JP2004276034A - Blanking method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To decide an optimum blanking plan excellent in calculation efficiency by eliminating a combination, which does not satisfy equipment restrictions, and a redundant combination, and by making all combinations searchable. <P>SOLUTION: When the blanking plan is prepared by allotting one or more orders to a plurality of steel slabs, after all the combinations, which can be considered under the equipment restrictions and the restrictions for eliminating the redundant combination, are cited by a branch and bound method, the steel slab, which makes the target evaluation function maximum under the restrictions of the number of the ordered sheets, is selected by using the 0-1 programming from among the cited combinations. As a result, the optimum blanking plan is decided. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a sheet picking method, particularly to a sheet picking method that is suitably applied to a case where one or more orders are assigned to a plurality of billets in an ironworks.
[0002]
[Prior art]
In general, in a board drawing plan in which one or more orders are allocated (applied) to a plurality of billets, an initial combination is first determined according to a certain rule, and thereafter, a calculation time is determined by a heuristic method such as a genetic algorithm or simulated annealing. In general, a method of improving the initial combination is allowed (for example, see Patent Document 1).
[0003]
[Patent Document 1]
JP-A-6-142725 [0004]
[Problems to be solved by the invention]
However, in the above-mentioned method of improving the initial combination by a heuristic method such as a genetic algorithm or simulated annealing as long as the calculation time permits, the method of Japanese Patent Application Laid-Open No. 7-96311 has been proposed. As shown in the official gazette, there is only a method of improving the rule of the initial value combination, or excluding a combination having a high evaluation function value from the target of the combination at any time. It was limited to heuristics such as mutation. Therefore, as shown in FIG. 6 (A), a combination which does not satisfy the equipment restrictions because it exceeds the rollable size, or a redundancy which does not need to be searched just because the order is changed as shown in FIG. 6 (B). Many combinations occur at the stage of the combination search, and there is a problem that the calculation efficiency for improvement is low. Further, such a heuristic method has a problem that the optimality is not guaranteed because the entire range of possible combinations is not searched.
[0005]
The present invention has been made to solve the above-mentioned conventional problems, and it is possible to prevent a combination that does not satisfy facility restrictions or a redundant combination that does not need to be searched from occurring at the stage of a combination search. It is an object of the present invention to provide a sheet-drawing method capable of improving the calculation efficiency and enabling an optimum sheet-drawing plan to be determined by making it possible to search the entire area of the combination.
[0006]
[Means for Solving the Problems]
The present invention relates to a method for preparing a board plan by assigning one or more orders to a plurality of billets, in which all possible combinations are restricted under facility restrictions and restrictions for eliminating redundant combinations. After listing by the branch-and-bound method, by using the 0-1 programming method from the listed combinations, and selecting the steel slab that maximizes the objective evaluation function under the constraint of the number of ordered sheets, the sheet removal planning is performed. Is determined, thereby solving the above-mentioned problem.
[0007]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0008]
FIG. 1 is a flowchart showing an outline of a procedure of a plate removing method according to an embodiment of the present invention.
[0009]
In the present embodiment, first, in a first step, combinations that satisfy equipment constraints and eliminate redundant combinations are listed by a branch and bound method (steps 1 and 2), and then in a second step, evaluation function values are evaluated. By selecting only high combinations by the 0-1 programming method (step 4), an optimal planing plan is determined.
[0010]
That is, in the first stage, all combinations satisfying facility restrictions and excluding redundant combinations are listed by the branch and bound method. At this time, according to steps 1 and 2 of the flowchart, respectively, two combinations as shown in the image in FIG. 2 are considered together.
(1) A branch-and-bound method for combining a combination in which orders are arranged in the longitudinal direction and further in the width direction,
{Circle around (2)} Lists are performed by two methods of branch-and-bound method for further combining the combinations arranged in the width direction in the longer direction. By the way, in Patent Document 1, the optimality is not guaranteed in that only the enumeration of (2) is performed.
[0011]
The processes of (1) in step 1 and (2) in step 2 are repeated until the number of remaining groups is less than N (step 3). This N is an integer for determining whether or not the number of orders sufficient to make the plan is appropriate, and is appropriately adjusted according to the size of the order and the amount of calculation time. However, it is desirable that the number be as small as possible.
[0012]
Here, the constraints used in the branch and bound method in the present embodiment will be summarized.
[0013]
(I) The main equipment restrictions are the following C1 to C6.
[0014]
C1: Maximum pressure extension C2: Maximum rolling width C3: Maximum slab length C4: Minimum slab length C5: Combination of component systems possible C6: Shearing equipment restriction C7: Quantity of order
(II) Restriction conditions for eliminating the redundant combination of the above (1) are the following D1 to D5.
