouping optimization is to divide the original problem into a plurality of groups, and solve the sub-problems after grouping, thereby obtaining the approximate optimal solution of the original problem. The grouping principle is to ensure that the solution set of the sub-problems after grouping is a feasible solution of the original problem, so that the function groups the rest blanks according to the whole stacking rule, and obtains a current candidate blank set (CI set) after each grouping. Sequentially inspecting all blank types during grouping, adding the blank types with larger demand into the CI set preferentially, selecting various blanks as much as possible, and keeping the blank type diversity of the CI set; when the blank demand is large, the number of raw materials cut each time reaches the upper limit of the number of each stack as much as possible. Through grouping operation, a layout diagram with higher utilization rate is obtained when blanks of the CI set are subjected to layout, and meanwhile, the scale of the CI set can be controlled, so that the complexity of a layout algorithm is reduced. The grouping aims to reduce the total stack number of the cutting of the raw materials, thereby reducing the cutting cost of blanking; meanwhile, the method is beneficial to increasing the use times of the same layout, so that the preparation cost generated by replacing the layout when cutting the raw materials is reduced. The pseudocode for this function implementation is as follows:
wherein k is max For the maximum possible number of stacks of all blank types, r i The number of the i-th blank selected to enter the CI set is represented, n and S are the number of the blank types of the CI set and the total area of the blank respectively, parameters eta and beta are used for controlling the number of the blank types entering the CI set and the total area of the blank, and the value ranges are eta E [3,15 respectively]And beta.epsilon.2, 8]. The code lines 2 to 7 represent that the CI set is determined according to the principle that k can be as large as possible on the premise that n and S can reach a specified threshold, wherein the line 5 ensures that the number of each blank selected into the CI set is an integral multiple of the maximum number p of raw materials per stack, and the aim is to enable the number of raw materials cut per time to reach the maximum number of the raw materials allowed by one stack as much as possible; line 6 shows that if the number ri of currently examined blank types can reach an integer multiple of p sheets per stack of raw material, adding the blank types into the CI set; line 7 shows that if the number of blank types of the CI set is less than eta or the total area of the blanks is less than beta LW, the rest blanks are continuously traversed, and the rest blanks meeting the conditions are added into the CI set; line 8 indicates if k max If the values of < 1 or n and S do not reach the prescribed threshold, all the rest blanks are added into the CI set, and the continuous grouping is finished.
2.3 GetPattern () function
The GetPattern () function determines the current layout by solving the bounded two-dimensional knapsack problem as follows:
the current layout is generated by adopting a recurrence method, and the aim is to maximize the value of the blank contained in the layout. Let v (y) and N (y, i) denote the value of the blank and the number of i-th blanks, respectively, contained in the layout with width y.
The recurrence formula is as follows:
the recurrence formula represents a layout diagram of width y, which has the characteristic of full capacity: once v (W) is calculated, v (y) has been calculated for all y ε [0, W ]. From the value of v (y), the value of N (y, i) can be determined. And (3) starting to roll back from y=W, and determining all the layout diagrams according to the blank arrangement condition recorded in the recursion process.
During recursion, whether the ith blank can be placed on the original material is judged according to the total value v (y) of the blanks arranged on the original material: if the total value v (y) of the blank on the raw material after being placed is greater than the total value v (y-w) of the blank before being placed i ) And placing the current blank, or else, not placing the current blank. The above is given by a recursion formula with the blank direction fixed, and the blank length and width can be interchanged on the assumption that the blank is allowed to turn, i.e. when a certain blank is placed on the raw material, the long edge of the blank can be in the horizontal direction, and the wide edge of the blank can be in the horizontal direction.
2.4 CorrectValue () function
By adopting the idea of value correction, the algorithm comprehensively considers the utilization rate of the current layout, the area of the blank and the value of the previous blank. And obtaining new blank value after each iteration, so that the blank value tends to be reasonable. The value correction formula used is as follows:
wherein sigma and rho are control parameters, and default values are respectively 0.75 and 1.02; u is the utilization rate of the current layout, and f is the number of times the current layout is used. Calculate g 2 The numerator is multiplied by f in order to increase the value adjustment amplitude.
The technical effects of the present invention will be further described in conjunction with experiments.
The algorithm is realized by adopting C# programming, the experimental platform is a win10 operating system, and the computer used for the experiment is configured as i5-8300,3.00GHz main frequency and 8GB memory.
