JP7163771B2 - Cast knitting device, cast knitting method, and program - Google Patents

Description

The present invention relates to a cast knitting device, a cast knitting method, and a program, and is particularly suitable for use in performing cast knitting in a continuous casting process.

In a steelmaking plant, molten iron supplied from a blast furnace is charged into a converter, and carbon is removed from the molten iron by blowing oxygen to produce molten steel. This is called primary refining. Next, the molten steel is poured into a container called a ladle and transported to the secondary refining process. This ladle full of molten steel is called a charge. As a secondary refining process, for example, there is an RH (Ruhrstahl Heraeus) process, in which impure gases in the molten steel are removed in a vacuum by circulating the molten steel in a vacuum tube to adjust the components of the molten steel. After finishing the secondary refining process, the ladle is transferred to the continuous casting machine. A continuous casting machine pours molten steel from a ladle into a mold and simultaneously cools it to produce a slab, which is a semi-finished product. A continuous casting machine can continuously cast a plurality of charges, and a group of continuously cast charges is called a cast. Continuous casting of multiple charges of molten steel is called continuous casting. If the number of continuous casting is too many, the components of the continuous casting machine (tundish, mold refractory, submerged nozzle, etc.) will be eroded. The number of charges to be carried out must be properly defined.

A slab produced in a continuous casting machine is called a slab and is transported to a rolling process. In the rolling process, the slab is reheated in a heating furnace, rolled to a thickness of several millimeters by a rolling mill at a high temperature, and wound into a coil. The number of slabs that can be continuously rolled by a rolling mill is limited depending on the shape and hardness of the slabs. A group of slabs continuously rolled in a rolling mill is called a chance.
Each slab is provided with information such as composition, shape, and desired hot-rolling date from order information, and lots such as cast and chance are organized in consideration of constraints in the steelmaking process and rolling process.

Also, in recent years, attempts have been made to shorten the lead time and reduce heat loss by making cast, which is a lot in the steelmaking process, the same as chance, which is a lot in the rolling process. In carrying out such an operation, it is necessary to determine a cast composition (slabs to be included in each cast) that simultaneously satisfies the constraints in the steelmaking process and the rolling process.

In cast organization, by incorporating a large number of slabs into the cast and making a large lot, the number of continuous castings is increased, and the number of slab defective parts at the start and end of continuous casting is reduced and preparations for the start of recasting are made. An increase in production volume can be expected due to the reduction in time. On the other hand, there are restrictions on the slabs that can be incorporated into the same cast depending on conditions such as composition, shape, and desired hot rolling date. For this reason, it is required to carry out cast formation with as large a lot as possible within the range that satisfies the constraint conditions.

Casting operations generally handle hundreds or thousands of slabs, resulting in a large number of combinations of slabs. Therefore, it takes a long time for the planner to form a cast that satisfies all the constraints.
Therefore, enumerate the cast candidates and solve the set partitioning problem for the enumerated cast candidates (that is, the enumerated casts so that the slabs to be manufactured are incorporated into the cast without omission and duplication. It is desirable to reduce the burden on the planner by deciding which casts to include in the cast formation from among the candidates.

As this type of technology, Patent Document 1 discloses the following technology. That is, for each target steel material to be divided, a set of target steel materials that satisfy the pile constraint is extracted, and by using a set operation of these sets, the pile constraint is resolved by the branching method to the selected steel materials that can be branched. Feasible peaks, which are a set of target steel materials that satisfy the conditions, are extracted. Then, from the extracted set of feasible peaks, a combination of feasible peaks in which the target steel materials are included without omission and duplication is determined so as to minimize the sum of the costs of the feasible peaks.

Patent Document 1 is a technique related to the problem of dividing steel materials (slabs) in a yard. required constraint), it can also be applied when creating cast formations.

JP 2016-81186 A JP 2017-211834 A JP 2018-101389 A

However, the technique described in Patent Document 1 is a technique for efficiently enumerating all possible combinations of mountains that can be taken from the target steel material to be divided, and all steel materials that can be branched for a certain steel material. Select (i.e., enumerate all feasible mountain combinations). Here, when the technique described in Patent Document 1 is applied to cast formation, the combination of subsets (casts) to be enumerated is 2 to the nth power (n is the number of slabs). The number of slabs to be cast may reach the order of hundreds or thousands. Therefore, if the technique described in Patent Document 1 is applied to cast organization, it is not easy to enumerate various subsets in a realistic calculation time.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described problems, and an object of the present invention is to enable cast formation to be performed in a short period of time without greatly degrading planning accuracy.

The cast knitting device of the present invention treats the problem of creating a cast knitting for collectively manufacturing a plurality of steel materials scheduled to be manufactured into a cast as a set division problem, and creates the optimum solution of the set split problem as a cast knitting. a cast knitting device, which acquires a plurality of pieces of steel information, each of which is information on one or a plurality of steels that are elements of the set division problem; and a predetermined manufacturing condition for the steels and a sorting means for sorting the plurality of steel material information in the order of values indicating Extraction means for extracting a plurality of subset enumeration targets consisting of a part of the steel product information of the plurality of rearranged steel product information; A first enumeration of a subset consisting of one steel material information that can be established as a cast, or a subset consisting of a combination of a plurality of steel material information that can be established as a cast, from the steel material information included in the subset enumeration target and cast knitting means for performing the cast knitting by solving the set division problem using the subsets enumerated by the first enumerating means , wherein the steel material information acquiring means is , each of which is information of one steel material or a plurality of steel materials of the same steel grade that are elements of the set partitioning problem, and the sorting means acquires a plurality of steel material information, each of which is information of a plurality of steel materials of the same steel grade, and the sorting means selects the steel materials whose predetermined manufacturing condition values are close to each other. The plurality of pieces of steel material information are rearranged for each steel type so that the sorting order becomes closer, and the extraction means sorts the plurality of steel material information rearranged by the sorting means according to a predetermined extraction rule. for each steel type, extracting a plurality of the subset enumeration targets, each consisting of one piece of the steel material information or a plurality of the steel material information adjacent in order, from the , for each of the plurality of subset enumeration targets extracted by the extraction means, a subset consisting of one piece of steel material information that can be established as a cast from the steel material information included in the subset enumeration target, or a cast For each steel type, a subset consisting of a plurality of combinations of the steel material information that can be established is listed as a cast frame candidate for the same steel type, and the cast formation means enumerates the same cast frames enumerated by the first enumeration means. steel The cast formation is created by solving the set division problem using seed cast frame candidates .

In the cast knitting method of the present invention, the problem of creating a cast knitting for collectively manufacturing a plurality of steel materials scheduled to be manufactured into a cast is set as a set division problem, and the optimal solution to the set split problem is created as a cast knitting. a steel material information acquisition step of acquiring a plurality of steel material information, each of which is information on one or a plurality of steel materials that are elements of the set division problem; and a predetermined manufacturing condition for the steel materials and a sorting step of sorting the plurality of steel product information in the order of values indicating an extracting step of extracting a plurality of subset enumeration targets consisting of part of the steel product information of the plurality of rearranged steel product information; A first enumeration of a subset consisting of one steel material information that can be established as a cast, or a subset consisting of a combination of a plurality of steel material information that can be established as a cast, from the steel material information included in the subset enumeration target and a cast knitting step of performing the cast knitting by solving the set division problem using the subsets enumerated in the first enumerating step , wherein the steel material information acquiring step is , obtaining a plurality of steel product information, each of which is information on one steel product or a plurality of steel products of the same steel grade that are elements of the set partitioning problem, and the sorting step is performed to determine whether the values of predetermined manufacturing conditions of the steel products are close to each other. The plurality of pieces of steel material information are rearranged for each steel type so that the sorting order becomes closer, and the extraction step is performed according to a predetermined extraction rule, wherein the plurality of pieces of steel material information rearranged by the sorting step are sorted according to a predetermined extraction rule. for each steel type, extracting a plurality of the subset enumeration targets each consisting of one piece of the steel material information or a plurality of the steel material information adjacent in order, from , for each of the plurality of subset enumeration targets extracted by the extraction step, a subset consisting of one steel material information that can be established as a cast from the steel information included in the subset enumeration target, or as a cast A subset consisting of a plurality of possible combinations of the steel material information is listed as a cast frame candidate for the same steel type for each steel type, and the cast formation step is performed for each steel type. steel The cast formation is created by solving the set division problem using seed cast frame candidates .

The program of the present invention causes a computer to function as each means of the cast organization device.

ADVANTAGE OF THE INVENTION According to this invention, cast organization can be performed in a short time, without reducing planning accuracy significantly.

It is a figure which shows an example of a functional structure of a cast organization apparatus. FIG. 4 is a diagram showing an example of slab group data; 3 is a diagram showing the result of rearranging the slab group data shown in FIG. 2; FIG. FIG. 4 is a diagram showing an example of all subsets obtained from (data of) slab groups of steel type A; FIG. 4 is a diagram showing an example of a subset enumerated from (data of) a slab group of steel type A by the method of the present embodiment; FIG. 10 is a diagram showing an example of cast frame candidates of the same steel type; FIG. 5 is a diagram showing an example of a steel type casting frame candidate; FIG. 2 is a diagram conceptually explaining a matrix; FIG. 5 is a diagram showing an example of the relationship between the number of extracted slabs Gr, the value of the objective function, and the calculation time; It is a flow chart explaining an example of a cast organization method. FIG. 11 is a flow chart for explaining an example of the same steel type sequence creating process; FIG. FIG. 11 is a flow chart illustrating an example of processing for creating a series of different steel grades; FIG.

An embodiment of the present invention will be described below with reference to the drawings. In this embodiment, a case where the steel material to be manufactured in the continuous casting machine is a slab will be described as an example. FIG. 1 is a diagram showing an example of a functional configuration of a cast knitting device 100. As shown in FIG. The hardware of the cast organizing device 100 is realized by using, for example, an information processing device having a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware.

<Steel material information acquisition unit 110>
In this embodiment, the cast knitting device 100 treats the problem of creating a cast knitting for manufacturing a plurality of slabs scheduled to be manufactured (a plurality of slabs to be cast knitted) together in a cast as a set division problem. , is created as a cast organization by deriving the optimal solution of the set partitioning problem. The steel material information acquisition unit 110 acquires steel material information, which is information on one or more steel materials (slabs) that are elements (subsets) of the set partitioning problem. Regarding the steel material information, when the element of the set division problem is one steel material, it is also referred to as slab data below. Also called data.
In this embodiment, the steel material information acquisition unit 110 has a slab data reading unit 111 and a slab group creation unit 112 .

<<Slab data reading unit 111>>
The slab data reading unit 111 reads slab data including manufacturing conditions for each of a plurality of slabs scheduled to be manufactured. The slab data is input to the cast organization device 100 by, for example, operating the cast organization device 100 by an operator, communicating with an external device, or reading from a portable storage medium, and stored in the HDD or the like in the cast organization device 100. Stored in a storage medium. The slab data reading unit 111 reads slab data stored in a storage medium such as an HDD in the cast knitting apparatus 100 .

The slab data is, for example, slab No. , steel type, slab weight, slab width, slab thickness, coil width, coil thickness, coil length, and desired hot rolling date are mutually associated information. Slab data is provided separately for each of the plurality of slabs scheduled for manufacture.

Slab no. is a number that identifies the slab.
The steel type indicates the type of slab determined according to the composition of the slab. Here, the steel type is represented by a symbol that identifies the steel type.
Slab weight, slab width, and slab thickness are the weight, width, and thickness of the slab, respectively. The steel type, slab weight, slab width, and slab thickness are manufacturing conditions in the slab manufacturing process (continuous casting process).

The coil width, coil thickness, and coil length are based on the slab No. is the width, thickness and length of the coil obtained by hot rolling the slab identified by . The coil width, coil thickness, and coil length are manufacturing conditions in the process (hot rolling process) after the process of manufacturing the slab.
A slab produced by a continuous casting machine is placed in a yard and then hot-rolled in the next hot-rolling process. The day desired by the factory as the day of hot rolling is the desired hot rolling day. That is, the desired hot rolling date is the delivery date of the slab to the hot rolling mill. The desired hot-rolling date is set, for example, based on the delivery date to the customer of the coil obtained by winding the hot-rolled steel sheet obtained by hot-rolling, the operation status of the equipment of the hot-rolling line, and the like.

<<Slab group creation unit 112>>
Based on the slab data read by the slab data reading unit 111, the slab group creation unit 112 assigns slabs whose manufacturing conditions match within a predetermined range to the same slab group, and the same slab is divided into a plurality of slabs. Group all of the slab data (slabs belonging to) so that they do not belong to a group. For example, the slab group creating unit 112 can make a plurality of slabs of the same steel type into the same slab group. Moreover, the slab group creating unit 112 can group a plurality of slabs in which at least one of the dimension (width) and desired hot rolling date is within a predetermined range as the same slab group. However, the slab group creating unit 112 needs to satisfy constraints that a slab group, which is a collection of multiple slabs, should have as a cast. Therefore, the slab group creating unit 112 creates slab groups so that the total weight of the slabs belonging to one slab group is within the maximum cast weight CastWMax or less. The maximum cast weight CastWMax is the upper limit of the weight (of molten steel) in one cast. In addition, since the rolling rolls wear during the hot rolling process, there is a limit to the number of slabs of the same width that are continuously hot rolled at the same opportunity. Therefore, instead of or in addition to the total weight of slabs belonging to one slab group, a constraint condition that the cast should have is that the number of slabs belonging to one slab group is an upper limit (for example, 40) or less. can do.

FIG. 2 is a diagram showing an example of slab group data 200. As shown in FIG. Here, a case will be described as an example in which a plurality of slabs of the same steel type and having the same slab width, slab thickness, and desired hot rolling date within a predetermined range are included in the same slab group. (In the following explanation, it is assumed that the slab group is created in this manner as well). As will be described later, in this embodiment, (data of) each slab group included in the slab group data 200 is rearranged based on the steel grade and slab width. Therefore, values are shown only for the steel type and slab width, and the illustration of specific values for other items is omitted as "...".

The slab group data 200 is a list of slab groups.
In FIG. 2, slab group data 200 includes slab group numbers. , steel type, slab width (maximum value, minimum value), slab thickness (maximum value, minimum value), slab weight, coil length, desired hot rolling date (earliest date, latest date), and number of slabs are correlated. It is information that has been obtained.

Slab Group No. (SGr. No) is a number that identifies a slab group.
The steel grade is the steel grade of the slab belonging to the slab group. As mentioned above, here each slab group consists of slabs of one steel grade.
The maximum slab width is the maximum width of the slabs included in the slab group (slab width). The minimum slab width is the minimum width of the slabs included in the slab group (slab width).

The maximum slab thickness is the maximum thickness of the slabs included in the slab group (slab thickness). The minimum slab thickness is the minimum thickness of the slabs included in the slab group (slab thickness).
The slab weight is the total weight of the slabs included in the slab group (slab weight).
The coil length is the total value of the coil lengths of the slabs included in the slab group.
The earliest desired hot-rolling date is the earliest desired hot-rolling date of the slabs included in the slab group. The latest desired hot-rolling date is the latest desired hot-rolling date of the slabs included in the slab group.
The number of slabs is the total number of slabs included in the slab group.
Although not shown in FIG. 2, each slab group data 200 includes a slab No. included in the slab group data 200. The slab numbers of the slabs included in the slab group specified by is linked.
The slab group creating unit 112 creates the slab group data 200 as described above. Although FIG. 2 shows only the slab group data for the slab group of steel grade A, slab group data of the same items as those shown in FIG. 2 are created for other steel grades (steel grades B, C, etc.). be. Also, since the slab group can be created as described in Patent Documents 2 and 3, for example, detailed description of the creation method is omitted here.
By combining multiple slabs included in the same cast into one slab group, the number of elements that can be selected in the set partitioning problem can be reduced, thus reducing the computational load.

<Same steel type sequence creation unit 120>
The same steel grade series creation unit 120 creates a subset including (data of) one or more slab groups that are made of the same steel grade and that can be cast as elements, using a rule-based technique. In this embodiment, the same steel grade sequence creating unit 120 has a sorting unit 121 , an extracting unit 122 and a first enumerating unit 123 .
<<Sorting unit 121>>
The sorting unit 121 rearranges the order of (data of) slab groups included in the slab group data 200 created by the slab group creating unit 112 in the order of the values indicating the predetermined manufacturing conditions of the slab groups. In this embodiment, the sorting unit 121 sorts (the data of) the slab groups included in the slab group data 200 based on the steel type and the slab width. Specifically, the sorting unit 121 extracts (data of) slab groups having the same steel type s value from (data of) the slab groups included in the slab group data 200 . Here, s is a number that identifies the steel type and is an integer of 1 or more and S or less (1≤s≤S). S is the total number of steel grades. For example, when steel grades A, B, and C are included in the slab group data 200, S is 3 (S=3).

Then, the sorting unit 121 changes the order of arrangement of the extracted slab groups (data thereof) such that the smaller the slab width, the higher the arrangement order of the extracted slab groups (data thereof). The slab widths of the slabs belonging to a slab group are usually not the same. Therefore, the sorting unit 121 arranges (the data of) the extracted slab groups so that the smaller the representative value of the slab width (for example, the maximum value, the minimum value, or the average value), the earlier the slab group is arranged. to change Also, when changing the arrangement order of the extracted slab group (data of) so that the smaller the first representative value (for example, the maximum value) of the slab width, the smaller the arrangement order, the slab width If there are slab groups with the same first representative value (for example, the maximum value), the sorting unit 121 arranges the smaller second representative value (for example, the minimum value) of the slab width in the earlier order.

The sorting unit 121 extracts (data of) slab groups of the same steel grade as described above and rearranges the extracted slab groups (data of) for each steel grade for all steel grades.
FIG. 3 is a diagram showing the result of rearranging (data of) each slab group included in the slab group data 200 shown in FIG. 2 so that the smaller the maximum value of the slab width, the earlier the slab group is arranged. . As with steel type A, each slab group (data of) for other steel types is rearranged such that the smaller the slab width, the earlier the slab group.

Here, the sorting unit 121 changes the order of arrangement of the extracted slab groups (data of) such that the smaller the slab width, the higher the order of arrangement of the extracted slab groups (data of the data). A case is shown as an example. However, this need not necessarily be the case. For example, the sorting unit 121 may change the order of arranging (data of) the extracted slab groups so that the smaller the slab width, the later the slab group (data of) is arranged.

<<extraction unit 122>>
FIG. 4A is a diagram showing all subsets (combinations of (data of) slab groups) obtained from (data of) slab groups of steel grade A sorted by the sorting unit 121 as shown in FIG. . In FIG. 4A, slab group no. (SGr.No) corresponds to those shown in FIGS. PA1 to P64A represent subsets of (data of) slab groups of steel grade A sorted by the sorting unit 121. FIG. These subsets correspond to steel grade A casting candidates. The slab group No. in the row marked with "1" in each cell. (SGr.No) is included in the subset of columns to which the "1" is attached. For example, subset PA2 is slab group No. (SGr.No) consists of (data of) slab groups "1", "2", "3", "5", and "6". Subset PA7 is slab group No. (SGr.No) consists of (data of) slab groups "1", "2", "3", and "4". Subset PA64 indicates a subset that does not include (data of) any slab group of steel type A.

As shown in FIG. 4A, even if the number of (data of) slab groups is 6, the total number of combinations of subsets is 64 (=2 ⁶ ). Cast formation work generally handles hundreds or thousands of slabs, so even if the slabs are grouped into slab groups, the number of combinations of slab groups (data) is enormous.
Therefore, the extraction unit 122 extracts some slab groups (one slab group or a plurality of slab groups that are adjacent in order) from the plurality of slab groups sorted by the sorting unit 121 according to a predetermined extraction rule. Extract each s separately.

An example of extraction rules in this embodiment will be described.
First, among the slab groups (data of) rearranged for the steel type s, a slab group (data of) to be the starting point of extraction is selected. At this time, if the number from the selected slab group to the last slab group (data) in the order is equal to or greater than a certain number N ^SG _s , then a certain number of consecutively ordered slab groups from the starting slab group Extract (data for) slab groups of N ^SG _s . After that, the slab group serving as the starting point is reselected while being shifted one by one according to the order of arrangement, and the extraction of a constant number N ^SG _s of slab groups with consecutive order of arrangement is repeated. Note that the slab group that is first selected as the slab group that serves as the starting point for extraction is the slab group that is arranged first.

In addition, if the number from the slab group (data) that is the starting point of the extraction to the slab group (data) that is the last in the order is less than a certain number N ^SG _s , then the slab group that is the starting point is extracts up to (the data of) the last slab group. Thereafter, the slab group serving as the starting point is reselected while being shifted one by one according to the order of arrangement, and extraction is repeated from there until the slab group with the last order of arrangement.

FIG. 4B shows subsets (slab groups (of It is a diagram showing a combination of data). FIG. 4B shows an example in which the constant number N ^SG _s is "4". Note that the view of FIG. 4B is the same as that of FIG. 4A.

According to the above extraction rule, in FIG. 4B, in the slab groups (data of) sorted for steel type A, the slab groups (data of) that are the starting point for extraction are the slab groups that are arranged in the first to third order. is selected, the number of data from the starting slab group to the last (=6th) slab group (data) is a certain number N ^SG _s (=4) or more. In this case, in the slab groups (data of) rearranged by the sorting unit 121, a certain number of N ^SG _s (=4) slab groups (data of) that are consecutive in order from the slab group that is the starting point of the slab group (data of) are Extract.

That is, (data of) the slab groups with the first to fourth order (slab group No. (SGr. No.) of "1", "2", "3", "5") and the order of 2. 3rd to 5th slab groups (Slab Group No. (SGr.No.) is "2", "3", "5", "6"), and 3rd to 6th (slab (data of) slab groups with group numbers (SGr.No) of "3", "5", "6", and "7") are extracted in this order. In FIG. 4B, (data of) these slab groups are indicated by bold frames 401a-401c.

On the other hand, in FIG. 4B, in the slab groups (data of) sorted for steel type A, when the slab groups with the order of 4th to 6th are selected as the slab group (data of) to be the starting point of extraction. is less than a certain number N ^SG _s (=4) from the starting slab group to the last (=6th) slab group (data). In this case, in the slab group (data) rearranged by the sorting unit 121, from the slab group (data) that is the starting point to the slab group (data) that is the last (=6th) slab group (data) Extract.

That is, (data of) the slab groups whose arrangement order is 4th to 6th (Slab Group No. (SGr. No.) is "5", "6", "4"), and slab groups whose arrangement order is 5th to 6th. (Slab group No. (SGr. No.) is "6", "4") and the slab with the sixth order (Slab group No. (SGr. No.) is "4") Groups (data of) are extracted in this order. In FIG. 4B, (data of) these slab groups are indicated by bold frames 402a-402c.

For other steel types, as with steel type A, one slab group (data) or a plurality of slabs adjacent in order are selected from the slab groups (data) sorted by the sorting unit 121 according to the extraction rule. Groups (data of) are extracted. In the following description, one slab group (data of) extracted in this manner or a plurality of slab groups (data of) adjacent in order of arrangement will be referred to as a subset enumeration target as necessary.

In the example shown in FIG. 4B, (data of) slab groups with the first to fourth order (slab group numbers (SGr. No.) of "1", "2", "3", "5") and , the slab groups (data) of the 2nd to 5th order (Slab Group No. (SGr.No) is "2", "3", "5", "6") and the 3rd order 6th (Slab Group No. (SGr.No) is "3", "5", "6", "7") and 4th to 6th (Slab Group (data of) slab groups with No. (SGr. , "4") and the (data of) the slab group in the sixth order (slab group No. (SGr. No.) is "4"), each of which is a subset be enumerated.
FIG. 4B shows all subsets for each of these subset enumeration targets (that is, all combinations of slab groups (data) that can be taken from the slab groups (data) included in the subset enumeration targets). . As described with reference to FIG. 4A, the slab group No. in the row marked with "1" in each cell. (SGr.No) is included in the subset of columns to which the "1" is attached.

<<First enumeration unit 123>>
The first enumeration unit 123 selects a subset consisting of (data of) one slab group that can be cast from among the plurality of subset enumeration targets extracted by the extraction unit 122, or a plurality of subsets that can be cast. Enumerate subsets of combinations of (data from) slab groups. In this embodiment, the first enumeration unit 123 enumerates all such subsets for each steel type s.

Since the combination of (data of) one slab group or (data of) a plurality of slab groups holds as a cast, in the present embodiment, the first enumeration unit 123 includes (data of) one slab group or It is determined whether or not a combination of (data of) a plurality of slab groups satisfies the two constraints of width shift constraint and cast weight constraint.

In the present embodiment, the first enumeration unit 123 first enumerates subsets (a combination of (data of) one slab group and (data of) a plurality of slab groups) obtained from the subset enumeration target of steel type s. For all, it is determined whether or not the width transition constraint is satisfied. After that, the first enumeration unit 123 determines whether or not only the subset that satisfies the width transition constraint satisfies the cast weight constraint.

The width transition constraint is a constraint that the absolute value of the difference between the minimum and maximum widths of the slabs included in the subset is less than or equal to a threshold.
As described above, in this embodiment, the sorting unit 121 sorts the slab groups (data thereof) for each steel type s so that the smaller the slab width (the maximum value), the earlier the slab group is arranged. . That is, for the same steel type s, the slab groups (data of) are rearranged in ascending order of slab width (maximum value).
Therefore, the first enumeration unit 123 determines the maximum slab width of the slab group with the preceding order among the two slab groups with consecutive order in the subset obtained from the subset enumeration object of the same steel type s. It is determined whether or not the absolute value of the difference between the value and the minimum value of the slab width of the later slab group is equal to or less than the threshold.

Taking the subset PA1 shown in FIG. 4B as an example, the first enumeration unit 123 determines the maximum value of the slab width of the slab group with the first arrangement order (slab group No. (SGr.No) is “1”). and the minimum value of the slab width of the slab group with the second order (slab group No. (SGr.No) is "2") is equal to or less than the threshold, and the order is the second The maximum value of the slab width of the slab group (slab group No. (SGr.No) is “2”) and the slab group that is third in order (slab group No. (SGr.No) is “3”) The absolute value of the difference from the minimum slab width is equal to or less than the threshold, and the maximum slab width of the slab group that is third in the arrangement order (slab group No. (SGr. No.) is "3"), and the arrangement order is less than or equal to the threshold, the subset PA1 satisfies the width transition constraint If not, it is determined that the subset PA1 does not satisfy the width transition constraint.

In this embodiment, each slab group is created by the slab group creation unit 112 so that the slab widths of the slabs belonging to one slab group are within a predetermined range so that the cast is established. Therefore, when the number of (data of) slab groups included in a subset is one, the subset always satisfies the width transition constraint. Therefore, the first enumeration unit 123 does not have to determine whether or not such a subset satisfies the width transition constraint.

As described above, the first enumeration unit 123 determines whether or not only the subsets that satisfy the width shift constraint among the subsets obtained from the subset enumeration target of the steel type s satisfy the cast weight constraint. do.
The cast weight constraint is a constraint that the total weight tW of the slabs included in the subset is equal to or less than the cast maximum weight CastWMax. Therefore, the first enumeration unit 123 selects when the total weight tW of the slabs included in the subsets satisfying the width transition constraint among the subsets obtained from the subset enumeration target of steel type s is equal to or less than the maximum cast weight CastWMax If not, it is determined that the subset satisfies the cast weight constraint; otherwise, it is determined that the subset does not satisfy the cast weight constraint.

The first enumeration unit 123 determines whether or not the width transition constraint is satisfied for all subsets obtained from the subset enumeration target of the steel type s, and cast weight constraints for the subsets that satisfy the width transition constraint. is satisfied, and By the above determination method, subsets satisfying the width shift constraint and the cast weight constraint are enumerated from all the subsets obtained from the enumeration target of a certain subset of a certain steel type s. The first enumeration unit 123 enumerates subsets that satisfy the above width transition constraint and cast weight constraint for all subsets of all steel types s.

Here, in order to reduce the overall calculation time, it is determined whether or not the constraint condition is satisfied from the constraint condition that is frequently violated, and the determination of the other constraint conditions is terminated when the violation occurs, or , it is preferable to perform the judgment from the constraint conditions with short calculation time for judging whether or not the constraint conditions are satisfied. From this point of view, it can be determined which of the width transition constraint and the cast weight constraint should be performed first. Here, the width transition constraint is more often not satisfied than the cast weight constraint, and the calculation time is often short, so the width transition constraint is determined before the cast weight constraint. A case of doing so has been described as an example. However, for example, if the calculation time is long when the cast knitting device 100 is actually operated, the order of determination of the width transition constraint and the cast weight constraint is reversed to operate the cast knitting device 100, and the calculation time is is shorter, the cast knitting apparatus 100 may be operated by reversing the order of determination of the width transition constraint and the cast weight constraint. In this way, it is not necessary to determine whether or not the width transition constraint is satisfied, and it is not necessary to determine whether or not the cast weight constraint is satisfied only for those that satisfy the width transition constraint, and the order of determination is reversed. may

The first enumeration unit 123 individually calculates a cost C _j represented by the following equation (1) for each subset j that satisfies the width transition constraint and the cast weight constraint.
_Cj= CY* _Y +CG* _G +CD* _D +CN* _SN (1)
Here, Y is the amount of surplus material and is calculated by the following formula (2).
Y=CW×NC-tW (2)

CW is the weight [ton] of (molten steel) in one charge and is predetermined. The weight CW of (molten steel) in one charge is, for example, 300 [ton]. tW is the total weight tW [ton] of the slabs included in the subset, as described above.
NC is the number of charges required to cast the total weight tW of the slabs included in the subset, and is calculated by the following equation (3).
NC=ceil(tW/CW) (3)
ceil() represents the ceiling function, and ceil(tW/CW) represents the smallest integer greater than or equal to tW/CW.

In formula (1), G is the number of steel grades included in the subset. In the first enumeration part 123, subsets are enumerated for each steel type s (subsets of the same steel type s are enumerated), so G=1. Incidentally, in the calculation of formula (1) in the first enumeration unit 123, "C _G ×G" may be 0 (zero).
D is the earliest desired hot rolling date of the slab group (data) belonging to the subset, from the earliest date to the latest desired hot rolling date of the slab group (data) belonging to the subset It is the number of days until the latest day. For example, among the earliest desired dates for hot rolling of slab groups (data of) belonging to a certain subset, the earliest date is October 1, and hot rolling of slab groups (data of) belonging to the subset is If the latest date among the latest desired dates is October 15, D=14 [days].

SN is the number of slabs belonging to the subset.
C _Y is the weighting factor for Y, C _G is the weighting factor for G, C _D is the weighting factor for D, and C _N is the weighting factor for SN. The weighting coefficients C _Y , C _G , C _D , and C _N represent the balance (relative importance (weight)) of the evaluation of each evaluation index (G, D, SN) with respect to other evaluation indices, preset. In the present embodiment, since the cost C _j in equation (1) is minimized, the value of the weighting factor is increased for the evaluation index with relatively high importance.

The first enumeration part 123 is a subset whose elements are slab groups (data of) of the same steel type s only, and which satisfies the width transition constraint and the cast weight constraint (information specifying) Register as a cast frame candidate for the same steel grade. Further, the first enumeration unit 123 stores (information specifying the subset), the cost C _j of the subset, and the total weight tW of the slabs included in the subset in association with each other.

FIG. 5 is a diagram showing an example of cast frame candidates of the same steel type. In FIG. 5, slab group No. (SGr.No) is the slab group No. shown in FIGS. 2, 3 and 4B. (SGr. No). The column indicates (one of) cast frame candidates of the same steel type. “PA8”, “PA4” and “PA12” shown in parentheses for columns 1, 2 and 3 correspond to “PA8”, “PA4” and “PA12” shown in FIG. 4B, respectively. That is, in FIG. 5, of the subsets PA1 to PA31 shown in FIG. 4B, a subset satisfying the width shift constraint and the cast weight constraint (that is, a subset registered as a cast frame candidate of the same steel type) is the subset PA8. , PA4, PA12, and other subsets PA1-PA3, PA5-PA7, PA9-PA11, PA12-PA31 do not satisfy at least one of the width transition constraint and the cast weight constraint. Regarding steel types B and C, slab group No. (SGr. No.), but since illustration of specific examples of subsets of steel types B and C is omitted, slab group numbers for steel types B and C are shown in FIG. (SGr. No) is written as "...".

As is clear from comparing FIG. 4A and FIG. 4B, the number of subsets to be enumerated in the set partitioning problem can be reduced by using the extraction rule. For example, if there are 30 slab groups of steel type A, the constraint conditions (width transition constraint and cast weight constraint) must be determined for 2 ³⁰ ways, that is, more than 1 billion subsets, and the cost C _j must be calculated. must. On the other hand, in the present embodiment, the sorting unit 121 sorts the slab groups (data of) for each steel type s so that the smaller the slab width (the maximum value) is, the earlier the slab group is arranged, and the extraction Subset enumeration targets are extracted according to the rules, and all combinations of (data of) slab groups that hold as casts are enumerated from the extracted subset enumeration targets as subsets. Therefore, it is possible to omit the determination of the constraints (width transition constraint and cast weight constraint) and the calculation of the cost C _j for the combination of (data of) slab groups with greatly different slab widths, and the constraints (width transition constraint and Processing time for determining cast weight constraints and calculating costs can be reduced.

<Different steel type sequence creation unit 130>
The different steel grade sequence creation unit 130 selects a combination of cast frame candidates (subset) of the same steel type for mutually different steel grades s, which is a combination of a plurality of cast frame candidates of the same steel grade that can be established for casting, as cast frame candidates. Enumerate as In the present embodiment, the different steel grade series creation unit 130 has a second enumeration unit 131 .

The second enumeration part 131 consists of one of the same steel grade cast frame candidates (subset) of the same steel grade s created by the same steel grade row creation part 120 and one or more steel grades s' different from the steel grade s. One of the combinations of the steel grade s′ included in one steel grade group of the steel grade group and the cast frame candidate (subset) of the same steel grade is selected. When the steel grade s' included in the steel grade group is a combination of a plurality of steel grades, one cast frame candidate (subset) of the same steel grade is selected from each of the plurality of steel grades. In the example shown in FIG. 5, the combination of columns 1 and 4, the combination of columns 1 and 5, the combination of columns 1 and 6, the combination of columns 1, 4, and 6, and the combination of columns 1, 4, and 6; a combination of columns 5 and 6; a combination of columns 2 and 4; a combination of columns 2 and 5; a combination of columns 2 and 6; a combination of columns 2, 5 and 6; a combination of columns 3 and 4; a combination of columns 3 and 5; a combination of columns 3 and 6; A combination, a combination of columns 3, 5, and 6, a combination of columns 4 and 6, and a combination of columns 5 and 6 are selected.

The second enumeration unit 131 sets each of the combinations of cast frame candidates (subsets) of the same steel type of the selected steel types s and s' as a new subset B _temp (as described above, the steel type s' It is one or a plurality of steel grades different from the steel grade s, and the steel grades s and s' are not limited to two steel grades, but may be two or more steel grades). The second enumeration unit 131 determines whether or not each of the subsets B _temp satisfies the width transition constraint. After that, the second enumeration unit 131 determines whether or not only the subset B _temp that satisfies the width transition constraint satisfies the cast weight constraint.

The width transition constraint and cast weight constraint are the same as those described in the section <<first enumeration section 123>>.
Here, the slab groups (data of) included in the cast frame candidates of the same steel type are sorted by the sorting unit 121 so that the smaller the maximum value of the slab width, the earlier the slab group (FIGS. 2 and 4). 3, and FIG. 4B). Therefore, the second enumeration part 131 lists the slab widths of the slab groups (data of) that are the first and last in the order of the steel grade casting frame candidates (subset) of the steel grades s and s' that constitute the subset B _temp . Only the information (maximum value and minimum value) is referred to determine whether the width transition constraint is satisfied. In this way, it is not necessary to determine whether or not the width transition constraint is satisfied for all the slab groups constituting the same steel type cast frame candidates (subset) of the steel types s and s' that constitute the subset B _temp . , it can be determined whether the subset B _temp satisfies the width transition constraint.

Further, as described above, the first enumeration unit 123 stores the total weight tW of the slabs in the cast frame candidate of the same steel type. Therefore, the second enumeration unit 131 adds the total weight tW of the slabs in the cast frame candidate of the same steel type to derive the total weight of the slabs in the subset B _temp , and uses the total weight of the slabs to calculate the partial Determine if the set B _temp satisfies the cast weight constraint. In this way, it is possible to determine whether the subset B _temp satisfies the cast weight constraint without adding again the weight of the slabs constituting the cast frame candidate of the same steel type (the slab weight shown in FIGS. 2 and 3). can be determined.
As described above, it is possible to quickly determine whether or not the subset B _temp (a combination of cast frame candidates (subsets) of the same steel type of a plurality of different steel types) satisfies the width transition constraint and the cast weight constraint. .

The second enumeration unit 131 is for each subset j (subset B _temp ) that is a combination of steel grade cast frame candidates of the steel grades s and s′ that satisfy the width shift constraint and the cast weight constraint. Calculate separately the costs C _j .
The second enumeration unit 131 registers (information specifying the subset B _temp ) as a cast frame candidate for a different steel type. Also, the second enumeration unit 131 stores (information specifying the subset B _temp ) and the cost C _j of the subset B _temp in association with each other.

FIG. 6 is a diagram showing an example of a cast frame candidate of a different steel type obtained from the combination of cast frame candidates of the same steel type shown in FIG. In FIG. 6, slab group No. (SGr.No) is the slab group No. shown in FIGS. (SGr. No). Columns indicate (one of) cast frame candidates for different steel grades.
In FIG. 6, the combination of columns 1 and 4 (column 7), the combination of columns 1, 5, and 6 (column 8), the combination of columns 2 and 6 (column 9), and the combination of columns 3 and The combination of column 4 (column 10) and the combination of columns 3 and 6 (column 11) are registered as subsets B _temp (that is, different steel type cast frame candidates) that satisfy the width shift constraint and cast weight constraint. Subset) will be shown as an example.

<Cast formation department 140>
In this embodiment, the optimization problem (set partitioning problem) for deriving the optimal cast is formulated by the following formulas (4) to (5). That is, in the present embodiment, the cast formation unit 140 sets the decision variable x _j when minimizing the value of the objective function f of the following expression (4) within the range satisfying the constraint expression of the following expression (5): derive The optimization problem (set partitioning problem) can be solved by, for example, a known mixed integer programming method, and a commercial solver (such as cplex) can also be used.

Cast candidate j is a cast frame candidate of the same steel type created by the same steel grade sequence creation unit 120 (first enumeration unit 123) and a different steel type cast created by the different steel grade sequence creation unit 130 (second enumeration unit 131). It is a frame candidate. In the examples shown in FIGS. 5 and 6, columns 1 to 11 are cast candidates j. Also, the decision variable x _j is a 0-1 variable (x _j ∈ {0, 1}) that is "1" when the cast candidate j is adopted as a cast and "0" when not adopted. . In addition, C _j represents the evaluation value of casting candidate j, and is derived by performing the calculation of formula (1) for a subset included in casting candidate j (same steel type casting frame candidate and different steel type casting frame candidate) It is. As described above, the cost C j of the steel grade cast frame candidate and the cost C _j of the different steel grade cast frame candidate are _calculated by the same steel grade sequence creation unit 120 (first enumeration unit 123) and the different steel grade sequence creation unit 130 (first enumeration unit 123), respectively. 2 enumeration unit 131) and stored.

A _ij in equation (5) is a matrix whose rows are slab groups i and whose columns are cast candidates j, and whose elements are "0" and "1".
FIG. 7 is a diagram conceptually explaining the matrix A _ij . Let iεN _I be the set of slab groups i included in casting candidate j, and jεN _J be the set of casting candidates j.
In FIG. 7, each column indicates a slab group i included in one cast candidate j. "1" is given to the row corresponding to the slab group i included in the cast candidate j, and "0" is given to the row corresponding to the slab group i not included in the cast candidate j. For example, cast candidate 1 (j=1) includes slab group 1 (i=1) and no other slab group.

The cast formation unit 140 selects the same steel type cast frame candidates created by the same steel grade row creation unit 120 (first enumeration unit 123) and the different steel grades created by the different steel grade row creation unit 130 (second enumeration unit 131). The result of such assignment of "1" or "0" for each casting slot candidate (that is, each casting candidate j) is the matrix _Aij . The portion below the arrow line in FIG. 7 indicates that the evaluation value C _j and decision variable x _j are obtained for each casting candidate j.
In the examples shown in FIGS. 5 and 6, the matrix A _ij is represented by the following equation (6).

Therefore, the constraint condition of formula (5) is always adopted once as a slab group to be included in a cast (the same slab group is not included in multiple casts, and the slab group is not included in any cast). is not included).
The cast organization unit 140 derives the decision variable x _j as described above. A cast candidate j corresponding to a decision variable x _j to which "1" is given is determined as a cast.

<Output unit 150>
The output unit 150 outputs the cast determined by the cast formation unit 140 and the information of the slab included in the cast as a result of the cast formation. The output unit 150, for example, performs at least one of displaying on a computer display, transmitting to an external device, and storing in an internal or external storage medium, so that the information on the slabs included in each cast is displayed. to output For example, the output unit 150 outputs a cast number, which is a number that identifies a cast. and information on the slabs included in the cast. Slab information can include, for example, steel grade, slab width, slab thickness, weight, and coil length.

<Number of extracted slab groups N ^SG _s >
As described above, the same steel grade sequence creating unit 120 (extracting unit 122) extracts (data of) one slab group from (data of) the slab groups sorted by the sorting unit 121 according to a predetermined extraction rule or sort order A plurality of adjacent slab groups (data of) are extracted by a constant number N ^SG _s . In the following description, this constant number N ^SG _s will be referred to as the extraction slab Gr number as required.
FIG. 8 is a diagram showing an example of the relationship between the extracted slab Gr number N ^SG _s , the value of the objective function f, and the calculation time.
The objective function f is shown in equation (4). In this embodiment, the optimization problem (set partitioning problem) is taken as the minimization problem. Therefore, the smaller the value of the objective function f, the better the solution. The calculation time is the time required for processing in the steel material information acquisition unit 110, the same steel grade sequence creation unit 120, the different steel grade sequence creation unit 130, the cast formation unit 140, and the output unit 150. Note that FIG. 8 shows the results of calculations performed under the same conditions except for the number of extracted slabs Gr N ^SG _s . Also, the extracted slab Gr number N ^SG _s can be determined for each steel type s, but here, the extracted slab Gr number N ^SG _s is assumed to be the same for all steel types s.

As shown in FIG. 8, when the extracted slab Gr number N ^SG _s is increased from 1, the number of combinations of subsets created by the same steel grade sequence creation unit 120 increases, so the value of the objective function f improves. do. However, since the first enumeration unit 123 needs to enumerate a large number of subsets, the computation time increases. In the example shown in FIG. 8, if the extracted slab Gr number N ^SG _s is about 10, a solution with an optimized objective function f can be obtained in a practical computation time. For example, a graph as shown in FIG. 8 is created from past slab data, and the extracted slab Gr number N ^SG _s is determined so that both the value of the objective function f and the calculation time are practical values. be able to. By setting the extracted slab Gr number N ^SG _s to be less than the total number of slab groups created by the slab group creating unit 112, the calculation time can be shortened. , the number of extracted slabs Gr, N ^SG _s , should be the same as the total number of slab groups created by the slab group creation unit 112 .

<Flowchart>
An example of a cast knitting method using the cast knitting device 100 of the present embodiment will be described with reference to the flowcharts of FIGS. 9 to 11. FIG.
FIG. 9 is a flowchart for explaining an example of a cast organization method.
In step S901, the slab data reading unit 111 reads a slab group including manufacturing conditions for each of a plurality of slabs scheduled to be manufactured.

Next, in step S902, based on the slab data read by the slab data reading unit 111, the slab group creating unit 112 creates a slab group by grouping the slabs included in the slab data (see FIG. 2). slab group data 200). At this time, the slab group creation unit 112 determines that slabs whose manufacturing conditions match within a predetermined range belong to the same slab group and that the same slab does not belong to a plurality of slab groups. Group each of the slabs.

Next, in step S903, the same steel grade row creation unit 120 performs same steel grade row creation processing for creating same steel grade cast frame candidates based on the slab group created in step S902. The details of the same steel grade series creating process will be described later with reference to FIG. 10 .
Next, in step S904, the different steel grade row creation unit 130 performs a different steel grade row creation process for creating a different steel grade cast frame candidate based on the same steel grade cast frame candidate created in step S903. The details of the different steel type series creating process will be described later with reference to FIG. 11 .

Next, in step S905, the cast formation unit 140 sets the same steel type cast frame candidate created in step S903 and the different steel type cast frame candidate created in step S904 as the cast candidate j, and the objective function f A decision variable x _j is derived when the value of is minimized within a range that satisfies the constraint expression (5). The cast organization unit 140 determines the cast candidate j corresponding to the decision variable x _j to which "1" is given as a cast.
Next, in step S906, the output unit 150 outputs the cast determined in step S905 and information on the slabs included in the cast as a result of cast organization. Then, the processing according to the flowchart of FIG. 9 ends.

Next, an example of the process for creating the same steel grade series in step S903 of FIG. 9 will be described with reference to the flowchart of FIG.
In step S1001, the same steel grade sequence creation unit 120 selects one unselected steel grade s from among the steel grades s of a plurality of slabs scheduled to be manufactured.
Next, in step S<b>1002 , the sorting unit 121 extracts (data of) the slab group of the steel type s selected in step S<b>1001 from (data of) the slab group included in the slab group data 200 . Then, the sorting unit 121 changes the order of arrangement of the extracted slab groups (data thereof) such that the smaller the slab width, the higher the arrangement order of the extracted slab groups (data thereof). As a result, for example, the arrangement order of (data of) each slab group included in the slab group data 200 shown in FIG. 2 is changed as shown in FIG.

Next, in step S1003, the extraction unit 122 extracts unextracted subset enumeration targets from the subset enumeration targets for the steel type s selected in step S1001. Subset enumeration targets are extracted according to predetermined extraction rules. As described above, the predetermined extraction rule in this embodiment is to extract (data of) a constant number N ^SG _s of slab groups (data of) that are consecutively arranged in the slab groups (data of) rearranged in step S1002. , the order of slab groups (data of) from which extraction is started is shifted one by one from the initial order, and the extraction is repeated. In addition, the subset enumeration target is (data of) one slab group extracted in this way or (data of) a plurality of slab groups adjacent in order (see bold frames 401a to 401c in FIG. 4B). ).

Next, in step S1004, the first enumeration unit 123 selects one unselected subset among the subsets to be enumerated extracted in step S1003.
Next, in step S1005, the first enumeration unit 123 determines whether the subset selected in step S1004 satisfies the width transition constraint. As a result of this determination, if the subset selected in step S1004 does not satisfy the width transition constraint (NO in step S1005), the subset is not a cast frame candidate of the same steel type. In this case, the processing of steps S1006 to S1008 is omitted, and the processing proceeds to step S1009, which will be described later.

On the other hand, if the subset selected in step S1004 satisfies the width transition constraint (YES in step S1005), the process proceeds to step S1006. When the process proceeds to step S1006, the first enumeration unit 123 determines whether the subset selected in step S1004 satisfies the cast weight constraint. As a result of this determination, if the subset selected in step S1004 does not satisfy the cast weight constraint (NO in step S1006), the subset is not a cast frame candidate of the same steel type. In this case, the processing of steps S1007 and S1008 is omitted, and the processing proceeds to step S1009, which will be described later.

On the other hand, if the subset selected in step S1004 satisfies the cast weight constraint (YES in step S1006), the process proceeds to step S1007. When the process proceeds to step S1007, the first enumeration unit 123 calculates the cost C _j represented by Equation (1) for the subset selected in step S1004.
Next, in step S1008, the first enumeration unit 123 registers the subset selected in step S1004 (information specifying the subset) as a cast frame candidate of the same steel type (see FIG. 5). Further, the first enumeration unit 123 stores (information specifying the subset), the cost c _j of the subset, and the total weight tW of the slabs included in the subset in association with each other.

Next, in step S1009, the same steel grade sequence creation unit 120 determines whether or not all subsets to be enumerated extracted in step S1003 have been selected. As a result of this determination, if all subsets to be enumerated extracted in step S1003 have not been selected (NO in step S1009), the process returns to step S1004. Then, the processes of steps S1004 to S1009 are repeatedly executed until the processes of steps S1004 to S1009 are executed for all the subsets to be enumerated extracted in step S1003.

Then, in step S1009, if it is determined that all the subsets to be enumerated extracted in step S1003 have been selected (YES in step S1009), the (one) subset enumerated extracted in step S1003 is selected. For all combinations of (data of) slab groups that can be taken as combinations of (data of) slab groups (for example, eight subsets PA1 to PA8 in the thick frame 401a in FIG. 4B), cast frame candidates of the same steel type and The determination of whether or not to perform the casting and the registration of the cast frame candidate of the same steel grade are completed. In this case, the process proceeds to step S1010.

When the process proceeds to step S1010, the same steel grade sequence creation unit 120 determines whether or not all of the subset enumeration targets for the steel grade s selected in step S1001 have been extracted. For example, in the example shown in FIG. 4B, for steel type A, it is determined whether six subset enumeration targets indicated by thick frames 401a to 401c and 402a to 402c have been extracted. As a result of this determination, if all the subset enumeration targets for the steel type s selected in step S1001 have not been extracted (NO in step S1010), the process returns to step S1003. Then, the processes of steps S1003 to S1010 are repeatedly executed until the processes of steps S1003 to S1010 are executed for all of the subset enumeration targets for the steel type s selected in step S1001.

Then, in step S1010, if it is determined that all of the subset enumeration targets for the steel type s selected in step S1001 have been extracted (YES in step S1010), the steel type A selected in step S1001 is cast for the same steel type. A frame candidate is obtained. In this case, the process proceeds to step S1011. When the process proceeds to step S1011, the same steel grade sequence creation unit 120 determines whether or not all steel grades s of a plurality of slabs scheduled to be manufactured have been selected. As a result of this determination, if all of the steel types s of the plurality of slabs scheduled to be manufactured have not been selected (NO in step S1011), the process returns to step S1001. Then, the processes of steps S1001 to S1011 are repeatedly executed until the processes of steps S1001 to S1011 are executed for all steel types s of the plurality of slabs scheduled to be manufactured. Then, if it is determined in step S1011 that all the steel types s of the plurality of slabs scheduled to be manufactured have been selected (YES in step S1011), all of the steel types s of the plurality of slabs scheduled to be manufactured of the same steel type cast frame candidate can be obtained. In this case, the process according to the flowchart in FIG. 10 ends, and the process proceeds to step S904 in FIG. 9 described above.

Next, an example of the process of creating a different steel type sequence in step S904 of FIG. 9 will be described with reference to the flowchart of FIG.
In step S1101, the second enumeration unit 131 selects one unselected steel type s from the steel types s of a plurality of slabs scheduled to be manufactured.
Next, in step S1102, the second enumeration unit 131 selects one unselected same-steel-type cast frame candidate from among the same-steel-type cast frame candidates for the steel-type s selected in step S1101. If there are a plurality of cast frame candidates of the same steel type for the steel type s, the plurality of cast frame candidates of the same steel type are treated as other candidates of the same steel type cast frame in step S1101.

Next, in step S1103, the second listing unit 131 selects one unselected steel type group from the steel type group consisting of one or more steel types s' different from the steel type s selected in step S1101.
Next, in step S1104, the second enumeration unit 131 selects one unselected combination of cast frame candidates of the same steel type s' included in the steel type group selected in step S1103. If the number of steel types s' included in the steel type group is "1", one cast frame candidate of the same steel type s' is selected in step S1104. Further, when the number of steel types s' included in the steel type group is plural, one cast frame candidate of the same steel type is selected from the plurality of steel types s'. If there are a plurality of same steel type casting frame candidates for a certain steel type s', the plurality of same steel type casting frame candidates are treated as another same steel type casting frame candidate in step S1104.

Next, in step S1105, the second enumeration unit 131 creates a new combination of the same steel type cast frame candidate for the steel type s selected in step S1102 and the same steel type cast frame candidate for the steel type s' selected in step S1104. Create as subset B _temp .
Next, in step S1106, the second enumeration unit 131 determines whether the subset B _temp created in step S1105 satisfies the width transition constraint. As a result of this determination, if the subset B _temp created in step S1105 does not satisfy the width transition constraint (NO in step S1106), the subset B _temp does not become a different steel grade cast frame candidate. In this case, the processing of steps S1106 to S1109 is omitted, and the processing proceeds to step S1010, which will be described later.

On the other hand, if the subset B _temp created in step S1105 satisfies the width transition constraint (YES in step S1106), the process proceeds to step S1107. When the process proceeds to step S1107, the second enumeration unit 131 determines whether the subset B _temp created in step S1105 satisfies the cast weight constraint. As a result of this determination, if the subset B _temp created in step S1105 does not satisfy the cast weight constraint (NO in step S1107), the subset B _temp does not become a different steel grade cast frame candidate. In this case, the processing of steps S1108 and S1109 is omitted, and the processing proceeds to step S1110, which will be described later.

On the other hand, if the subset B _temp created in step S1105 satisfies the cast weight constraint (YES in step S1107), the process proceeds to step S1108. When the process proceeds to step S1108, the second enumeration unit 131 calculates the cost C _j expressed by Equation (1) for the subset B _temp created in step S1105.
Next, in step S1109, the second enumeration unit 131 registers (information specifying the subset B _temp ) created in step S1105 as a cast frame candidate for a different steel type (see FIG. 6). Further, the second enumeration unit 131 stores (information specifying the subset B _temp ) and the cost c _j of the subset B _temp in association with each other.

Next, in step S1110, the second enumeration unit 131 determines whether or not all possible combinations of cast frame candidates of the same steel type s′ included in the steel type group selected in step S1103 have been selected. . As a result of this determination, if all possible combinations of steel grade s' included in the steel grade group selected in step S1103 have not been selected as combinations of cast frame candidates of the same steel grade s' (NO in step S1110), the process proceeds to step Return to S1104. Then, the processes of steps S1104 to S1110 are repeatedly executed for all possible combinations of cast frame candidates of the same steel type of steel type s' included in the steel type group selected in step S1103.

Then, in step S1110, if it is determined that all possible combinations of cast frame candidates of the same steel type s' included in the steel type group selected in step S1103 have been selected (YES in step S1110), Whether all of the subset B _temp consisting of the same steel type cast frame candidates for steel type s and the same steel type cast frame candidates for steel type s′ included in the steel type group selected in step S1103 are treated as different steel type cast frame candidates and the registration of cast frame candidates for different steel grades are completed. In this case, the process proceeds to step S1111.
When the process proceeds to step S1111, the second enumeration unit 131 determines whether or not all steel grade groups that can be taken as a steel grade group consisting of one or a plurality of steel grades s' different from the steel grade s selected in step S1101 have been selected. judge. As a result of this determination, if all the steel grade groups that can be taken as the steel grade group consisting of one or more steel grades s' different from the steel grade s selected in step S1101 have not been selected (NO in step S1111), the process is as follows. Return to step S1103. Then, the processes of steps S1103 to S1111 are repeated for all possible steel grade groups consisting of one or more steel grades s' different from the steel grade s selected in step S1101.

Then, in step S1111, if it is determined that all possible steel grade groups consisting of one or more steel grades s′ different from the steel grade s selected in step S1101 have been selected (YES in step S1111), selection is made in step S1102. Same steel type cast frame candidate for steel type s (one same steel type cast frame candidate for steel type s) and same steel type cast frame candidate for steel type included in a steel type group consisting of one or more steel types s' different from steel type s The determination of whether or not to be a different steel type casting frame candidate and the registration of the different steel type casting frame candidate are completed for all of the subset B _temp consisting of . In this case, the process proceeds to step S1112.

When the process proceeds to step S1112, the second enumeration unit 131 determines whether or not all cast frame candidates of the steel type s selected in step S1101 have been selected. As a result of this determination, if all of the same steel type cast frame candidates for the steel type s selected in step S1101 have not been selected (NO in step S1112), the process returns to step S1102. Then, the processes of steps S1102 to S1112 are repeatedly executed for all cast frame candidates of the same steel type s selected in step S1101. If it is determined in step S1112 that all cast frame candidates of the steel type s selected in step S1101 have been selected (YES in step S1112), cast frame candidates of the same steel type s selected in step S1101 (all cast frame candidates of steel type s Each of the same steel type cast frame candidates) and the same steel type cast frame candidates of the steel type included in the steel type group _consisting of one or more steel types s' different from the steel type s. The determination of whether or not to be a cast frame candidate and the registration of the different steel type cast frame candidate are completed. In this case, the process proceeds to step S1113.

When the process proceeds to step S1113, the second enumeration unit 131 determines whether or not all steel types s of a plurality of slabs scheduled to be manufactured have been selected. As a result of this determination, if all of the steel types s of the plurality of slabs scheduled to be manufactured have not been selected (NO in step S1113), the process returns to step S1101. Then, the processes of steps S1101 to S1113 are repeatedly executed for all steel types s of a plurality of slabs scheduled to be manufactured. In step S1113, if it is determined that all the steel types s of the plurality of slabs scheduled to be manufactured have been selected (YES in step S1113), the same steel type cast frame candidates for the steel types s of the plurality of slabs scheduled to be manufactured ( Subset B consisting of all cast frame candidates of the same steel type for all steel types s) and cast frame candidates of the same steel type included in a steel type group consisting of one or more steel types s' different from the steel type s For all of _temp , the determination of whether or not to be used as a different steel type casting frame candidate and the registration of the different steel type casting frame candidate are completed. In this case, the process according to the flowchart in FIG. 11 ends, and the process proceeds to step S905 in FIG. 9 described above.

<Summary>
As described above, in the present embodiment, the cast knitting apparatus 100 changes the order of slab groups (data of) in the order of values of predetermined manufacturing conditions for each steel type s, and according to a predetermined extraction rule, From the rearranged slab group (data), subset enumeration targets (one slab group (data) or multiple slab groups (data) adjacent in order) are extracted individually for each steel type s . The cast organization device 100 creates a cast organization by solving a set partitioning problem for a plurality of extracted subset enumeration targets. Therefore, it is possible to omit determination of constraint conditions (width transition constraint and cast weight constraint) and calculation of cost, and to shorten calculation time, as compared with the case of enumerating all subsets. In addition, since the combination of (data of) slab groups with similar manufacturing conditions (slab width) is included in the determination target of whether or not to be cast, it is possible to suppress a significant decrease in the planning accuracy of cast formation. Therefore, cast formation can be performed in a short time without greatly degrading planning accuracy.

In addition, in the present embodiment, the cast knitting apparatus 100 changes the arrangement order of (data of) slab groups for each steel type s in the order of the values of the predetermined manufacturing conditions. Create a steel type cast frame candidate. When creating a combination of the same steel type cast frame candidates as a different steel type cast frame candidate, the cast formation device 100 arranges the same steel type cast frame candidates (subset) in the first and last slab groups (data of) slab width information (maximum value and minimum value) to determine whether the width transition constraint is satisfied. Therefore, without referring to all the slab groups that make up the multiple cast frame candidates (subset) of the same steel grade to be combined and determining whether or not the width transition constraint is satisfied, the same It is possible to determine whether or not the subset B _temp obtained by combining the steel grade cast frame candidates satisfies the width transition constraint. Therefore, the calculation time can be further shortened.

In addition, in the present embodiment, the cast knitting apparatus 100 stores the total weight tW of the slabs in the same steel type cast frame candidate, and adds the total weight tW of the slabs in the same steel type cast frame candidates to obtain a plurality of the same steel type cast frame candidates. The total weight of the slabs in the subset B _temp consisting of combinations of steel grade casting frame candidates is derived, and the total weight of the slabs is used to determine whether the subset B _temp satisfies the cast weight constraint. Therefore, it is possible to determine whether or not the subset B _temp satisfies the cast weight constraint without adding again the weight of the slabs constituting the cast frame candidate of the same steel type (the slab weight shown in FIGS. 2 and 3). can be done. Therefore, the calculation time can be further shortened.

Further, in the present embodiment, the cast knitting apparatus 100 organizes a plurality of slabs scheduled to be manufactured into a slab group. Therefore, the calculation time can be shortened. This is particularly preferred when the number of slabs to be produced is large.

<Modification>
<<First Modification>>
In the present embodiment, the case where one slab group includes one steel grade has been described as an example. However, this need not necessarily be the case. For example, two or more steel types may be included in one slab group in order to shorten the calculation time. In this case, the steel grades to be included in one slab group can be specified in advance. For example, during continuous casting, one slab group can include a plurality of steel grades that can be continuously cast without providing a partition plate. In this case, the combination of steel grades s included in one slab group may be regarded as one steel grade s, and the processing described in this embodiment may be performed.

In addition, if a plurality of slabs scheduled to be manufactured are put together into a slab group as in this embodiment, the calculation time can be reduced. However, this need not necessarily be the case. For example, if the number of slabs scheduled to be manufactured is small, the plurality of slabs scheduled to be manufactured may not be grouped into a slab group. In this case, the processing described in this embodiment may be performed with each slab group as an individual slab. In this case, the slab data becomes information (steel material information) of one steel material that is an element of the set partitioning problem.