[0016]
D1: In the long direction, the items are arranged in order from the one with the widest order.
D2: Items with the same width are arranged in order from the longest order.
D3: Items having the same width and length are arranged in ascending order number.
D4: Those having a width difference of δ1 or more are not adjacent to each other.
D5: Combinations that result in a combined yield of δ2 or less are not performed.
D6: E1 to E5 are satisfied when the combination in the length direction is combined in the width direction.
[0017]
(III) The constraint conditions for eliminating the redundant combination of the above (2) are the following E1 to E5.
[0018]
E1: In the width direction, the longest ones are ordered.
E2: Items with the same length are arranged in order from the one with the widest order.
E3: Items having the same length and width are arranged in ascending order number.
E4: Those having a length difference of ε1 or more are not adjacent to each other.
E5: Combination that does not exceed yield ε2 after combination is not performed.
E6: D1 to D5 are satisfied when the combination in the width direction is combined in the long direction.
[0019]
Note that D1 to D3 and E1 to E3 are restrictions for excluding, when combining plates in the longitudinal direction and the width direction, those that differ only in the order of arrangement.
[0020]
Next, the branch-and-bound method will be specifically described. The methods (1) and (2) are substantially the same in procedure except that the directions are reversed. {Circle around (1)} A branch-and-bound method for combining and arranging orders in the length direction and then combining them in the width direction will be described.
[0021]
The processing procedure of the branch and bound method (1) can be represented by a flowchart shown in FIG. In FIG. 3, constraints (1) to (4) represent the following constraints, respectively, among the constraints described above.
[0022]
Restriction (1): C5, C7, D1, D2, D3, D4, D5
Restriction (2): C1
Restriction (3): C5, C7, D6 (= E1 to E5)
Restriction (4): C2, C3, C4, C6
[0023]
In order to facilitate understanding of the process according to the flowchart of FIG. 3, FIG. 4 shows an example in which the number of orders is small and which is replaced with a search diagram for six cases.
[0024]
First, one order serving as a vertex is selected from the order group shown in FIG. 4A, and it is determined whether or not the vertex satisfies the constraint (1) in the longitudinal direction (steps 12 and 13). However, although illustration is omitted, in the actual processing, at the stage when the vertex is selected in step 11, the constraint condition is determined for only one pattern, and if it is satisfied, only one pattern is left as a candidate.
[0025]
If filled with constraints (1) in step 13, add the order in the longitudinal direction (step 14), the constraint (2), namely the length by arranging the long direction C ₁ of the "Maximum rolling length" It is determined whether the order is satisfied (step 15), and if it is OK, the order is generated as a new node (step 16), and the yield and rolling efficiency are calculated for use in the 0-1 programming method to be performed later (step 17). . This calculation may be performed at the end of the flowchart.
[0026]
Next, it is determined in step 16 whether or not a new node has been created (step 18). If the creation of a new node has been confirmed for the order at that depth (Y), the next step following the order is continued. In order to proceed to the depth order, the process returns to step 12 and the same processing is performed (step 19).
[0027]
If the constraints are not satisfied in steps 13 and 15, and if no new node has been generated in step 18, if all orders have not been added, the process returns to step 12 similarly. Is selected (step 20).
[0028]
After all the orders have been added in step 20, if there are any remaining orders to be selected as new vertices, the process returns to step 11, and the same processing is repeated.
[0029]
The above steps 11 to 20 are repeated until there is no more order as a new vertex (step 21).
[0030]
By the way, in FIG. 4 (B), for the order 1 selected in the step 11, the orders 2, 3,..., 6 are selected as the depth 1, but all the D ₁ in the constraint (1) are selected from the widest one. Since the “arrange” is not satisfied, none of the cases indicates that a new node is not generated as indicated by a black circle.
[0031]
In the same figure (C), when an order having a depth of 1 is similarly added to order 2 selected as a vertex, orders 1 and 3 satisfy constraint (1) and constraint (2) at the same time. As shown, when the new node is determined in step 18 and the next order of depth 2 is added to this new node, order 3 did not satisfy constraint (1), but order 1 did not. Therefore, the state is further generated as a new node, and the determined state is shown. Next, for this new node, the process proceeds to the next depth, and the order is added in the longitudinal direction to increase the depth to 3, 4,..., And when the new node is no longer generated, finish.
[0032]
If there is no longer any order that can be selected as a new vertex in the longitudinal direction in step 21, the process proceeds to step 22 in order to search for a combination in the width direction. Then, the combination of the remaining nodes satisfying both the constraints (1) and (2) by the repetitive processing of the steps 11 to 21 is added in the width direction by processing according to steps 22 to 32, and the final steel is added. A piece combination candidate is determined. The search method in steps 22 to 32 is the same as that in the algorithm for adding an order to a vertex in steps 11 to 21 except that “order” → “combination”, “long direction” → “width direction” is replaced. Therefore, detailed description is omitted.