(1) Comparing the invention with the result of the existing algorithm
Compared with the prior art 1, the invention can realize a blanking mode of 'one-step cutting', and can meet the simplicity of numerical control blanking. However, the grouping rules adopted by the two are different, and in the prior art 1, the number of workblank types which can be laid out for each raw material is simply limited, and the number of workblank types is practically limited to 3 in the given example. To fully compare the effectiveness of the algorithm, a test was performed using the example of prior art 1, the required blank data information is shown in table 1, the stock size used is 2440mm x 1220mm, and the resulting layout is shown in fig. 3.
The blank required in the blanking scheme of the invention and the prior art I are satisfied, and two raw materials are used, so that the utilization rate obtained by the two algorithms is the same and is 75.8%. Although the utilization rate of the blanking scheme obtained by the two algorithms is the same, the layout diagram of the blanking method is more compact, so that the residual material blocks are relatively concentrated to form larger available residual materials, on one hand, the subsequent blanking can be facilitated, and on the other hand, the blank with other requirements can be arranged by allowing the spare raw materials.
Table 1 prior art one blank demand table
(2) Policy comparison of per-stack grouping to non-grouping
The algorithm design of the invention aims at solving the problem of cutting and blanking according to stack with larger demand, thus adopting two groups of test example problems in the prior art 8, and expanding the demand of each blank of sample data by 10 times as new blank demand. Each set of examples contained 10 test samples, 50 blanks each, with 3000mm by 1500mm stock sizes. In calculating the total cost, it is assumed that the cost per log and the cost per stack of cuts are 60 yuan. Let the maximum number of sheets per stack p=5, the maximum number of iterations G of the algorithm max =50, calculating all (η, β) combinations in the value range, and selecting the solution with the minimum total cost as the optimal solution output. Table 2 lists the test results, grouped by stack and not, where delta represents the difference in the corresponding parameters for the two algorithm results. As can be seen from the table, the total cut stack number after grouping was reduced by 29.82% ((1244-873)/1244), and the total grouping and ungrouping costs were 234120 and 254280, respectively, the former being reduced by 20 compared to the latter160-fold numbers 873 and 1244, respectively, the former being reduced by 371 fold compared to the latter. The reduction in stack number greatly reduces the blanking cost compared to no grouping, and the overall cost is also significantly reduced. From the calculation time, the average calculation time of the non-grouping algorithm is 6.17s, the average calculation time of the grouping algorithm is 2.83s, and the grouping algorithm is superior to the non-grouping algorithm. It follows that the sequential stacked heuristic proposed by the present invention is effective in reducing the number of stacks and reducing the overall cost.
Table 2 test results of stacked grouping and ungrouping
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (5)
1. The furniture plate stacking blanking grouping heuristic method is characterized in that a candidate blank set is generated by adopting a whole stacking rule in a grouping process according to the furniture plate stacking blanking grouping heuristic method; selecting blanks from the candidate blank sets to generate a current layout, adding the current layout into a current blanking scheme, and repeating until the requirements of all the blanks are met; after a blanking scheme is obtained, correcting blank values by adopting a value correction algorithm, continuing iteration to obtain a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost;
the grouping heuristic method for the furniture boards according to the stacking blanking comprises the following steps:
(1) Inputting blank and raw material data, initializing the current blanking scheme to be empty, wherein G=1, the blanks are all regular rectangles, namely, cutting m kinds of rectangular blanks required from raw materials with the size of L multiplied by W,its size is l i ×w i ；
(2) If G > G max Turning to Step9, otherwise, let b i ＝d i ；
(3) Calling a GetGroup () function, and grouping by using the whole stacking rule;
(4) Calling a GetPattern () function to generate a current layout;
(5) Calculating the use times f and the stacking number omega of the current layout, and adding the current layout into the current blanking scheme;
(6) Let b i ＝b i -fy i The remaining requirements of the blank are updated, wherein i=1 and wherein, m; if b is present i > 0, step (3);
(7) Calculating the total cost of the current blanking scheme;
(8) Calling a CorrectValue () function to correct the value of the blank, enabling G=G+1, and turning to the step (2);
(9) Selecting a blanking scheme with the minimum total cost from all blanking schemes as an optimal scheme to output;
wherein G is the current iteration number, G max For maximum iteration number, b i The remaining demand for the ith blank, c i For the value of the ith blank, d i Initial demand for ith blank, y i For the number of i-th blanks in the current map (i=1,., m), f is the number of current map uses;
in the step (5), the method for calculating the number of times f and the number of stacks ω of the current layout includes:
determining the number of times f of use of the current layout and determining the log cutting stack number omega by using the following steps:
p is the maximum number of sheets of raw materials in each stack, and the stacking rule means that the number of selected blanks is an integer multiple of P during grouping layout; after each generation of the map, the number of uses of the map is determined to be an integer multiple of p.
