Planning device, planning program, and planning method

Abstract

To easily execute cast frame layout consolidated to a cast frame in a short time.SOLUTION: A plan creation apparatus (100) comprises: an initial set creation unit (34) creating a plurality of initial sets (C0) in such a manner that the breakdowns of an included virtual steel material (s) are changed; a dual problem solving unit (35) solving the dual optimum solution of dual problems of set partitioning problems; a promising set extraction unit (36) having a candidate set creation unit (361) creating candidate sets and a calculation unit (362) calculating contracted expenses (ηj) of the candidate sets, and extracting all the candidate sets in which the contracted expenses satisfy prescribed standards as promising sets (Ce); and an original problem solving unit (37) solving the optimum solution of the set partitioning problems based on the initial sets and the promising sets.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a planning device, a planning program, and a planning method. [Background technology]

[0002] When manufacturing multiple steel materials by continuous casting, a planning process (hereinafter referred to as "cast frame design") is carried out in advance to consolidate multiple virtual steel materials corresponding to the multiple steel materials to be manufactured into several cast frames, which are the casting units. In continuous casting, increasing the number of molten steel charges can reduce the number of defects that occur when switching steel types and shorten the preparation time required to restart casting. For this reason, it is desirable to include as many virtual steel materials as possible in a single cast frame. On the other hand, among the multiple steel materials to be manufactured, there are mixed materials with different manufacturing conditions (composition, shape, desired hot rolling date, etc.). Therefore, there are limitations on the number of virtual steel materials that can be included in the same cast frame. In other words, in cast frame design, it is necessary to consolidate virtual steel materials while considering these trade-offs. Furthermore, it is common to handle a large number of virtual steel materials, ranging from several hundred to several thousand, in cast frame design. As the number of virtual steel materials increases, the number of combinations of virtual steel materials that can be included in a single cast frame becomes enormous. Traditionally, this work was carried out by the planning person. However, this work was extremely burdensome for the planning person.

[0003] Therefore, various techniques have been proposed for a machine to perform cast frame design on behalf of the planning staff. For example, in Patent Document 1, there is described a planning device having column generation means for generating candidates of feasible lots that constitute an optimal solution of an original problem for obtaining an optimal combination of a plurality of feasible lots, column addition means for adding a candidate lot to a set of feasible lots when the candidate lot satisfies the column addition requirement, and optimal solution derivation means for deriving an optimal solution of the original problem based on the obtained set when the candidate lot does not satisfy the column addition requirement. In addition, in Patent Document 2, there is described a billet sorting planning device having dual problem solving means for repeatedly extracting feasible billets for solving a dual problem based on enumeration of feasible billets, derivation of a column master dual gap for the same, and comparison between the column master dual gap and a first threshold value, and deriving a dual optimal solution for them; selection enumeration means for repeatedly performing selection enumeration of feasible billets for solving an original problem based on enumeration of feasible billets and comparison between a column master dual gap for the feasible billets and a second threshold value; and optimal solution derivation means for solving a set partitioning problem and deriving a set of feasible billets from the feasible billets selected and enumerated. Note that billet sorting refers to an operation of dividing a large number of steel materials transported to a storage yard of steel materials into groups that constitute several optimal billets and stacking them in the form of billets respectively.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] Conventional planning devices, such as the one described in Patent Document 1, derived the optimal solution using a conventional column generation method. Therefore, it was necessary to solve sub-problems during the derivation process. Solving sub-problems requires describing them as mathematical models, but this modeling is not easy. Furthermore, conventional column generation methods are computationally intensive (especially due to loops between the main problem and sub-problems). Therefore, even with a model of the sub-problems, planning for a large number of elements, such as cast frame design, requires an enormous amount of computation time. The planning device described in Patent Document 2 derives the optimal solution using a selection-enumeration type column generation method. However, the selection-enumeration type column generation method described in Patent Document 2 is for the field of distribution planning, which optimizes how to divide multiple steel materials after casting. A challenge exists in that the computational scale of cast frame design is significantly larger compared to distribution planning.

[0006] One aspect of the present invention aims to enable the design of cast frames to be carried out easily and quickly. [Means for solving the problem]

[0007] To solve the above problems, a planning device according to one aspect of the present invention is a planning device that creates a cast frame organization plan by solving a set partitioning problem in which a first number of virtual steel materials corresponding to a first number of steel materials to be cast by continuous casting are aggregated into a second number of cast frames which is less than the first number, and comprises an initial set generation unit that generates multiple initial sets which are the first set of virtual steel materials containing at least one of the virtual steel materials, each with a different breakdown of the virtual steel materials included in the initial set, and solves the set partitioning problem for the multiple initial sets. The system includes: a dual problem solving unit that finds the dual optimal solution to the dual problem of the given subject; a candidate set generation unit that generates candidate sets of virtual steel materials whose breakdown of virtual steel materials differs from that of each initial set, such that they satisfy the conditions for being valid as a cast frame; a calculation unit that calculates the reduced cost of the candidate sets based on the dual optimal solution; a promising set extraction unit that extracts all of the candidate sets whose reduced cost satisfies a predetermined criterion as promising sets; and an original problem solving unit that finds the optimal solution to the set partitioning problem based on a plurality of initial sets and the promising sets.

[0008] Each aspect of the present invention may be implemented by a computer, in which case the planning program for the planning device, which enables the computer to implement the planning device by operating the computer as each part (software element) of the planning device, and a computer-readable recording medium on which the program is recorded also fall within the scope of the present invention.

[0009] Furthermore, another aspect of the present invention relates to a planning method for creating a cast frame organization plan by solving a set partitioning problem that aggregates a first number of virtual steel materials corresponding to a first number of steel materials to be cast by continuous casting into a second number of cast frames which is less than the first number, and the method comprises the steps of: generating a plurality of initial sets, which are the first sets of virtual steel materials containing at least one of the virtual steel materials, by changing the breakdown of the virtual steel materials included in each initial set; solving the dual optimal solution of the dual problem of the set partitioning problem for the plurality of initial sets; generating candidate sets, which are sets of virtual steel materials whose breakdown of included virtual steel materials differs from that of each initial set, in such a way that they satisfy the conditions for being valid as cast frames; calculating the reduced cost of the candidate sets based on the dual optimal solution, and extracting all of the candidate sets whose reduced cost satisfies a predetermined standard as promising sets; and solving the optimal solution of the set partitioning problem based on the plurality of initial sets and the promising sets. [Effects of the Invention]

[0010] According to one aspect of the present invention, the design of the cast frame can be carried out easily and quickly. [Brief explanation of the drawing]

[0011] [Figure 1] This is a block diagram showing the functional configuration of a planning device according to one embodiment of the present invention. [Figure 2] This figure shows an example of the conditions required for a role to be considered. [Figure 3] This diagram shows the method for generating a candidate set. [Figure 4] This flowchart shows the flow of a plan creation method according to another embodiment of the present invention. [Modes for carrying out the invention]

[0012] One embodiment of the present invention will be described in detail below.

[0013] <Set partitioning problem> First, the set partitioning problem (which the following planning device 100 attempts to solve) dealt with in the present invention will be described.

[0014] The set partitioning problem MP dealt with in the present invention is to aggregate a first number of virtual steel materials s corresponding to a first number of steel materials to be cast by continuous casting into a second number of casting frames that is less than the first number.

[0015] In this set partitioning problem MP, one casting frame m j (subset) must be selected from the subset family S(i)⊆M that includes each unit group i∈N (see Equation 1 below). Here, N = {1, 2, ···, n} is the set of unit groups i of the virtual steel material s. The unit group i refers to a collection of virtual steel materials s that are not divided (the smallest unit) during the casting frame design. S(i) is the set of casting frames m j that include the virtual steel material s. M = {S1, S2, …, S m}(S j ⊆N) is the set of casting frames m j (subsets of N) that satisfy the conditions for forming a casting frame (hereinafter referred to as casting frame formation conditions), and has m elements. x[j] is a 0-1 variable that is 1 when the casting frame m j is adopted and 0 when it is not adopted.

[0016]

Equation

[0017] Also, in this set partitioning problem MP, the sum of the main evaluation values (penalties) c j of the selected casting frames m j (S j ∈M) is minimized (see Equation 2 below). Here, the main evaluation value c j is the weighted linear sum of the evaluation indicators of the casting frame m j . The evaluation indicators in the casting frame design are the evaluation indicators of the casting frame m jThis value is calculated based on at least one of the following items: the number of pieces, the number of connected pieces of different steel types, and the amount of surplus material.

[0018]

number

[0019] In summary, the above set partitioning problem MP can be formulated as a 0-1 programming problem, as shown in equation 3 below.

[0020]

number

[0021] Furthermore, by defining the set partitioning problem MP as described above, the dual problem DP for the set partitioning problem MP can be formulated as shown in equation 4 below, where the dual variable is p[i] (i∈N). Here, m j m is a cast frame (subset) and is a vector with n elements. j [i] is a cast slot m j The i-th element, and the cast frame m j The value is 1 if unit group i is included, and 0 otherwise. j is the cast frame m. j This is a parameter for identifying [the set]. Note that while the set partitioning problem MP described above was a 0-1 programming problem, the dual problem DP here is a linear programming problem with relaxed 0-1 conditions.

[0022]

number

[0023] <Planning device> Next, an embodiment of the planning device 100, which is one aspect of the present invention, will be described. Figure 1 is a block diagram showing the functional configuration of the planning device 100.

[0024] The planning device 100 is for creating a cast frame organization plan by solving the set partitioning problem MP described above. The planning device 100 according to this embodiment comprises an input unit 1, an output unit 2, and a calculation unit 3, as shown in Figure 1.

[0025] [Input section] The input unit 1 consists of at least one of the following: a communication module for receiving data and signals from other devices, terminals for connecting to other devices, a drive for reading information from a recording medium, and user-operated devices. The user-operated devices include at least one of a keyboard, mouse, and touch panel.

[0026] [Output section] Output unit 2 consists of at least one of the following: a communication module for transmitting data and signals to other devices (such as display devices), terminals for connecting to other devices, a drive for writing information to a recording medium, and a display device such as a display for displaying images.

[0027] [Calculation section] The calculation unit 3 includes an acquisition unit 31, a unit group aggregation unit 32, a large group generation unit 33, an initial set generation unit 34, a dual problem solving unit 35, a promising set extraction unit 36, an original problem solving unit 37, and an output control unit 38.

[0028] [Acquisition Department] The acquisition unit 31 acquires information on multiple virtual steel materials s to be aggregated via the input unit 1. The information on virtual steel materials s includes at least one of property information and factory operation information. The property information includes at least one of steel type, weight, and shape. The factory operation information includes the desired hot rolling date, etc.

[0029] [Unit Group Aggregation Section] The unit group aggregation unit 32 aggregates a first number (e.g., about 1000) of virtual steel materials s into a third number (e.g., about 100) of unit groups i for planning purposes, which is smaller than the first number, based on manufacturing conditions (e.g., composition, shape, desired hot rolling date, etc.). Unit group i is the smallest unit that cannot be further divided. A unit group contains one or more virtual steel materials s. That is, since the unit group i determines which cast frame each virtual steel material belongs to, virtual steel materials s within the same group will always be incorporated into the same cast. Each virtual steel material s will always be included in one of the unit groups i. In this embodiment, the unit group aggregation unit 32 aggregates virtual steel materials s included in a unit group i so that the aggregation conditions are the same. The aggregation conditions include at least the steel type. The aggregation conditions may also include at least one of weight and shape.

[0030] [Large Group Generation Unit] The large group generation unit 33 generates a fourth large group based on a third number of unit groups i. Each large group includes at least one unit group i and is composed of unit groups i of the same steel type. In other words, a large group is a collection (same steel type cast) whose members are one or more unit groups i of the same steel type. The large group generation unit 33 according to this embodiment generates large groups within the range of predetermined operational constraints. Operational constraints include, for example, shape and weight. For example, if shape is the operational constraint, large groups are generated such that at least one of the lengths, widths, and thicknesses of each virtual steel material s included in each unit group i is the same or falls within a predetermined range. If weight is the operational constraint, large groups are generated such that the total weight of each virtual steel material s included in each unit group i is the same or falls within a predetermined range. In the generation of large groups, one unit group i may belong to multiple large groups. For this reason, the fourth number may be larger than the third number. The cast frame has a structure in which multiple large groups (nodes) are linked together (node ​​connections). Therefore, by generating such large groups, the design of the cast frame can be made even easier. The large group generation unit 33 may be configured to generate large groups using machine learning techniques.

[0031] Furthermore, the large group generation unit 33 according to this embodiment stores information on the generated large groups separately by steel type and charge number. In addition, the large group generation unit 33 according to this embodiment calculates a main evaluation value (details described later) based on the operational constraints common to each unit group i included in the generated large group.

[0032] [Initial set generator] The initial set generation unit 34 generates multiple initial sets, which are sets of the first unit group i consisting of at least one unit group i, each with a different breakdown of the virtual steel materials s included in the initial set. In this embodiment, in order to efficiently perform computer processing, these sets of unit group i are managed as columns, and the initial set generation unit 34 generates multiple initial columns, which are columns of the first unit group i, each with a different breakdown of the virtual steel materials s included in the initial column. Here, a column means a set (subset) of unit group i whose members are one or more unit group i. In this embodiment, a set partitioning problem with n unit group i as elements is solved, and a column is a list (array) of a number (n) of variables corresponding to all (n) unit group i. Each variable is set to a value, character, or symbol (e.g., 1) if the corresponding unit group i is included in that column (set), and to a value (e.g., 0) if it is not included, thereby indicating which unit group i is included in each column (set) by the variable value, etc.

[0033] The initial set generation unit 34 according to this embodiment stores initial columns, with 1 representing the case where each unit group i is included and 0 representing the case where it is not included. That is, the column (initial column, candidate column) here refers to an array of 0s and 1s. Furthermore, the initial set generation unit 34 according to this embodiment generates at least one initial column containing only one unit group i, for each unit group i. Since there are n unit groups i, n initial columns containing only one unit group i will also be generated. Then, the initial set generation unit 34 further generates initial columns containing two or more unit groups i. Hereinafter, the collection of multiple initial columns that the initial set generation unit 34 has finished generating will be referred to as the initial column group C0.

[0034] In the above explanation, the set of unit groups i has been described as a column, because the unit group aggregation unit 32 aggregates multiple virtual steel materials s into unit group i. Therefore, if such aggregation of virtual steel materials s is not performed, the column may be a set of virtual steel materials s.

[0035] [Department for solving dual problems] The dual problem solving unit 35 solves the dual optimal solution p[i] (dual price) (i∈N) of the dual problem DP of the set partitioning problem MP for multiple initial sets. In this embodiment, the dual problem solving unit 35 solves the dual optimal solution p[i] (dual price) (i∈N) for the initial sequence group C0 generated by the initial set generation unit 34. This dual optimal solution p[i] is then calculated by the calculation unit 362, which will be described later, using the reduced cost η j This is used when calculating the dual problem solving unit 35 in this embodiment calculates the dual optimal solution p[i] by solving the above equation 4.

[0036] [Promising set extraction unit] The promising set extraction unit 36 ​​calculates the reduced cost η j A predetermined number of candidate sets that satisfy predetermined criteria (details described later) are extracted as promising sets. The promising set extraction unit 36 ​​according to this embodiment extracts candidate columns as promising columns. The promising set extraction unit 36 ​​according to this embodiment calculates the reduced cost η j The system extracts all candidate columns that meet predetermined criteria as promising columns. As shown in Figure 1, the promising set extraction unit 36 ​​comprises a candidate set generation unit 361, a calculation unit 362, a first decision unit 363, and a second decision unit 364.

[0037] (Candidate set generation unit) The candidate set generation unit 361 generates candidate columns in which the breakdown of the included unit group i differs from that of each initial column, in such a way that the cast frame formation conditions are met. The cast frame formation conditions include cast capacity, number of consecutive different steel types, adjacent width transfer amount, etc. Cast capacity is a constraint on the amount of molten steel that can be included in one cast. As shown on the left side of Figure 2, if the cast capacity is set to be less than or equal to C charge (C=1,2...), it is not possible to generate a candidate column that requires C+1 charge or more. The number of consecutive different steel types is a constraint on the number of steel types that can be included in one cast. As shown in the center of Figure 2, if the number of consecutive different steel types is set to be less than or equal to K steel type (K=1,2...), it is not possible to generate a candidate column that includes K+1 or more steel types. Width transfer amount is a constraint on the width difference between adjacent virtual steel materials s. As shown on the right side of Figure 2, if the width transfer amount is set to be less than or equal to W mm, it is not possible to generate a candidate column in which the width difference between adjacent virtual steel materials s is W+α mm.

[0038] The candidate set generation unit 361 according to this embodiment first acquires the large group generated by the large group generation unit 33. Then, the candidate set generation unit 361 generates candidate sequences using the large group as the constituent unit. The candidate set generation unit 361 according to this embodiment uses the large group as a single node and first generates the first candidate sequence. Specifically, it generates the first (single) candidate sequence by connecting a predetermined number of nodes (for example, five). The selection of nodes used to generate the first candidate sequence is done randomly (however, the above-mentioned casting frame conditions must be met) or according to some rule.

[0039] The candidate set generation unit 361 then generates the first (previous) candidate sequence, and then generates the second and subsequent (next) candidate sequences. In this embodiment, the candidate set generation unit 361 generates the second and subsequent candidate sequences by branching enumeration. Specifically, in the branching enumeration process, the k-th large group from the beginning is defined as node k. As shown in Figure 3, the same nodes as the first (one) candidate sequence are arranged from the 1st to the k(determined)th node, and the next candidate sequence is generated by connecting a node k+1 that is different from the k+1 (the node after the predetermined)th node in the first candidate sequence to the k(determined)th node k.

[0040] Furthermore, if a predetermined termination condition is met before connecting the k+1 (next) node, the candidate set generation unit 361 will stop connecting the k+1 (next) node k+1 (terminate the branch of node k). In this embodiment, the candidate set generation unit 361 terminates the connection when the second determination unit 364, described later, determines that the connection of node k should be terminated. For example, the predetermined termination conditions are: the next node k to be connected does not satisfy the cast frame condition; the next node k to be connected does not satisfy the candidate set generation condition; or connecting the node would result in a reduced cost η j It may include at least one condition indicating that it is unlikely to meet the prescribed criteria.

[0041] For example, a method that prepares all candidate sequences and then determines whether or not the casting frame conditions and candidate set generation conditions are met would take too much computation time. However, the candidate set generation unit 361 terminates node connections as needed, thereby generating a promising sequence group C e The time required to enumerate them can be further reduced.

[0042] The candidate set generation unit 361 may also be configured to acquire a unit group i of a third number and generate a candidate sequence using the unit group i as the constituent unit. Alternatively, the candidate set generation unit 361 may be configured to acquire a virtual steel material s of a first number and generate a candidate sequence using the virtual steel material s as the constituent unit.

[0043] (Calculation section) The calculation unit 362 calculates the reduced cost η of the candidate sequence based on the dual optimal solution p[i]. j The calculation unit 362 in this embodiment calculates the following equation 5 and the main evaluation value c calculated by the large group generation unit 33. j By substituting the dual optimal solution p[i] (dual price) calculated by the dual problem solving unit 35 above, the reduced cost η j Calculate.

[0044]

number

[0045] In this embodiment, the calculation unit 362 calculates the reduced cost η each time a node k is connected to a candidate sequence in the process of generation. j The calculation unit 362 calculates the value. In doing so, it passes on the information obtained when connecting the previous node k to the next node k. Therefore, when connecting the next node, it is possible to omit calculations that are duplicated with the calculations performed when connecting the previous node. As a result, the time required to extract promising columns can be shortened. The calculation unit 362 may be configured to calculate the main evaluation value instead of the large group generation unit 33.

[0046] (First Judgment Department) The first determination unit 363 determines whether to terminate the generation of candidate sequences (connection of node k) by the candidate set generation unit 361. In this embodiment, the first determination unit 363 makes this determination each time the candidate set generation unit 361 connects node k. In this embodiment, the first determination unit 363 determines whether the next node k to be connected does not satisfy the cast frame establishment condition, the next node k to be connected does not satisfy the candidate set generation condition, or whether connecting the node will result in reduced cost η j If it is not expected that the predetermined criteria will be met, the generation of candidate sequences will be terminated. The candidate set generation conditions are the same as the initial set generation conditions described above. "Reduced cost η j For "to meet the prescribed criteria," for example, the contracted cost η jThis includes the fact that is less than a predetermined value (for example, 0). In this embodiment, the first determination unit 363 determines that if the following equation 6 is satisfied, the reduced cost η can be maintained even if the connection of node k is continued after column j. j It is determined that no candidate sequences will appear where the value is less than the predetermined value. Note that Δη in Math 6 j The reduced cost η is achieved by connecting node k after a certain column j. j This is the amount of change.

[0047]

number

[0048] However, depending on the problem, the change Δη within an acceptable time frame may be... j In some cases, it may not be possible to calculate the change Δη accurately. j We consider a pseudo-representation of this using only values ​​that can be decomposed for each node k that can be connected after column j (Δη j ≒Σ k Δη jk First, the sum of the dual optimal solutions p[i] of column j (Σ i∈N p[i]×m j Let's consider [i]). This is obtained by adding up the dual optimal solutions p[i] corresponding to the unit group i in column j, for each unit group i. Also, since node k is the set (large group) of unit groups i that make up the column, the sum of the dual optimal solutions p[i] that node k has can also be calculated from the dual optimal solutions p[i] of unit group i. The sum of the dual optimal solutions p[i] of a column can be calculated by adding up the sum of the dual optimal solutions p[i] that the nodes k that make up the column have. That is, the sum of the dual optimal solutions p[i] of a column can be decomposed into the sum of the dual optimal solutions p[i] of each node k. On the other hand, the principal evaluation value cj of column j can be decomposed into principal evaluation values ​​of node k, or into those that cannot (cannot be calculated unless multiple nodes k are determined). Here, the principal evaluation value of the node k that is added after column j is c jk The sum of the dual optimal solutions p[i] is Σ i∈N p[i]×m jk When [i], Δη jk =c jk -Σ i∈Np[i]×m jk [i] so min[Σ k (c jk -Σ i∈N p[i]×m jk [i]) is Δη j The minimum value of can be pseudo-represented. The reason it is pseudo-represented is that the change in the principal evaluation value that cannot be decomposed into the principal evaluation value of node k is not included in the calculation. However, if the principal evaluation value cj can only take positive values, the change Δη j This means we are underestimating the number, and there will be no omissions in the list.

[0049] The candidate set generation unit 361, through the operations described above, completes the connection of node k to the end, and the reduced cost η j Candidate columns that meet the specified criteria are designated as promising column C. e Extract it as follows.

[0050] (Second Judgment Department) The second determination unit 364 determines that the candidate set generation unit 361 has a promising sequence C e When extracted, all promising columns C e Determine whether or not the desired result was extracted. All promising columns C e If it is determined that the desired result has not been extracted, the candidate set generation unit 361 repeats its operation.

[0051] The promising set extraction unit 36, through the operations described above, reduces the cost η j The system extracts all candidate columns that meet predetermined criteria as promising columns. The promising set extraction unit 36 ​​extracts promising columns using logic rather than solving subproblems. This allows the promising set extraction unit 36 ​​to extract promising columns even when the constraints that the candidate columns must satisfy and the calculation of evaluation values ​​are complex.

[0052] [Original problem solving department] The original problem solving unit 37 solves the optimal solution to the set partition problem based on a plurality of initial sets and promising sets. In this embodiment, the original problem solving unit 37 solves the optimal solution to the set partition problem MP based on the initial sequence group C0 and promising sequences. Specifically, the original problem solving unit 37 uses the initial sequence group C0 generated by the initial set generation unit 34 and the promising sequence group C extracted by the promising set extraction unit 36. e The combined column group C0+C e Regarding the set partitioning problem MP(C0+C) shown in equation 3 above, e ) Solve the obtained solution x opt [j](j∈C0+C e ) is considered the optimal solution.

[0053] [Output Control Unit] The output control unit 38 controls the output unit 2 to output the optimal solution found by the original problem solving unit 37 as a cast frame organization plan to be proposed to the user (including influencing the OS (Operating system) that controls the output unit 2).

[0054] [others] The functions of the planning device 100 (hereinafter referred to as "device") can be realized by a planning program (hereinafter referred to as "program") that causes the device to function as a computer, and which causes each control block of the device (particularly each part included in the arithmetic unit 3) to function as a computer. In this case, the device includes a computer having at least one control device (e.g., arithmetic unit 3) and at least one storage device (e.g., memory) as hardware for executing the program. By executing the program using this control device and storage device, each function described in each of the above embodiments is realized. The program may be recorded on one or more computer-readable recording media, not just temporarily. This recording media may or may not be provided by the device. In the latter case, the program may be supplied to the device via any wired or wireless transmission medium.

[0055] Furthermore, some or all of the functions of each of the above control blocks can also be realized by logic circuits. For example, an integrated circuit in which logic circuits functioning as each of the above control blocks are formed is also included in the scope of the present invention. In addition, it is also possible to realize the functions of each of the above control blocks by, for example, a quantum computer.

[0056] [Effects and Effects] According to the planning device 100 described above, the casting frame m of the virtual steel material s j A new method that uses a selection enumeration type column generation method for aggregation into a subset, namely the reduced cost η j All candidate sequences that meet predetermined criteria are extracted as promising sequences, and these are aggregated. Therefore, there is no need to solve sub-problems to find the best single sequence, as in the conventional method. As a result, the effort required to model and solve sub-problems is reduced, and the creation of the production plan can be made easier than before. Then, by performing continuous casting based on the obtained results, the first number of steel materials corresponding to the first number of virtual steel materials s can be cast in a short period of time and at low cost.

[0057] Furthermore, the number of virtual steel members s in cast frame design is very large (for example, on the order of 1000). On the other hand, the technology described in Patent Document 2 deals with a small number of elements, about 50 to 80. Therefore, even if one were to conceive of applying the technology of Patent Document 2 to cast frame design, further ingenuity would be required to make it actually usable. In contrast, the planning device 100 includes a unit group aggregation unit 32. This unit group aggregation unit 32 aggregates the virtual steel members s into unit groups as described above, thereby appropriately reducing the number of virtual steel members s in the set partitioning problem MP. As a result, the design of cast frames can be made easier.

[0058] [How to create a plan] Next, another embodiment of the plan creation method of the present invention will be described. Figure 4 is a flowchart showing the flow of the plan creation method.

[0059] The planning method is for creating a cast frame organization plan by solving a set partitioning problem MP that aggregates a first number of virtual steel materials s to be cast by continuous casting into a second number of cast frames which is less than the first number. The planning method according to this embodiment, as shown in Figure 4, includes a unit group aggregation step S1, a large group generation step S2, an initial set generation step S3, a dual problem solving step S4, a promising set extraction step S5, and an original problem solving step S6.

[0060] [Unit Group Aggregation Step] The unit group consolidation step S1 consolidates a first number of virtual steel materials s into a third unit group i, which is less than the first number, based on the manufacturing conditions. In the unit group consolidation step S1 according to this embodiment, the unit group consolidation unit 32 of the planning device 100 performs the consolidation. In this unit group consolidation step S1, a person may also consolidate the units into unit group i.

[0061] [Large Group Generation Step] The large group generation step S2 generates a fourth large group based on a third number of unit groups i. Each large group includes at least one of the above unit groups i and is composed of unit groups i of the same steel type. In this embodiment, the large group generation step S2 is performed by the large group generation unit 33 of the planning device 100. In this large group generation step S2, a person may also create the large groups.

[0062] [Initial set generation step] In the initial set generation step S3, multiple initial sets are generated, each containing at least one virtual steel material, with varying compositions of the virtual steel materials included in the initial set. In the initial set generation step S3 according to this embodiment, an initial column group C0 is generated. In the initial set generation step S3 according to this embodiment, the initial set generation unit 34 of the planning device 100 generates the initial set. In this initial set generation step S3, another device may generate the initial column group C0. Also, in this initial set generation step S3, the initial set generation unit 34 may generate the initial column group C0 using a calculation method other than that described above.

[0063] [Steps for solving the dual problem] In the dual problem solving step S4, the dual optimal solution p[i] of the dual problem DP of the set partition problem MP is solved for the initial set. In the dual problem solving step S4 according to this embodiment, the dual optimal solution p[i] is solved for the initial sequence group C0. In the dual problem solving step S4 according to this embodiment, the dual problem solving unit 35 of the plan creation device 100 solves the problem.

[0064] [Promising Set Extraction Step] After generating candidate columns and calculating the reduced costs, the process moves to the promising set extraction step S5. In the promising set extraction step S5, the reduced cost η j All candidate sets that satisfy predetermined criteria are extracted as promising sets. In the promising set extraction step S5 according to this embodiment, the promising set extraction unit 36 ​​of the planning device 100 performs the extraction. The promising set extraction step S5 according to this embodiment also includes a candidate set generation step S51, a calculation step S52, a first judgment step S53, and a second judgment step S54. In the promising set extraction step S5 according to this embodiment, promising sets are extracted by repeating these candidate set generation step S51, calculation step S52, first judgment step S53, and second judgment step S54.

[0065] [Candidate set generation step] In the candidate set generation step S51, a candidate set is generated such that the composition of the included unit group i differs from that of each initial set, and that the cast frame establishment condition is met. In the candidate set generation step S51 according to this embodiment, the candidate set is generated by the candidate set generation unit 361 of the planning device 100.

[0066] [Calculation Steps] After generating the candidate set, the process moves to calculation step S52. In calculation step S52, the reduced cost η of the candidate set is calculated based on the dual optimal solution p[i]. j The calculation is performed by the calculation unit 362 of the planning device 100 in calculation step S52 of this embodiment.

[0067] [First decision step] After calculating the contracted costs, the process moves to the first decision step S53. In the first decision step S53, it is determined whether or not to terminate the generation of the candidate set (connection of node k) in the candidate set generation step described above. In the first decision step S53 according to this embodiment, the first decision unit 363 of the plan creation device 100 makes the decision.

[0068] [Second decision step] After the candidate set has been generated (the promising set has been extracted) without being terminated midway, the process moves to the second decision step S54. In the second decision step S54, all promising sequences C e It is determined whether or not the item has been extracted. In the second determination step S54 according to this embodiment, the second determination unit 364 of the plan creation device 100 makes the determination.

[0069] [Steps to solve the original problem] In the promising set extraction step S5 described above, if it is determined that all promising sets have been extracted, the process moves to the original problem solving step S6. In the original problem solving step S6, the optimal solution to the set partitioning problem is found based on multiple initial sets and promising sets. In the original problem solving step S6 according to this embodiment, the initial set generation step C0 generated in the initial set generation step and the promising set extraction unit C extracted by the promising set extraction unit 36 ​​are used. e The combined column group C0+C eRegarding the set partitioning problem MP(C0+C) shown in equation 3 above, e ) Solve the obtained solution x opt [j](j∈C0+C e ) is considered the optimal solution. In the original problem solving step S6 according to this embodiment, the original problem solving unit 37 of the planning device 100 solves the problem.

[0070] [Effects and Effects] According to the planning method described above, the casting frame m of the virtual steel material s j A new method that uses a selection enumeration type column generation method for aggregation into a subset, namely the reduced cost η j All candidate sets that satisfy predetermined criteria are extracted as promising sets, and these are aggregated. Therefore, there is no need to solve sub-problems to find the best single set, as in the conventional method. As a result, the effort of modeling and solving sub-problems can be saved, and the creation of the organization plan can be made easier than before. Then, by performing continuous casting based on the obtained results, the first number of steel materials corresponding to the first number of virtual steel materials s can be cast in a short period of time and at low cost.

[0071] The present invention is not limited to the embodiments described above, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention. For example, at least a portion of each functional unit of the planning device, such as the initial set generation unit 34, the dual problem solving unit 35, and the original problem solving unit 37, may be provided in another device (such as a computer) in a separate enclosure that is connected in a communicative manner. [Explanation of Symbols]

[0072] 100 Planning device 1 Input section 2 Output section 3 Arithmetic section 31 Acquisition Department 32 Unit Group Aggregation Department 33 Large Group Generation Unit 34 Initial set generator 35. Solving Bilateral Problems 36. Expected to be collected and extracted from the department. 361 Candidate Set Generating Department 362 Calculation Department 363 First Judgment Department 364 Second Judgment Section 37 Original Problem Solving Department 38 Contribute to the Control Department

Claims

1. A planning device for creating a cast frame organization plan by solving a set partitioning problem that aggregates a first number of virtual steel materials, corresponding to a first number of steel materials to be cast by continuous casting, into a second number of cast frames that is less than the first number, wherein An initial set generation unit generates multiple initial sets, which are the first set of virtual steel materials containing at least one of the virtual steel materials, by changing the composition of the virtual steel materials included in each initial set. A dual problem solving unit that finds the dual optimal solution of the dual problem of the set partitioning problem for multiple initial sets, A candidate set generation unit generates a candidate set in which the breakdown of the virtual steel materials included is different from that of each initial set, by sequentially connecting multiple constituent units, which are aggregated to a number smaller than the first number, in a predetermined method that is not solving a subproblem in the column generation method, so as to satisfy the conditions for being established as a cast frame; and a calculation unit calculates the reduced cost of the candidate set based on the dual optimal solution, and a promising set extraction unit extracts all of the candidate sets whose reduced cost satisfies a predetermined criterion as promising sets. A problem solving unit that finds the optimal solution to the set partitioning problem based on a plurality of initial sets and a promising set, A planning device equipped with the following features.

2. The predetermined method is: The aforementioned unit is considered as one node, A set of candidates is generated by connecting a predetermined number of the aforementioned nodes. After generating the aforementioned candidate set, the process involves duplicating the same nodes from the first to a predetermined number, and connecting a node different from the next node in the candidate set to the predetermined node. The planning apparatus according to claim 1.

3. The candidate set generation unit, A third number of unit groups, which is less than the first number, is obtained by aggregating the first number of virtual steel materials based on manufacturing conditions. The candidate set is generated using the aforementioned unit group as the constituent unit. The planning apparatus according to claim 1.

4. The candidate set generation unit, A fourth number of large groups is obtained, which include at least one unit group and are composed of the same type of virtual steel material, generated based on the third number of unit groups. The candidate set is generated using the aforementioned large group as the constituent unit. The planning apparatus according to claim 3.

5. The candidate set generation unit stops connecting the next node if a predetermined termination condition is met before connecting the next node. The planning apparatus according to claim 2.

6. The aforementioned collection of virtual steel materials is managed as a row, The candidate set generation unit generates a new candidate set each time it finishes generating the candidate set. The promising set extraction unit adds the new promising set each time a new candidate set is generated in which the reduced cost satisfies a predetermined criterion. A planning device according to any one of claims 1 to 5.

7. A planning program for causing a computer to function as a planning device according to any one of claims 1 to 5, A planning program for causing the computer to function as the initial set generation unit, the dual problem solving unit, the candidate set generation unit, the calculation unit, the promising set extraction unit, and the original problem solving unit.

8. A planning method for creating a cast frame organization plan by solving a set partitioning problem in which a first number of virtual steel materials corresponding to a first number of steel materials to be cast by continuous casting are aggregated into a second number of cast frames which is less than the first number, The steps include generating multiple initial sets, which are sets of virtual steel materials containing at least one of the virtual steel materials, by varying the composition of the virtual steel materials included in each initial set, The steps include finding the dual optimal solution to the dual problem of the set partitioning problem for multiple initial sets, The steps include: generating a candidate set in which the breakdown of the virtual steel materials included is different from that of each initial set, by sequentially connecting multiple constituent units, which are aggregated to a number smaller than the first number, in a predetermined method that is not solving a subproblem in the column generation method, so as to satisfy the conditions for being valid as a cast frame; and calculating the reduced cost of the candidate set based on the dual optimal solution, and extracting all the candidate sets whose reduced costs satisfy a predetermined criterion as a promising set. A step of finding the optimal solution to the set partitioning problem based on a plurality of initial sets and a promising set, A method for creating a plan that includes [something].

Images