[0033]
FIG. 4D shows the result of selecting the combination in the width direction of the combinations in the long direction of the orders 2, 3, and 1 in which the new node shown in FIG. An example in which the constraints (3) and (4) are satisfied is shown by a white circle, and an example that is not satisfied is shown by a black circle. The same processing is repeated a required number of times in the width direction.
[0034]
For each combination generated by the branch and bound method in this way, an evaluation index is calculated that comprehensively considers the yield, rolling efficiency, shear efficiency, delivery date achievement rate, component cost, and the like. After that, as shown in step 4 of FIG. 1, an optimal combination is selected from the generated combinations using the 0-1 programming method under the constraint that the number of ordered sheets is satisfied. FIG. 5 shows an image of the process according to the 0-1 programming method. According to this method, assuming that the pattern generation results for up to four orders generated according to the flowchart of FIG. 3 are the eight types shown in the long circles in the upper part of FIG. The two patterns shown in the long circles can be determined for the optimized billet.
[0035]
The algorithm of the 0-1 programming is omitted because it is a general-purpose algorithm. However, due to the recent development of computer technology, the 0-1 programming having a decision variable of several thousands to 10,000 is within 5 minutes. To find the optimal solution.
[0036]
This problem can be expressed as follows. N is a matrix having 1 as an element (order number × 1 matrix), ai is a matrix representing an order required for each combination i (order number × 1 matrix), and xi is a decision variable (1 × 1 matrix) and Ji are evaluation function values (1 × 1 matrix) of each combination ai,
ΣJi ・ xi → max
(However, Σai · xi = N)
Meet.
[0037]
【Example】
Next, examples of the present invention will be described.
[0038]
For a group of 212 orders,
{Circle around (1)} As a result of performing a branch and bound method for further combining the combinations in which orders are arranged in the longitudinal direction in the width direction, 8650 combinations were obtained.
[0039]
or,
{Circle around (2)} As a result of performing a branch and bound method for further combining the combinations arranged in the width direction in the longer direction, 4607 combinations were obtained.
[0040]
Then, from the total of 13,257 combinations, the steel slab which maximizes the objective function value ΣJi · xi described above was obtained by the 0-1 programming method, and 36 combinations were obtained.
[0041]
In this way, the group of 212 pieces could be optimally allocated to 36 billets.
[0042]
The calculation time at this time by a general personal computer was 3 minutes and 14 seconds for the branch and bound method part and 2 minutes and 56 seconds for the 0-1 programming method part, which was a sufficiently practical calculation time.
[0043]
In this embodiment described in detail above, first, in a first stage, combinations that satisfy facility restrictions and eliminate redundant combinations are enumerated by a branch and bound method, and then, in a second stage, combinations having a high evaluation function value are enumerated. By selecting only one by the 0-1 programming method, the optimal planing is determined. As a result, an optimal combination of orders, that is, a plan drawing plan, can be achieved within a practical time without resorting to a heuristic method such as a genetic algorithm or simulated annealing.
[0044]
Although the embodiments of the present invention have been specifically described above, the present invention is not limited to the embodiments described above, and can be variously modified without departing from the gist.
[0045]
【The invention's effect】
As described above, according to the present invention, it is possible to prevent a combination that does not satisfy facility restrictions or a redundant combination that does not need to be searched from occurring at the stage of a combination search, and to search the entire range of possible combinations. By doing so, it is possible to improve the calculation efficiency and determine the optimal plan for taking a sheet.
[Brief description of the drawings]
FIG. 1 is a flowchart showing an outline of a processing procedure according to an embodiment of the present invention. FIG. 3 is a flowchart showing the procedure of the branch-and-bound method in the width direction after the long direction. FIG. 4 is a search diagram showing an example of the procedure of the branch-and-bound method in the width direction after the long direction. FIG. 6 is a flowchart showing an image of an action obtained by combining the 0-1 programming method. FIG.
1-6… Order number

Claims (2)

When applying one or more orders to a plurality of billets to create a board plan, all possible combinations are subject to the branch-and-bound method under facility restrictions and restrictions to eliminate redundant combinations. After enumerating, using the 0-1 programming method from among the enumerated combinations, and determining the billet plan by selecting the billet that maximizes the objective evaluation function under the constraint of the number of ordered pieces. A sheet picking method characterized by the following. As the branch-and-bound method,
A branch-and-bound method for combining a combination of orders arranged in the longitudinal direction and further in the width direction
2. The method according to claim 1, wherein a combination in which orders are arranged in the width direction is combined with a branch and bound method for further combining in the long direction. 3.

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