2. The method of grouping heuristic blanking of furniture boards by stack of claim 1, wherein the method of grouping heuristic blanking of furniture boards by stack of furniture further comprises:
firstly, selecting blanks, namely rectangular pieces, according to the whole stacking rule of the plate blanking problem based on a heuristic algorithm grouped by stacking, and determining the blanks grouped to form a candidate set;
step two, grouping and layout are carried out by utilizing the demand blanks of the candidate set to generate a current layout, and the using times of the current layout are determined according to the stacking rule;
step three, repeating the step two until all blanks meet the requirements; determining a blanking scheme;
and fourthly, correcting the blank value by adopting a blank value correction algorithm, constructing an optimized model with a target structure with the minimum total cost of material cost and cutting cost, iterating for a plurality of times to generate a plurality of different blanking schemes, and outputting the blanking scheme with the minimum total cost.
3. The method of claim 1, wherein in step (3), the GetGroup () function includes: the GetGroup () function groups the rest blank according to the whole stacking rule, and obtains the current candidate blank set, namely CI set after each grouping; sequentially inspecting all blank types during grouping, adding the blank types with larger demand into the CI set preferentially, selecting various blanks, and keeping the blank type diversity of the CI set; when the blank demand is large, the number of raw materials cut each time reaches the upper limit of the number of each stack.
4. The method of claim 1, wherein in step (4), the GetPattern () function includes: the GetPattern () function determines the current layout by solving the bounded two-dimensional knapsack problem as follows:
generating a current layout by adopting a recurrence method;
v (y) and N (y, i) respectively represent the value of the blank and the number of the ith blank contained in the layout with the width of y; the recurrence formula is as follows:
and (3) a recursion formula represents a layout diagram with the width of y, and during recursion, judging whether the ith blank can be placed on the raw material according to the total value v (y) of the blanks arranged on the raw material: if the total value v (y) of the blank on the raw material after being placed is greater than the total value v (y-w) of the blank before being placed i ) And placing the current blank, or else, not placing the current blank.
5. The method of claim 1, wherein in step (8), the correct value () function includes: a value correction formula is adopted, the utilization rate of the current layout, the area of the blank and the value of the previous blank are integrated, and a new blank value is obtained after each iteration; the value correction formula is as follows:
wherein σ and ρ are control parameters; u is the utilization rate of the current layout, and f is the use times of the current layout; calculate g 2 The numerator is multiplied by f for increasing the value adjustment amplitude.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010136723.XA CN111368421B (en) | 2020-03-02 | 2020-03-02 | Grouping heuristic method for stacking and blanking furniture boards |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010136723.XA CN111368421B (en) | 2020-03-02 | 2020-03-02 | Grouping heuristic method for stacking and blanking furniture boards |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111368421A CN111368421A (en) | 2020-07-03 |
| CN111368421B true CN111368421B (en) | 2023-07-28 |
Family
ID=71210265
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010136723.XA Active CN111368421B (en) | 2020-03-02 | 2020-03-02 | Grouping heuristic method for stacking and blanking furniture boards |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111368421B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113361755A (en) * | 2021-05-31 | 2021-09-07 | 上海工程技术大学 | Optimal grouping-based layout optimization method in automobile welding fixture |
| CN117131989B (en) * | 2023-09-04 | 2024-08-09 | 晞德求索(北京)科技有限公司 | Two-dimensional blanking method and system based on dynamic allocation |
| CN117314316B (en) * | 2023-10-17 | 2024-07-30 | 湘南学院 | Warehouse-in and warehouse-out scheduling method of customized furniture plate automatic sorting system |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| BE707161A (en) * | 1966-12-13 | 1968-05-28 | ||
| CN101533418A (en) * | 2008-03-14 | 2009-09-16 | 上海卡休智能科技有限公司 | Method for toy pieces blanking |
| CN103164752A (en) * | 2013-04-03 | 2013-06-19 | 中国计量学院 | Heuristic one-dimensional blanking method based on stratified random search algorithm |