<<Second modification>>
In the present embodiment, an example has been described in which the arrangement order of (data of) slab groups is changed so that the smaller the slab width, the higher the order of arrangement. However, if the order of arrangement is determined in the order of values indicating predetermined manufacturing conditions, it is not always necessary to do so. For example, the order of arrangement may be determined in the order of slab weight, slab thickness, or desired hot rolling date.
<<Third Modification>>
Also, the predetermined extraction rule is not limited to the one described in this embodiment. For example, a slab group whose desired hot rolling date is earlier than the earliest date may be excluded from the targets of extraction.

<<Fourth Modification>>
In the present embodiment, the case where the optimization problem (set partitioning problem) is the minimization problem has been described as an example. However, the optimization problem (set partitioning problem) may also be a maximization problem. In this case, for example, the right side of equation (3) multiplied by (-1) can be used as the objective function f.

<<Other Modifications>>
The embodiments of the present invention described above can be implemented by a computer executing a program. A computer-readable recording medium recording the program and a computer program product such as the program can also be applied as embodiments of the present invention. Examples of recording media that can be used include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, nonvolatile memory cards, and ROMs.
In addition, the embodiments of the present invention described above are merely examples of specific implementations of the present invention, and the technical scope of the present invention should not be construed to be limited by these. It is. That is, the present invention can be embodied in various forms without departing from its technical concept or main features.

100: Cast knitting device, 110: Steel material information type head, 111: Slab data reading unit, 112: Slab group creation unit, 120: Same steel type sequence creation unit, 121: Sorting unit, 122: Extraction unit, 123: First enumeration unit 130: different steel type series creation unit 131: second enumeration unit 140: cast formation unit 150: output unit

Claims (10)

A cast knitting device for creating a cast knitting for collectively manufacturing a plurality of steel materials scheduled to be manufactured into a cast as a set splitting problem, and creating an optimal solution to the set splitting problem as a cast knitting,
steel information acquisition means for acquiring a plurality of steel information, each of which is information on one steel or a plurality of steels that are elements of the set partitioning problem;
sorting means for sorting the plurality of pieces of steel material information in the order of values indicating predetermined manufacturing conditions of the steel material;
A plurality of pieces of steel material information each composed of a part of the plurality of steel material information sorted by the sorting means according to a predetermined extraction rule based on the order of arrangement of the plurality of steel material information sorted by the sorting means an extraction means for extracting a subset enumeration target of
For each of the plurality of subset enumeration targets extracted by the extraction means, a subset consisting of one steel material information that can be established as a cast from the steel material information included in the subset enumeration target, or established as a cast a first enumeration means for enumerating a subset consisting of a plurality of possible combinations of the steel material information;
and cast organization means for performing the cast organization by solving the set partitioning problem using the subsets enumerated by the first enumeration means.death,
SaidSteel informationAcquisition meansAcquiring a plurality of pieces of steel information, each of which is information of one piece of steel or a plurality of pieces of steel of the same steel type that are elements of the set partitioning problem;
The sorting means sorts the plurality of steel material information for each steel type so that the closer the value of the predetermined manufacturing condition of the steel material is, the closer the order is.
According to a predetermined extraction rule, the extraction means extracts a plurality of pieces of steel material information, each of which is one piece of steel material information or a plurality of pieces of steel material information adjacent in order, from the plurality of pieces of steel material information sorted by the sorting means. Extracting the subset enumeration target of each steel type,
The first enumeration means comprises, for each of the plurality of subset enumeration targets extracted by the extraction means, one piece of steel material information that can be established as a cast from the steel material information included in the subset enumeration target. Listing, for each steel type, a subset, or a subset consisting of a combination of a plurality of the steel material information that can be established as a cast, as cast frame candidates of the same steel type,
The cast formation means creates the cast formation by solving the set division problem using the cast frame candidates of the same steel type enumerated by the first enumeration means. A cast knitting device characterized by: A second enumeration means for enumerating, as a different steel type cast frame candidate, a combination of a plurality of the same steel type cast frame candidates for mutually different steel types, the combination of the plurality of the same steel type cast frame candidates that can be established for casting. further having
The cast organization means uses the same steel type cast frame candidates enumerated by the first enumeration means and the different steel type cast frame candidates enumerated by the second enumeration means to solve the set division problem 2. The cast knitting apparatus according to claim 1 , wherein the cast knitting is created by solving . The second enumeration means selects a combination of a plurality of the same steel type cast frame candidates for mutually different steel grades based on the steel material information that is the first and the last in the same steel type cast frame candidate as a cast. 3. The cast knitting apparatus according to claim 2 , wherein it is determined whether or not it can be established, and the cast frame candidates for the different steel type are listed based on the determined result. The first enumeration means determines whether or not one piece of the steel material information or a combination of a plurality of the steel material information included in the subset enumeration object can be established as a cast, which is specified by the steel material information. Judgment is made based on the result of summarizing the values of the manufacturing conditions of the steel material, and based on the judged result, the cast frame candidates of the same steel type are listed, and whether or not the cast frame candidate of the same steel type can be established as a cast. Stores information indicating the results aggregated when determining whether
The second enumerating means uses the information stored by the first enumerating means to determine whether or not a combination of a plurality of cast frame candidates of the same steel type for mutually different steel grades can be cast. 4. The cast knitting apparatus according to claim 2 , wherein the cast frame candidates for the different steel type are listed based on the determined result. The predetermined extraction rule is that when the number of pieces of steel information selected as the starting point of extraction to the last piece of steel information in the order is equal to or greater than a certain number, the steel information as the starting point to extract the constant number of the steel material information whose order is continuous from the Repeatedly extracting a certain number of the steel information in continuous order from the steel information that is the starting point, and the number from the steel information that is selected as the steel information that is the starting point of the extraction to the steel information that is the last in the order. is less than the certain number, the steel information that is the starting point is extracted from the steel information that is the starting point to the steel information that is the last in the order, and the steel information that is the starting point is extracted according to the order of the steel information. The method of claims 1 to 4 is characterized in that re-selection is performed while shifting one by one, and extraction is repeatedly performed from the steel material information that is the starting point of the re-selection to the steel material information that is the last in the order of arrangement. The cast knitting device according to any one of the items. The steel material information acquisition means groups the plurality of steel materials scheduled to be manufactured into a plurality of steel material groups based on manufacturing conditions of the steel materials, and creates information on the steel material groups as the steel material information. The cast knitting device according to any one of claims 1 to 5 , characterized by: The cast knitting apparatus according to any one of claims 1 to 5 , wherein the steel material information acquiring means acquires the steel material information for each steel material. The cast organization according to any one of claims 1 to 7, wherein the number of the steel material information included in the subset enumeration target is less than the total number of the plurality of steel materials scheduled to be manufactured. Device. A cast knitting method for creating a cast knitting for collectively manufacturing a plurality of steel materials scheduled to be manufactured into a cast as a set splitting problem, and creating an optimal solution to the set splitting problem as a cast knitting,
a steel material information acquisition step of acquiring a plurality of steel material information, each of which is information on one steel material or a plurality of steel materials that are elements of the set partitioning problem;
a sorting step of rearranging the plurality of pieces of steel material information in the order of values indicating predetermined manufacturing conditions of the steel material;
A plurality of pieces of steel material information, each of which is a part of the plurality of steel material information sorted in the sorting step, according to a predetermined extraction rule based on the order of arrangement of the plurality of steel material information sorted in the sorting step An extraction step of extracting a subset enumeration target of
For each of the plurality of subset enumeration targets extracted by the extraction step, a subset consisting of one steel material information that can be established as a cast from the steel material information included in the subset enumeration target, or established as a cast a first enumeration step of enumerating a subset consisting of a plurality of possible combinations of the steel material information;
and a cast organization step of performing the cast organization by solving the set partitioning problem using the subsets enumerated by the first enumeration step.death,
The steel material information acquisition step acquires a plurality of steel material information, each of which is information of one steel material or a plurality of steel materials of the same steel type that is an element of the set division problem,
In the sorting step, the plurality of pieces of steel material information are sorted for each steel type so that the closer the value of the predetermined manufacturing condition of the steel material is, the closer the order is.
In the extraction step, according to a predetermined extraction rule, each of the plurality of pieces of steel material information sorted by the sorting step is one piece of the steel material information, or a plurality of pieces of the steel material information adjacent in order of arrangement. Extracting the subset enumeration target of each steel type,
In the first listing step, for each of the plurality of subset enumeration targets extracted by the extraction step, one piece of steel information that can be established as a cast from the steel information included in the subset enumeration target. Listing, for each steel type, a subset, or a subset consisting of a combination of a plurality of the steel material information that can be established as a cast, as cast frame candidates of the same steel type,
The cast formation step creates the cast formation by solving the set division problem using the cast frame candidates of the same steel type listed in the first enumeration step. A cast formation method characterized by: A program for causing a computer to function as each means of the cast knitting apparatus according to any one of claims 1 to 8 .

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