JP2019012488A - Constraint expression generating device and constraint expression generating method - Google Patents

Abstract

To present information for supporting modification of an expression to be input to mathematical programming.SOLUTION: A constraint expression generating device 1 includes a premise rule application section 12a for reading a premise rule 13a defined by a combination of a collation part and an expansion part from a storage unit, and when an input premise model 11a inputted matches the collation part of the read premise rule 13a, generating one or more constraint expressions 17 indicated by the expansion part corresponding to the matched collation part as a constraint expression 17 to be expanded from the input premise model 11a, and a display control unit 19 for, at a time of displaying the constraint expression 17 generated by the premise rule application section 12a, displaying the input premise model 11a used for the generation in association with the constraint expression 17 to be displayed.SELECTED DRAWING: Figure 2

Description

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

  Mathematical programming that optimizes along 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 using mathematical formulas, so that advanced mathematical expertise is required. In Patent Document 1, in order to make it easy for beginners who do not have specialized knowledge to use mathematical programming, information that is familiar to the production site, such as production processes, production varieties, and product orders, is input. A scheduling method is described in which a plan is automatically made by a computer by mathematical programming.

JP2013-218644A

Kubo, Mikio, Applied Mathematical Programming Handbook, Asakura Shoten, 2002

  Rather than letting the user input the constraint equation or objective function to be input to the mathematical programming solver (solver), the model data that becomes the clue of the constraint equation is input to the user, and the computer automatically constrains from the model data. Generating an expression is more convenient because it places less burden on the user. However, when a user models an actual mathematical programming problem into model data, if the wrong model data is input, the constraint equation generated from the model data is also incorrect.

  A solver with an incorrect constraint expression may only output that there is a defect such as “no feasible solution”. However, the user does not know which part of many model data or constraint equations will correct the solver to output the correct optimal solution as a whole. Or, in the first place, the mathematical programming problem itself may be an essentially unsolved problem. In other words, when mathematical programming is modeled, it is required to present information useful for appropriate correction.

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

In order to solve the above-described problem, the constraint expression generation device of the present invention reads knowledge for model development defined by a combination of a collation unit and a development unit from a storage unit, and the model development read by input model data A rule that generates one or more constraint expressions indicated by the expansion unit corresponding to the matching unit to be matched as a constraint equation of a mathematical programming problem developed from the model data when the knowledge matching unit matches Application section;
And a display control unit configured to display the constraint formula generated by the rule application unit and the model data used for generating the constraint formula in association with each other.
Other means will be described later.

  ADVANTAGE OF THE INVENTION According to this invention, the information which assists correction | amendment of the numerical formula input into mathematical programming can be shown.

It is a flowchart which shows the outline | summary of a process of the constraint equation production | generation apparatus regarding one Embodiment of this invention. 1 is a configuration diagram of a constraint expression generation apparatus according to an embodiment of the present invention. It is explanatory drawing of the overflow evaluation problem at the time of plant piping fracture | rupture as an example to which the constraint type | formula production | generation apparatus regarding one Embodiment of this invention is applied. It is a data table which stores the model variable regarding one Embodiment of this invention. It is an input screen figure of the model data regarding one Embodiment of this invention. 6 is a data table for storing model data input from the input screen of FIG. 5 according to an embodiment of the present invention. It is a data table which stores the knowledge for model expansion by the mixed integer linear programming concerning one Embodiment of this invention. It is a data table which further stores the collation part of FIG. 7 regarding one Embodiment of this invention for every element. It is an input screen figure of the rule for establishment regarding one Embodiment of this invention. It is an input screen figure of the rule for premise regarding one embodiment of the present invention. It is a flowchart which shows the detail of the production | generation process of the constraint formula regarding one Embodiment of this invention. It is explanatory drawing which shows the example for supplementarily explaining the process of FIG. 11 regarding one Embodiment of this invention. It is a data table which stores the constraint type | formula regarding one Embodiment of this invention. It is a display screen figure of the constraint type | formula regarding one Embodiment of this invention. It is a display screen figure of the optimal solution which the solver part concerning one embodiment of the present invention outputs. FIG. 16 is another form of the display screen diagram of FIG. 15 relating to one embodiment of the present invention. 1 is a configuration diagram of a constraint expression generation apparatus according to an embodiment of the present invention. It is a screen figure which shows the detailed input screen of the objective function by the constraint expression production | generation apparatus of FIG. 17 regarding one Embodiment of this invention. It is a screen figure which shows the result confirmation screen of a solver part along the setting input from the screen figure of FIG. 18 regarding one Embodiment of this invention. It is a flowchart which shows the detail of the solution calculation process by a solver part among the processes of the constraint expression production | generation apparatus of FIG. 17 regarding 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 equation generation apparatus 1.
The constraint expression generation apparatus 1 accepts input of model development knowledge in S11 and accepts input of model data and objective functions in S12.
The constraint expression generation device 1 expands the model data of S12 into a constraint expression using the model expansion knowledge of S11 (S13).
The constraint equation generation device 1 displays the constraint equation expanded in S13 on the screen (S14), and accepts corrections to the constraint equation (S15). When the correction is made (S15, Yes), the constraint expression generation device 1 returns to S12 and accepts re-input of the model data and the objective function.
The constraint expression generation device 1 solves a mathematical programming problem (such as a mixed integer linear programming problem) that maximizes the objective function while satisfying the constraint expression in the solver unit (S16), and displays the optimal solution that is the solution result on the screen. (S17).
Then, when there is a next problem, the constraint equation generation apparatus 1 returns to S12 and accepts re-input of model data and an objective function. On the other hand, the model development knowledge in S11 is general-purpose knowledge that can be used in common for a plurality of problems, so it is not necessary to re-input each problem.

FIG. 2 is a configuration diagram of the constraint equation generation apparatus 1.
The constraint equation generation device 1 is configured as a computer having a CPU (Central Processing Unit), a memory, 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 executes a program (also referred to as an application or its abbreviated application) read on the memory, thereby operating a control unit (control means) configured by each processing unit.

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

  The model development knowledge 13 is data input in S11, and details of the data contents will be described later with reference to FIGS. The model development knowledge 13 is classified as either the premise rule 13a or the establishment rule 13c. This classification shows the hierarchical structure of the rules. The premise rule 13a is an upper hierarchy, and the establishment rule 13c is a lower hierarchy. That is, “premise” and “establishment” are used separately because of the relationship between rules that one premise rule 13a is established and one or more establishment rules 13c are established.

  The model data 11 is data input in S12, and details of the data contents will be described later with reference to FIGS. Similarly to the model development knowledge 13, the model data 11 is also classified into “premise” and “established”. That is, this is a relationship between models in which one or more input establishment models 11c (lower models) are established on the assumption that one input assumption model 11a (upper model) is established. Furthermore, the input premise model 11a and the input establishment model 11c are each expressed by a mathematical expression using the model variable 11b, but the definition of the model variable 11b is also input separately.

The objective function 16 is input in S12, and is referred to 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 processing of the constraint equation 17 is performed separately for “premise” and “establishment”.
The premise rule application unit 12a collates the input premise model 11a with the model development knowledge 13 and outputs a 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 and the model development knowledge 13 and outputs a template expression of the constraint expression 17 in the model development knowledge 13 that matches in the collation. The formation variable generation unit 14c newly generates a variable used in the template expression output by the formation rule application unit 12c.
The generation coefficient setting unit 15 sets coefficients for multiplying the newly generated variables for the template expressions output from the premise variable generation unit 14a and the established variable generation unit 14c, respectively. As a result, the template expression is converted into the constraint expression 17.

The solver unit 18 solves the mathematical programming problem that maximizes (optimizes) the objective function 16 while satisfying the constraint equation 17 by mathematical programming as shown in S16.
The display control unit 19 displays the expanded constraint equation 17 and the objective function 16 on the screen (S14), or displays the optimal solution, which is the solution obtained by the solver unit 18, on the screen (S17). Inform the details of the mathematical programming problem.

Here, as a main feature of the present embodiment, the display control unit 19 uses the model data used for the expansion processing of the constraint equation 17 (the source of expansion) when the constraint equation 17 is displayed on the screen in S14. 11 and knowledge 13 for model development are displayed in association with the constraint expression 17 at the deployment destination. As a result, when an erroneous constraint equation 17 is found, it is possible to retrospectively correct the model data 11 and model development knowledge 13 of the development source.
That is, when one model data 11 is expanded into a plurality of constraint expressions 17 and an error is found in one of the constraint expressions 17, the model data 11 of the expansion source is corrected to be another expansion destination. The constraint equation 17 can also be corrected 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 equation generation apparatus 1 is applied. This explanatory diagram is a view of the four rooms L1 to L4 seen from the lateral direction, with the upper part being higher from the ground and the lower part being closer to the ground. Each room is a cube with a side of 4 m.
The rooms L1, 2 are located on the floor above the rooms L3, L4.
The floor of the room L3 is 1 m higher than the floor of the room L4, and the floor height of the room L1 and the floor height of the L2 are the same.
There is an opening / closing door P12 in the passage between the rooms L1-L2, and there is an opening / closing door P34 in the passage between the rooms L3-L4. Each open / close door has only two states, fully open and fully closed.
The passage P13 between the rooms L1 and L3 is directly connected without a door, and water can always flow from the room L1 to the room L3.
In the passage between the rooms L2 and L4, in addition to the open / close door P24, a weir with a height of 0.5 m exists at the entrance of the passage on the room L2 side. That is, when the amount of water exceeding 8 cubic meters, which is 0.5 m over the floor area of 16 square meters in the room L2, is accumulated in the room L2, the excess water flows out to the room L4 through the weir.