| CN109118002A (en) * | 2018-08-09 | 2019-01-01 | 广东工业大学 | A kind of board-like product cutting stock and branch mailbox divide frame integrated optimization method |
| CN110110980A (en) * | 2019-04-25 | 2019-08-09 | 广西大学 | A kind of wafer discharging measuring method that clout is generated and utilized |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9626638B2 (en) * | 2012-03-19 | 2017-04-18 | Northeastern University | Method and device for assigning surplus slabs in the slab yard before hot rolling process |
| CN102637272B (en) * | 2012-03-19 | 2016-05-04 | 东北大学 | Distribution method and the device of the front storehouse of hot rolling slab residue slab |
-
2020
- 2020-03-02 CN CN202010136723.XA patent/CN111368421B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| BE707161A (en) * | 1966-12-13 | 1968-05-28 | ||
| CN101533418A (en) * | 2008-03-14 | 2009-09-16 | 上海卡休智能科技有限公司 | Method for toy pieces blanking |
| CN103164752A (en) * | 2013-04-03 | 2013-06-19 | 中国计量学院 | Heuristic one-dimensional blanking method based on stratified random search algorithm |
| CN109118002A (en) * | 2018-08-09 | 2019-01-01 | 广东工业大学 | A kind of board-like product cutting stock and branch mailbox divide frame integrated optimization method |
| CN110110980A (en) * | 2019-04-25 | 2019-08-09 | 广西大学 | A kind of wafer discharging measuring method that clout is generated and utilized |
Non-Patent Citations (2)
| Title |
|---|
| 圆形件下料顺序分组启发式算法的设计与实现;陈燕;《图学学报》;20170228;第38卷(第1期);第5-9页 * |
| 考虑余料生成及利用的圆片下料算法;王婷婷;《锻压技术》;20190430;第44卷(第4期);第40-47页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111368421A (en) | 2020-07-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111368421B (en) | Grouping heuristic method for stacking and blanking furniture boards | |
| CN110991755B (en) | Optimized blanking method for multi-size rectangular plate piece considering machinability | |
| CN106845726B (en) | Rectangular piece optimized blanking method oriented to excess material concentration | |
| CN105809297B (en) | A kind of thermal power plant's environmental economy dispatching method based on multiple target differential evolution algorithm | |
| CN109240202A (en) | A kind of Milling Process Cutting tool method for optimizing route towards low-carbon | |
| Liu et al. | Energy-oriented bi-objective optimisation for a multi-module reconfigurable manufacturing system | |
| CN109597304A (en) | Die storehouse Intelligent partition storage method based on artificial bee colony algorithm | |
| CN111311004B (en) | Layered iterative layout optimization method considering cutting efficiency and utilization rate | |
| CN108090650A (en) | A kind of row's case optimization method based on genetic algorithm | |
| CN111783254A (en) | Steel cutting control method and device based on multi-target mixed integer programming | |
| CN109993639A (en) | A kind of virtual plant participates in the optimization bidding strategy of Day-ahead electricity market | |
| CN110110980A (en) | A kind of wafer discharging measuring method that clout is generated and utilized | |
| CN104570997A (en) | Method for discharge and processing production scheduling integration optimization of metal structure components | |
| Mejia et al. | Medium-term planning of active distribution systems considering voltage-dependent loads, network reconfiguration, and CO2 emissions | |
| CN105605610A (en) | Boiler combustion optimization method based on particle swarm algorithm | |
| CN115660169A (en) | Optimal configuration method and device for comprehensive energy system of fishing ground | |
| CN106971243A (en) | It is a kind of to reduce the hot rolling Optimization Scheduling of productive power cost | |
| CN107370191B (en) | A kind of fired power generating unit generation schedule production method based on improvement ant group algorithm | |
| CN117649091A (en) | Dynamic collaborative optimization method and system for multi-objective scheduling of water engineering | |
| CN117455264A (en) | Rural typical application scene carbon emission reduction comprehensive value evaluation method | |
| CN116956730A (en) | Plate stacking layout optimization method and system | |
| Golfeto et al. | A genetic symbiotic algorithm applied to the one-dimensional cutting stock problem | |
| CN112448411B (en) | Method for planning gathering station site selection and delivery capacity of multi-wind power plant access system | |
| CN116933932A (en) | Two-dimensional rectangular plate layout optimization method | |
| CN106169106B (en) | One-dimensional blanking optimization algorithm based on uniform distribution ordered search |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |