JP6830415B2 - Constraint expression generator and constraint expression generation method - Google Patents

Description

The present invention relates to a constraint expression generator and a constraint expression generation method.

The mathematical programming method, which optimizes according to the objective function while satisfying the constraint equation, is applied in various fields such as finding the shortest route of the transportation system and planning the minimum cost of the production system. Non-Patent Document 1 introduces Mixed-Integer Linear Programming (MILP), which is a kind of mathematical programming.

In order to use mathematical programming, it is necessary to accurately describe constraint equations and objective functions with mathematical formulas, which requires a high degree of mathematical expertise. In Patent Document 1, in order to make it easy for beginners who do not have specialized knowledge to use the mathematical programming method, if information familiar at the production site such as the production process, production type, and product order is input, the production plan or distribution can be entered. A scheduling method is described in which a computer automatically formulates a plan by a mathematical planning method.

Japanese Unexamined Patent Publication No. 2013-218644

Mikio Kubo ed. Applied Mathematical Planning Handbook, Asakura Shoten, 2002

Rather than having the user input the constraint formula or objective function to be input to the solver (solving part) of the mathematical programming method as it is, the user is asked to input the model data that is a clue to the constraint formula, and the computer automatically constrains from the model data. It is more convenient to generate an expression because it reduces the burden on the user. However, if the user inputs incorrect model data when modeling an actual mathematical planning problem into model data, the constraint formula generated from the model data will also be incorrect.

A solver with an incorrect constraint expression may only output that there is a bug such as "no executable solution". However, the user does not know which part of many model data or constraint expressions should be modified so that the solver outputs the correct optimum solution as a whole. Or, the mathematical planning problem itself, which is the target in the first place, may be an essentially unsolved problem. In other words, when modeling a mathematical programming method, it is required to present information useful for appropriate correction.

Therefore, the main subject of the present invention is to present information that supports the correction of mathematical expressions to be input to the mathematical programming method.

In order to solve the above-mentioned problems, the constraint expression generator of the present invention reads the knowledge for model development defined by the combination of the collation unit and the expansion unit from the storage unit, and the model data to be input reads the model expansion. A rule that generates one or more constraint expressions indicated by the expansion unit corresponding to the matching unit when the matching unit of the knowledge is matched as a constraint expression of a mathematical planning problem expanded from the model data. Applicable part and
It is characterized by having a display control unit that displays the constraint expression generated by the rule application unit in association with the model data used for generating the constraint expression.
Other means will be described later.

According to the present invention, it is possible to present information that assists in modifying mathematical formulas to be input to mathematical programming.

It is a flowchart which shows the outline of the process of the constraint expression generation apparatus which concerns on one Embodiment of this invention. It is a block diagram of the constraint type generator which concerns on one Embodiment of this invention. As an example to which the constraint formula generator according to the embodiment of the present invention is applied, it is explanatory drawing of the overflow evaluation problem at the time of breakage of a plant pipe. It is a data table which stores the model variable which concerns on one Embodiment of this invention. It is an input screen diagram of the model data which concerns on one Embodiment of this invention. It is a data table which stores the model data input from the input screen of FIG. 5 concerning one Embodiment of this invention. It is a data table which stores the knowledge for model development by the mixed integer linear programming method concerning one Embodiment of this invention. It is a data table which further stores the collation part of FIG. 7 concerning one Embodiment of this invention for each element. It is an input screen diagram of the establishment rule concerning one Embodiment of this invention. It is an input screen diagram of the premise rule concerning one Embodiment of this invention. It is a flowchart which shows the detail of the generation process of the constraint expression which concerns on one Embodiment of this invention. It is explanatory drawing which shows the example for supplementary explanation of the process of FIG. 11 concerning one Embodiment of this invention. It is a data table which stores the constraint expression which concerns on one Embodiment of this invention. It is a display screen figure of the constraint expression which concerns on one Embodiment of this invention. It is a display screen figure of the optimum solution output by the solver part which concerns on one Embodiment of this invention. It is another embodiment of the display screen view of FIG. 15 relating to one embodiment of the present invention. It is a block diagram of the constraint type generator which concerns on one Embodiment of this invention. It is a screen view which shows the detailed input screen of the objective function by the constraint expression generator of FIG. 17 concerning one Embodiment of this invention. It is a screen view which shows the result confirmation screen of the solver part according to the setting input from the screen view of FIG. 18 concerning one Embodiment of this invention. It is a flowchart which shows the detail of the solution processing by the solver part in the processing of the constraint expression generation apparatus of FIG. 17 concerning one Embodiment of this invention.

Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.

FIG. 1 is a flowchart showing an outline of processing of the constraint expression generation device 1.
The constraint expression generation device 1 accepts the input of the knowledge for model development in S11 and the input of the model data and the objective function in S12.
The constraint expression generation device 1 expands the model data of S12 into a constraint expression by using the model expansion knowledge of S11 (S13).
The constraint expression generation device 1 displays the constraint expression expanded in S13 on the screen (S14), and accepts the modification to the constraint expression (S15). When the correction is made (S15, Yes), the constraint expression generator 1 returns to S12 and accepts the re-input of the model data and the objective function.
The constraint equation generator 1 solves a mathematical programming problem (mixed integer linear programming problem, etc.) that maximizes the objective function while satisfying the constraint equation in the solver section (S16), and displays the optimum solution as the solution result on the screen. (S17).
Then, when the constraint expression generation device 1 has the following problem, it returns to S12 and accepts the re-input of the model data and the objective function. On the other hand, since the model development knowledge of S11 is general-purpose knowledge that can be commonly used in a plurality of problems, it is not necessary to re-enter each problem.

FIG. 2 is a configuration diagram of the constraint expression generation device 1.
The constraint expression generation device 1 is configured as a computer having a CPU (Central Processing Unit), a memory, a storage means (storage unit) such as a hard disk, an input unit such as a keyboard and a touch panel, and a network interface.
In this computer, the CPU operates a control unit (control means) composed of each processing unit by executing a program (also called an application or an abbreviation thereof) read in the memory.

The constraint expression generation device 1 includes a premise rule application unit 12a, a establishment rule application unit 12c, a premise variable generation unit 14a, a establishment variable generation unit 14c, a generation coefficient setting unit 15, a solver unit 18, and a display control unit. It has 19 as a processing unit.
In the storage unit of the constraint expression generation device 1, model data 11 (input premise model 11a, model variable 11b, input establishment model 11c), model development knowledge 13 (premise rule 13a, establishment rule 13c), and objectives The function 16 and the constraint expression 17 are stored.
Hereinafter, each element of FIG. 2 will be described in association with each process of FIG.

The model development knowledge 13 is the data input in S11, and the details of the data contents will be described later in FIGS. 7 to 10. The model development knowledge 13 is classified into either the premise rule 13a or the establishment rule 13c. This classification shows the hierarchical structure of rules, in which the premise rule 13a is the upper hierarchy and the establishment rule 13c is the lower hierarchy. That is, "premise" and "establishment" are used properly because of the relationship between the rules that one or more establishment rules 13c are established on the premise that one premise rule 13a is established.

The model data 11 is the data input in S12, and the details of the data contents will be described later in FIGS. 4 to 6. The model data 11 is also classified into "premise" and "establishment" in the same manner as the model development knowledge 13. That is, it is a relationship between models that one or more input establishment models 11c (lower model) are established on the premise that one input premise model 11a (upper model) is established. Further, the input premise model 11a and the input establishment model 11c are expressed by mathematical formulas using the model variables 11b, respectively, but the definition of the model variables 11b is also input separately.

The objective function 16 is input in S12 and is referred to in the solution processing in S16.
The constraint equation 17 is expanded (generated) from the model data 11 and the model expansion knowledge 13 in S13, and is referred to in the solution processing in S16 (details will be described later in FIGS. 11 to 13). Here, the generation process of the constraint equation 17 is performed separately for the "premise" and the "establishment".
The premise rule application unit 12a collates the input premise model 11a with the model development knowledge 13, and outputs the template expression of the constraint expression 17 in the model development knowledge 13 that matches in the collation. The premise variable generation unit 14a newly generates a variable used in the template expression output by the premise rule application unit 12a.
The establishment rule application unit 12c collates the input establishment model 11c with the model development knowledge 13, and outputs the template expression of the constraint expression 17 in the model development knowledge 13 that matches in the collation. The establishment variable generation unit 14c newly generates a variable used in the template expression output by the establishment rule application unit 12c.
The generation coefficient setting unit 15 sets a coefficient to be multiplied by each newly generated variable for the template expressions output by the premise variable generation unit 14a and the establishment variable generation unit 14c, respectively. As a result, the template expression is converted into the constraint expression 17.

As shown in S16, the solver unit 18 solves a mathematical programming problem that maximizes (optimizes) the objective function 16 while satisfying the constraint equation 17 by the mathematical programming method.
The display control unit 19 displays the expanded constraint equation 17 and the objective function 16 on the screen (S14), and displays the optimum solution, which is the solution result of the solver unit 18, on the screen (S17). Notify the details of the mathematical planning problem.

Here, as a main feature of the present embodiment, when the display control unit 19 displays the constraint expression 17 on the screen in S14, the model data used (becomes the expansion source) for the expansion process of the constraint expression 17 is displayed. 11 and the model development knowledge 13 are displayed in association with the constraint expression 17 of the development destination. As a result, when an erroneous constraint equation 17 is found, it is possible to trace back to the model data 11 of the expansion source and the model expansion knowledge 13 and correct it.
That is, when one model data 11 is expanded into a plurality of constraint equations 17, and an error is found in one of the constraint equations 17, the model data 11 of the expansion source is modified to be another expansion destination. The constraint equation 17 can also be modified at once.

FIG. 3 is an explanatory diagram of an overflow evaluation problem when a plant pipe is broken as an example to which the constraint expression generator 1 is applied. This explanatory view is a view of the four rooms L1 to L4 viewed from the side, and the upper part is higher than the ground and the lower part is closer to the ground. Each room is a cube with a side of 4 m.
Rooms L1 and 2 are located on floors above rooms L3 and 4.
The floor of room L3 is 1 m higher than the floor of room L4, and the floor height of room L1 and the floor height of L2 are the same.
The passage between rooms L1-L2 has an opening / closing door P12, and the passage between rooms L3-L4 has an opening / closing door P34. Each open / close door has only two states, fully open and fully closed.
The passage P13 between the rooms L1 to L3 is directly connected without a door, and water can always flow from the room L1 to the room L3.
In the passage between rooms L2 and L4, in addition to the opening / closing door P24, there is a weir with a height of 0.5 m at the entrance of the passage on the room L2 side. That is, when the floor area of room L2 is 16 square meters multiplied by 0.5 m and the amount of water exceeding 8 cubic meters is accumulated in room L2, the excess water flows out to room L4 through the weir.

Table 102 in FIG. 3 shows two piping systems, A system and B system, which are arranged in the four rooms L1 to L4. In system A, there is a possibility of breakage in room L1 or L2. In system B, there is a possibility of breakage in room L1 or L4. The amount of water at the time of breakage is 25 cubic meters for system A and 50 cubic meters for system B, and it is assumed that each breaks at only one place.
Based on the above premise, as an overflow evaluation problem, the maximum water level of each room and the open / closed state of the opening / closing door at that time are obtained. The result of this solution can be used for opening and closing the door in the event of an accident, or for creating a repair plan for the installation location, room, and door structure of equipment. Therefore, the user inputs the model data 11 that models the overflow evaluation problem of FIG. 3 into the constraint expression generation device 1.

FIG. 4 is a data table for storing the model variable 11b.
The model variable 11b input by the user is a variable indicating the amount of water after breaking of each room in FIG. For the model variable (variable name) in the first column, the user can see the variable type (real number or integer) in the second column, the upper limit (which the model variable can take) in the third column, and the fourth column. Enter the lower limit value (which the model variable can take) and the description in the fifth column in association with each other. In the mixed integer linear programming method, variables are divided into real variables and integer variables, and usually any variable can take a positive value or a value of 0.
Further, although not shown, the user also inputs an objective function 16 for optimizing (maximizing) the value of the variable W3 and stores it in the constraint expression generation device 1.

FIG. 5 is an input screen view of the model data 11.
This input screen diagram shows the input field 201 of the model data 11, the input field 202 of the model variable 11b, the save button 203, the delete button 204, the new button 205, and the list field 206 of the input model data 11. have. In each of the input fields 201 and 202 in the table format, the left column is the display location of the input item, and the right column is the input location of the item.
In the input field 201, the model name of the model data 11, the input premise model 11a, the input establishment model 11c, and the objective function 16 are input in order from the top. In the input field 202, one column is set as one model variable 11b, and the details (variable type, upper limit value, lower limit value) of the model variable 11b are input in order from the top.
When the save button 203 is pressed, the input contents of the input fields 201 and 202 are saved in the storage unit of the constraint expression generator 1 and are also reflected in the list field 206.
When the delete button 204 is pressed, the input contents of the input fields 201 and 202 and the saved contents of the list field 206 are deleted.
When the new button 205 is pressed, the input contents of the input fields 201 and 202 are reset, and new model data 11 can be input.

The input unit of the model data 11 may perform data duplication check processing in the input field 201 and the list field 206. For example, the input unit of the model data 11 displays a warning indicating duplication when the character string input as the model name in the input field 201 already exists in the model name in the list field 206.
In addition, as an input method for the input fields 201 and 202 in FIG. 5, a GUI (Graphical User Interface) capable of graphically inputting data by registering equal signs and inequality signs as drawing objects in advance instead of using text input. May be prepared.

FIG. 6 is a data table for storing the model data 11 input from the input screen of FIG.
In the first column "model name" of the data table, the input result of the "model name" in the input field 201 is stored.
In the input premise model 11a of the second column of the data table, the elements of the mathematical formula input in the "input premise model" of the input field 201 are stored as the left side, the right side, and the comparison operator by parsing.
In the input establishment model 11c of the third column of the data table, the elements of the mathematical expressions input in the "input establishment model" of the input field 201 are stored as the left side, the right side, and the comparison operator by parsing.

Here, the "number" column and the "logical" column of the data table will be described.
One model name is composed of one or more input premise model 11a mathematical expressions and one or more input establishment model 11c mathematical expressions. Therefore, when the input premise model 11a is composed of a plurality of mathematical expressions, a continuous number indicated by a "number" column is added to each mathematical expression for each mathematical expression. Since the number of mathematical expressions is variable, the serial number "-1" indicating that the mathematical expression is the last mathematical expression is also input in the "number" column.
Further, for the input premise model 11a, the logical relationship (AND relationship or OR relationship) between two mathematical expressions following consecutive numbers is described in the "logical" column. For example, when three mathematical formulas exist, they are interpreted in a nested format as follows.
((Formula of No. 1) ("Logic" of No. 2) (Formula of No. 2)) ("Logic" of No. 3) (Formula of No. 3)
On the other hand, since all the logical relationships between the mathematical expressions for the input establishment model 11c are AND, the "logical" column is omitted in the data table.

FIG. 7 is a data table that stores knowledge 13 for model development by the mixed integer linear programming method. Here, in order to make the explanation easy to understand, the model development knowledge 13 for the mixed integer linear programming method in which both the objective function 16 and the constraint equation 17 are expressed by linear equations is illustrated.
The model development knowledge 13 has a plurality of rules distinguished by a rule ID, and each rule has a "collation unit" for collating with the model data 11 and a development destination of the model data 11 matching the collation unit. It is described in combination with the "expansion part" which is a template expression.

Each element of A, B, and C of "if A then B ≥ C" of the collation unit is a linear expression including a variable and a constant. Then, the B element and the C element are related by an equation or an inequality. The model data 11 that needs to be satisfied when the A element below If holds is defined by an equation or inequality using the B element and C element below then.
The A element below If may be defined by only one variable A as shown in rules C1 and C2, or the logical product (and) between n variables A1 and An as shown in rules C11 and C21. It may be defined by the logical sum (OR) between n variables A1 to An as shown in rules C12 and C22.
Here, since the format of "left side ≤ right side" can be rewritten into the format of "left side ≥ right side" by moving the equation, the format of "left side = right side" and the format of "left side ≥ right side" are illustrated.

In addition to the model variable 11b, the following variables are used as artificial variables internally used in the calculation process in the expansion unit.
-The reserved variable "BigM" is a constant sufficiently larger than the model variable 11b.
-The reserved variable "SmallM" is a constant sufficiently smaller than the model variable 11b.
-The binary variable "ConF (A)" returns a value of 1 when the argument A is satisfied, and returns a value of 0 when the argument A is not satisfied.

Focusing on the first line "C1" in FIG. 7, there is a description of "[C1M]" at the beginning of the "collation part" and a description of "[C1E]" at the beginning of the "expansion part". is there. These [C1M] and [C1E] are the IDs of the formulas that follow, and mean M = Matching (collation part) and E = Expanding (expansion part) at the end of the ID.
For example, the first line "C1" is a binary variable Conf (A) when the format of the model data 11 that must be satisfied when one A element is satisfied is "left side (B) ≥ right side (C)". It is shown that the model data 11 is expanded in one constraint equation 17 of “B + BigM × (1-Conf (A)) ≧ C” using.

Focusing on the second line "C2" in FIG. 7, two expansion units [C2E1] and [C2E2] are associated with one collation unit [C2M]. This means that one model data 11 is expanded into two constraint equations 17.
Further, paying attention to the fifth line “C12” in FIG. 7, n expansion units [C12E1], ..., [C12En] are associated with one collation unit [C12]. This means that one model data 11 is expanded into n constraint equations 17.

Here, in the data table of FIG. 7, the rule whose beginning of the rule ID starts with "C" indicates the establishment rule 13c, and the rule whose beginning of the rule ID starts with "F" indicates the premise rule 13a.
The rules on the 7th line "F1" and the 8th line "F2" correspond to the newly introduced binary variable Conf (A). For example, the 7th line "F1" indicates that when the A element is in the form of "left side (Q) ≥ right side (R)", it is expanded into two constraint equations 17 [F1E1] and [F1E2]. .. If ConF (A) is 1, [F1E1] is trivial, and from [F1E2], it can be seen that QR ≧ 0, that is, the original equation Q ≧ R holds. If ConF (A) is 0, [F1E2] is trivial, and from [F1E1], it can be seen that R ≤ Q holds.

Strictly speaking, when R = Q, ConF (A) holds whether it is 0 or 1, but it is restricted because ConF (A) becomes 1 even though R <Q, and stricter conditions are not given. It does not matter if you are careful when creating Equation 17.
However, in order to apply the strict constraint equation 17, in the problem of maximizing the objective function, the objective function is c (A) × ConF (A) (coefficient c (A) is an appropriate small positive value). By artificially adding terms, if both hold, ConF (A) = 1 can be set.

Similarly, the rule of the 8th line "F2" is expanded into two constraint equations 17 [F2E1] and [F2E2] when the A element is in the form of "left side (Q) = right side (R)". Indicates that. It can be seen that when Conf (A) = 1, QR ≧ 0 and QR ≦ 0, and Q = R. When Conf (A) = 0, both equations are trivial.
Like the rule of "F1", the rule of "F2" may be Conf (A) = 0 when Q = R, but by devising the objective function 16, the constraint formula 17 is strictly defined. Can be applied.

FIG. 8 is a data table for further storing the collation unit of FIG. 7 for each element.
In this data table, for each collation unit ID, the type of the rule (“established” for the rule 13c for establishment, “premise” for the rule 13a for establishment), each element A, B, C, B element, and C element Stores a comparison operator that indicates the relationship between and.
The logical product (and) between n variables A1 and An like rule C11 is abbreviated as "And A (n)", and the logical sum (OR) between n variables A1 and An like rule C12 is abbreviated. ) Is abbreviated as "OR A (n)".

FIG. 9 is an input screen view of the establishment rule 13c.
This input screen diagram has an input field 211 of the establishment rule 13c, a save button 212, a delete button 213, a new button 214, and a list field 215 of the already entered establishment rule 13c. The display contents of the list column 215 can be updated vertically by the scroll bar.
In the input field 211, the rule ID of the establishment rule 13c, the collation unit of the establishment rule 13c, and the expansion unit of the establishment rule 13c are input in order from the top.
When the save button 212 is pressed, the input contents of the input field 211 are saved in the storage unit of the constraint expression generator 1 and are also reflected in the list field 215. When the delete button 213 is pressed, the input contents of the input field 211 and the saved contents of the list field 215 are deleted. When the new button 214 is pressed, the input content of the input field 211 is reset, and a new establishment rule 13c can be input.

FIG. 10 is an input screen view of the premise rule 13a.
This input screen diagram has an input field 221 of the premise rule 13a, a save button 222, a delete button 223, a new button 224, and a list field 225 of the premise rule 13a that has already been input.
In the input field 221, the rule ID of the premise rule 13a, the collation part (ID and mathematical formula) of the premise rule 13a, the expansion part of the premise rule 13a, and the additional item of the objective function 16 are input in order from the top. Will be done. For example, when the constraint equation 17 holds even when ConF (A) = 0, there is a specification method such as adding a term of "SmallM × Conf (A)" to the objective function 16.
When the save button 222 is pressed, the input contents of the input field 221 are saved in the storage unit of the constraint expression generator 1 and are also reflected in the list field 225. When the delete button 223 is pressed, the input contents of the input field 221 and the saved contents of the list field 225 are deleted. When the new button 224 is pressed, the input contents of the input field 221 are reset, and a new premise rule 13a can be input.

FIG. 11 is a flowchart showing the details of the generation process (S13) of the constraint equation 17.
FIG. 12 is an explanatory diagram showing an example for supplementary explanation of the process of FIG. Hereinafter, each process of FIG. 11 will be described with reference to FIG.
First, a loop (S111 to S116) for selecting the input premise models 11a one by one from the beginning is started, and further, a loop (S112 to S115) for selecting the premise rules 13a one by one from the beginning in the loop. To start. In the process of selecting one by one from the beginning, for example, a selection pointer is set in the first row of each data table of FIGS. 6 to 8, and the selection pointer is moved to the next row each time the loop is cycled. It is a process to update.
For example, in reference numeral 311 of FIG. 12, “W4 ≧ 16” input in the input screen diagram of FIG. 5 is selected as the input premise model 11a.

The premise rule application unit 12a determines whether or not they match by comparing the selected input premise model 11a with the collation unit of the selected premise rule 13a (S113). For example, the input premise model 11a “W4 ≧ 16” conforms to “Q ≧ R” of the collation unit [F1M] of the premise rule 13a “F1” because the comparison operator is ≧.
Therefore, the premise rule application unit 12a applies the premise rule 13a conformed by the collation of S113 to the input premise model 11a (S114). For example, if "W4 ≥ 16" is applied to "Q ≥ R", "W4 = Q, 16 = R", so the expansion part of the premise rule 13a "F1" in FIG. 7 is as follows ( Reference numeral 312).
・ [F1E1] W4-16-BigM × ConF (A) ≤ 0
・ [F1E2] W4-16 + BigM × (1-ConF (A)) ≧ 0
When an additional term is specified in the premise rule 13a as in the premise rule 13a "F2" of FIG. 10, the additional term is added to the objective function 16 in conjunction with the processing of S114. On the other hand, since no additional term is specified in the premise rule 13a "F1" this time, it is not necessary to change the objective function 16.

After the two loops, the set of expansion units applied in S114 is input to the premise variable generation unit 14a. In S117, the premise variable generation unit 14a generates a unique variable name based on the variable ConF (A) included in the input formula of the expansion unit. In FIG. 12, the variable name to be generated is "F", but when there are a plurality of variables to be generated, it is desirable to add a continuous number such as "F001, F002, F003 ..." as the variable name. As a result, the expansion formula in which ConF (A) is replaced with F is indicated by reference numeral 313.
The process of applying the premise rule 13a to the input premise model 11a and expanding it to the constraint equation 17 has been described above. Hereinafter, in S121 to S127, the process of applying the establishment rule 13c to the input establishment model 11c and expanding to the constraint equation 17 will be shown.

First, a loop (S121 to S126) for selecting the input establishment model 11c one by one from the beginning is started, and further, a loop (S122 to S125) for selecting the establishment rule 13c one by one from the beginning in the loop. To start. In reference numeral 321 the input establishment model 11c “W4 + 16 = W3” of FIG. 5 is selected.
The establishment rule application unit 12c determines whether or not they match by comparing the selected input establishment model 11c with the collation unit of the selected establishment rule 13c (S123). Then, the establishment rule application unit 12c applies the establishment rule 13c conformed by the collation of S123 to the input establishment model 11c (S124).

Then, for the input establishment model 11c "W4 + 16 = W3", the comparison operator is =, and the A element of the If part (input premise model 11a corresponding to the input establishment model 11c) is a single conditional expression. (And and OR are not set in the logical column of FIG. 6), so that the establishment rule 13c "C2" is met (reference numeral 322).
When "W4 + 16 = W3" is applied to "B = C", "(W4 + 16) = B, W3 = C", so the establishment rule application unit 12c is the expansion unit of the establishment rule 13c "C2". Is generated as in reference numeral 322 (S124).
・ [C2E1] W4 + 16 + BigM × (1-ConF (A)) ≧ W3
・ [C2E2] W4-16-BigM × (1-ConF (A)) ≤ W3
In S127, as in S117, the establishment variable generation unit 14c assigns a unique variable name “F” to the symbol 323 based on the variable ConF (A) included in the mathematical expression of the expansion unit generated in S124. Generate.

In S131, the generation coefficient setting unit 15 sets appropriate values for the reserved variables BigM and SmallM included in the output expressions of the premise variable generation unit 14a and the establishment variable generation unit 14c, respectively. Reference numeral 331 shows the constraint equation 17 as a result of substituting BigM → 48.
In BigM, even if F = 1 has a term of coefficient × F in the constraint equation 17, when F = 0 has a term of coefficient × (1-F) in the constraint equation 17. However, the minimum value for the constraint equation 17 to always hold is set. That is, the reserved variables BigM and SmallM are only used for the purpose of distinguishing between the case of F = 0 and the case of F = 1.
For example, if the first line “W4-16-BigM × F ≦ 0” of reference numeral 331 is transformed with F = 1, it becomes “W4-16 ≦ BigM”. In the upper limit value sequence of the model variable 11b in FIG. 4, since the upper limit value of W4 = 64, “W4-16 ≦ 48 ≦ Big M”. Therefore, if BigM = 48, the original formula always holds when F = 1. Set BigM like this.
On the other hand, it is preferable that the coefficient of the additional term of the objective function 16 described in S114 does not affect the original objective function 16 as much as possible. In this embodiment, it is assumed that 1/100 of the coefficient term of another model variable 11b having the coefficient term of the objective function 16 is set.

FIG. 13 is a data table for storing the constraint equation 17. Here, an example of storing the four constraint equations 17 represented by reference numeral 331 in FIG. 12 is shown. This data table stores the correspondence data between the constraint equation 17 generated from the model data 11 and the generated variables used in the constraint equation 17 for each model name.
The constraint formula 17 in the data table includes a constraint formula number, a "type" indicating whether the premise rule 13a or the establishment rule 13c is used, a model number of the model data 11 (number sequence in FIG. 6), and It is composed of an "application rule" indicating the applied model development knowledge 13 and each element (left side, right side, comparison operator) of the constraint expression 17.
The "generated variables" in the data table are the "original variable" that is the conversion source when the premise variable generation unit 14a and the established variable generation unit 14c convert the variables in the constraint equation 17, and the "variable name" that is the conversion destination. Consists of.

FIG. 14 is a display screen view of the constraint equation 17.
This display screen diagram shows the display field 232 of the model data 11 that is the generator of the constraint equation 17, the left side portion showing the correspondence relationship of the "premise" series, and the right side portion showing the correspondence relationship of the "established" series. It is composed of a display field 231 including the above and various button groups.
On the left side of the display field 231, the correspondence between the input premise model 11a of reference numeral 233 → the applied premise rule 13a “rule F1” → the two generated constraint equations 17 (reference numeral 234) is shown.
On the right side of the display field 231, the correspondence between the input establishment model 11c of reference numeral 235 → the applicable establishment rule 13c “rule C2” → the two generated constraint equations 17 (reference numeral 236) is shown.
Further, the hierarchical relationship between the input premise model 11a and the input establishment model 11c is also associated with the bidirectional arrows.
By referring to the display field 231, the user can confirm the correspondence between the model data 11 input by himself / herself and the constraint expression 17 generated by the constraint expression generation device 1.

Further, the display screen diagram includes an edit button 239a for switching to a mode for editing (correcting) the contents of the display field 231 and a registration button 239b for registering the edited (corrected) data contents in the storage unit. The add button 239c for adding new model data 11, the delete button 239d for deleting the existing model data 11, the objective function 16 and the constraint equation 17 are determined, and the process proceeds to the solution processing of the solver unit 18. It has a solution button 239e for the purpose.

FIG. 15 is a display screen view of the optimum solution output by the solver unit 18. This display screen view is displayed after the solution button 239e of FIG. 14 is pressed, and has a result display field 241 and a confirmation button 245.
The result display column 241 includes a list column 242 of numerical values for optimizing the objective function 16 while satisfying the constraint equation 17 for each model variable 11b, and a display column 243 showing the objective function 16 using the model variable 11b. Are displayed respectively. Further, in the result display column 241, a display column 244 indicating that the constraint of the model data 11 is satisfied and various data indicating the calculation progress (whether the value of Conf (A) is 1 or 0, etc.) are also displayed. You may.
The result display field 241 allows the user to easily confirm whether or not the model data 11 and the model development knowledge 13 are appropriate. When the confirmation button 245 is pressed, the process proceeds to S18 in FIG.

FIG. 16 is another form of the display screen view of FIG. FIG. 16 shows a case where the solver unit 18 cannot solve the mathematical programming problem that maximizes (optimizes) the objective function 16 while satisfying the constraint equation 17. The display contents correspond to FIG. 14 and FIG. 16 as follows.
-Input premise model 11a: reference numeral 233 → reference numeral 253
Constraint formula 17 generated from the input premise model 11a: reference numeral 234 → reference numeral 254
Input establishment model 11c: reference numeral 235 → reference numeral 255
Constraint formula 17 generated from the input establishment model 11c: reference numeral 236 → reference numeral 256
Here, in FIG. 16, it is assumed that the user inadvertently mistypes the second term of reference numeral 255 as "160" instead of "16".

In addition to the display 252 indicating that the solution could not be obtained, the display control unit 19 includes an error display 257 indicating a contradiction between the input premise model 11a and the input establishment model 11c, which is the cause thereof, and the constraint equation 17 of reference numeral 254. An error display 258 indicating a contradictory relationship with the constraint equation 17 of reference numeral 256 is also displayed. A contradiction relationship is a state in which there is no solution that can be satisfied at the same time between a plurality of mathematical expressions.
As a result, the user notices the typo in the input establishment model 11c (reference numeral 255), which is the root cause thereof, rather than modifying the constraint equation 17 of the reference numeral 256 one by one, so that the model data 11 can be quickly obtained. It can be corrected accurately.

In the present embodiment described above, since the constraint expression generation device 1 generates the constraint expression 17 from the input model data 11, the labor for inputting the constraint expression 17 to be input to the solver unit 18 can be saved. Further, the display control unit 19 associates the expansion source data (model data 11 and model expansion knowledge 13) with the expansion destination data (constraint formula 17) on the display screen of the constraint equation 17 of FIG. indicate. As a result, the generation process of the constraint equation 17 can be traced (in other words, traceability is ensured), and it is possible to easily find out in which part the incorrect data is mixed.

FIG. 17 is a configuration diagram of the constraint expression generation device 1. In FIG. 17, a solver control unit 18b and a matching solution list 18c are added to the constraint expression generation device 1 of FIG.
The solver control unit 18b sets the details of the objective function 16 in the solver unit 18 for the mathematical programming problem defined by the combination of the objective function 16 and the constraint equation 17. The details of the objective function 16 are as follows, for example.
-When solving so that the variable value of the objective function 16 becomes the optimum value (one way), the optimum value is set as the minimum value or the maximum value.
-When solving so that the variable value of the objective function 16 is within the predetermined range, the lower limit value and the upper limit value within the predetermined range are set. Since there may be a plurality of solutions within a predetermined range, a new matching solution list 18c for storing a set of the solutions is prepared.

FIG. 18 is a screen view showing a detailed input screen of the objective function 16 by the constraint expression generation device 1 of FIG. In this screen diagram, the input field 261 of the variable name to be optimized as the objective function 16, the input field 262 of the result output condition, the input field 263 of the number of output of the solution result, and the optimum solution are the minimum value or the maximum value. It has an input field 264 and an input field 265 for a range of solutions to be output to the matching solution list 18c.
In the input field 262 of the result output condition, the group name is input as the result output condition in which the combination of the input values of the input fields 263 to 265 is grouped.
When "single" is selected from the input field 263 of the radio button, the variable value of the objective function 16 is set to the optimum value (one way), so whether the optimum value is the minimum value or the maximum value from the input field 264 of the radio button. Let them choose one of them.
When "plurality" is selected from the input field 263 of the radio button, a predetermined range of the variable value of the objective function 16 is input from the input field 265.

FIG. 19 is a screen view showing a result confirmation screen of the solver unit 18 according to the settings input from the screen view of FIG. This screen view shows the result output condition display field 271 (corresponding to the input field 262) used for the solution processing of the solver unit 18 and the solution range display field 272 (input field) in the result output condition of the display field 271. (Corresponding to 265), and as the solution result of the solver part 18, the result list composed of the model variable 11b (value of the discrete variable, the representative value of the real variable) of the constraint equation 17 and the variable value of the objective function 16. It has a display field 273 and a display field 274 of the constraint equation 17 used for the solution processing.
In the display column 273, as a matching solution list 18c, two sets of matching solutions that are variable values (F2 = 60) of the objective function 16 that fit the range of the display column 272 (range of 25 or more and 80 or less) are listed. There is.
In the display field 271, for example, one result output condition can be selected from a plurality of result output conditions pre-registered via FIG. 18 by a pull-down menu. Along with the change in the result output condition, the solver unit 18 recalculates the solution processing and causes the display control unit 19 to update the display content of the calculation result.

FIG. 20 is a flowchart showing details of the solution processing (S16 in FIG. 1) by the solver unit 18 in the processing of the constraint equation generation device 1 of FIG.
In S201, the solver unit 18 performs solution processing based on the objective function 16 and the constraint equation 17 according to the result output condition input in FIG.
In S202, the solver unit 18 determines whether or not "plurality" is selected from the input field 263. If No in S202 (if "single" is selected), the solver unit 18 finds the optimal solution solved in S201 where the objective function 16 is the minimum or maximum value, as specified in the input field 264. It is added to the matching solution list 18c (S211), and the process proceeds to S212. On the other hand, if Yes in S202, the process proceeds to S203.

In S203, the solver unit 18 determines whether or not the result obtained in S201 is within the predetermined range (within the range of the lower limit value to the upper limit value) input from the input field 265. If No in S203 (outside the range), the process returns to S201. On the other hand, if Yes in S203, the process proceeds to S204.
In S204, the solver unit 18 excludes the combination of discrete variable values of the optimum solution (for example, “K1 = 1, K2 = 0, K3 = 0”) within the range in S203 (for example, “K1 =”). The constraint equation 17) including "0, K2 = 1, K3 = 1" is added. That is, in the case of specifying to enumerate a plurality of solutions, another solution can be output within the range of the specified solution by sequentially adding the constraint equation 17 excluding the set of variables giving the optimum solution.

In S205, the solver unit 18 adds the optimal solution (solution that fits the range) to the matching solution list 18c and returns the process to S201.
In S212, the display control unit 19 displays the solution results (optimal solution, matching solution) in the matching solution list 18c added in S205 and S211 on the screen as in the display column 273. This makes it possible to enumerate the set of variables that give the optimum solution and the set of variables that are near the optimal solution.

The present invention is not limited to the above-described embodiment, and includes various modifications. For example, the above-described embodiment has been described in detail in order to explain the present invention in an easy-to-understand manner, and is not necessarily limited to those having all the described configurations.
Further, it is possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment.
Further, it is possible to add / delete / replace a part of the configuration of each embodiment with another configuration. Further, each of the above configurations, functions, processing units, processing means and the like may be realized by hardware by designing a part or all of them by, for example, an integrated circuit.
Further, each of the above configurations, functions, and the like may be realized by software by the processor interpreting and executing a program that realizes each function.

Information such as programs, tables, and files that realize each function can be stored in memory, hard disks, recording devices such as SSDs (Solid State Drives), IC (Integrated Circuit) cards, SD cards, DVDs (Digital Versatile Discs), etc. Can be placed on the recording medium of.
In addition, the control lines and information lines indicate those that are considered necessary for explanation, and do not necessarily indicate all the control lines and information lines in the product. In practice, it can be considered that almost all configurations are interconnected.
Further, the communication means for connecting each device is not limited to the wireless LAN, and may be changed to a wired LAN or other communication means.

1 Constraint expression generator 11 Model data 11a Input premise model 11b Model variable 11c Input establishment model 12a Premise rule application part 12c Establishment rule application part 13 Model development knowledge 13a Premise rule 13c Establishment rule 14a Prerequisite variable generation part 14c Establishment variable Generation unit 15 Generation coefficient setting unit 16 Objective function 17 Constraint expression 18 Solver unit 18b Solver control unit 18c Applicable solution list 19 Display control unit

Claims (6)

The model expansion knowledge defined by the combination of the collation unit and the expansion unit is read from the storage unit, and when the input model data matches the collation unit of the model expansion knowledge read, the collation unit is matched. A rule application unit that generates one or more constraint expressions indicated by the expansion unit corresponding to the above as constraint expressions of a mathematical planning problem developed from the model data.
A constraint expression generation device including a display control unit that displays the constraint expression generated by the rule application unit in association with the model data used for generating the constraint expression. The display control unit is further characterized in that when the constraint expression and the model data are displayed in association with each other, the knowledge for model development applied to the model data is also associated and displayed. The constraint expression generator according to claim 1. The claim is characterized in that the rule application unit adds a value of an artificial variable calculated based on a range of possible values of a model variable used for the input model data to the constraint expression to be generated. Item 1. The constraint expression generator according to item 1. The constraint equation generator further has a solver unit for solving the mathematical programming problem based on the constraint equation generated by the rule application unit and the input objective function.
The solver unit is characterized in that there is no solution that satisfies the plurality of constraint equations at the same time, and when the plurality of constraint equations have a contradiction relationship, the display control unit displays information indicating the contradiction relationship. The constraint expression generator according to any one of claims 1 to 3. The constraint equation generator further has a solver unit for solving the mathematical programming problem based on the constraint equation generated by the rule application unit and the input objective function.
The solver unit solves a set of variable values of each variable used in the constraint equation in which the variable values of the objective function are within a specified range, and causes the display control unit to display the set of the solution results. The constraint equation generator according to any one of claims 1 to 3, wherein the constraint expression generator is characterized by the above. The constraint expression generator has a rule application unit and a display control unit.
The rule application unit reads the model expansion knowledge defined by the combination of the collation unit and the expansion unit from the storage unit, and when the input model data matches the collation unit of the model expansion knowledge read. , One or more constraint equations indicated by the expansion unit corresponding to the matching collation unit are generated as constraint expressions of the mathematical planning problem expanded from the model data.
The display control unit is a constraint expression generation method, characterized in that the constraint expression generated by the rule application unit and the model data used for generating the constraint expression are displayed in association with each other.

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