The table 102 of FIG. 3 shows two piping systems, A system and B system, which are arranged in the four rooms L1 to L4. In the A system, there is a possibility of breaking in the room L1 or L2. In the B system, there is a possibility of breaking in the room L1 or L4. The amount of water at the time of breakage is 25 cubic meters for the A line and 50 cubic meters for the B line.
Based on the above assumptions, the maximum water level of each room and the open / closed state of the open / close door at that time are determined as an overflow evaluation problem. This solution result can be used to open / close the door in the event of an accident, or to create a renovation plan for the installation location / room / door structure of the facility. Therefore, the user inputs model data 11 obtained by modeling the overflow evaluation problem of FIG.

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 breakage of each room in FIG. For the model variable (variable name) in the first column, the user sets the variable type (whether real or integer) in the second column, the upper limit (possible model variable) in the third column, and the fourth column The lower limit (which can be taken by the model variable) and the description in the fifth column are input in association with each other. In mixed integer linear programming, variables are divided into real variables and integer variables, and usually any variable can take a positive value or a zero value.
Further, although not shown, the user also inputs the objective function 16 for optimizing (maximizing) the value of the variable W3 and stores it in the constraint expression generation apparatus 1.

FIG. 5 is an input screen diagram of the model data 11.
This input screen diagram includes an input field 201 for model data 11, an input field 202 for model variable 11b, a save button 203, a delete button 204, a new button 205, and a list field 206 for already input model data 11. have. In each of the input columns 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 column 202, one column is set as one model variable 11b, and details (variable type, upper limit value, lower limit value) of the model variable 11b are sequentially input from the top.
When the save button 203 is pressed, the input contents of the input fields 201 and 202 are stored in the storage unit of the constraint expression generation device 1 and 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 stored 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.

Note that the input unit of the model data 11 may perform data duplication check processing in the input column 201 and the list column 206. For example, 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, the input unit of the model data 11 displays a warning indicating that there is a duplication.
Further, as an input method to the input fields 201 and 202 in FIG. 5, instead of using text input, an equal sign or an inequality sign is registered in advance as a drawing object, and a GUI (Graphical User Interface) capable of executing data input graphically. 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 “model name” in the input field 201 is stored.
In the input premise model 11a in the second column of the data table, elements extracted from the mathematical formula input in the “input premise model” of the input column 201 as a left side, a right side, and a comparison operator by syntax analysis are stored.
In the input establishment model 11c in the third column of the data table, elements extracted from the mathematical expression input in the “input establishment model” in the input field 201 as a left side, a right side, and a comparison operator by syntax analysis are stored.

Here, the “number” column and the “logic” column of the data table will be described.
One model name is composed of one or more formulas of the input premise model 11a and one or more formulas of the input establishment model 11c. Therefore, when the input premise model 11a is composed of a plurality of mathematical expressions, a serial number indicated by a “number” column is added to each mathematical expression for each mathematical expression. Since the number of mathematical expressions is variable, a serial number “−1” indicating the last mathematical expression is also entered in the “number” column.
Further, regarding the input premise model 11a, a logical relationship (AND relationship or OR relationship) between two mathematical expressions that are continued by a serial number is described in the “logic” column. For example, when there are three mathematical expressions, they are interpreted in a nested format as follows.
((Number 1 formula) (number 2 "logic") (number 2 formula)) (number 3 "logic") (number 3 formula)
On the other hand, since the logical relationships between the mathematical formulas for the input establishment model 11c are all AND, the “logic” column is omitted in the data table.

FIG. 7 is a data table for storing knowledge 13 for model development by mixed integer linear programming. Here, for ease of explanation, model development knowledge 13 for mixed integer linear programming in which both the objective function 16 and the constraint equation 17 are expressed by linear equations is illustrated.
The model development knowledge 13 includes a plurality of rules that are distinguished by rule IDs. Each rule has a “collation unit” for collation with the model data 11 and a deployment destination of the model data 11 that matches the collation unit. It is described in combination with a “development part” which is a template expression.

In addition, each element of A, B, C of “if A then B ≧ C” of the collation unit is a linear expression including a variable and a constant. The B element and the C element are related by an equation or an inequality. Model data 11 that needs to be satisfied when an A element below If holds is defined by an equation or an inequality using a B element and a C element below then.
The A element below If may be defined by only one variable A as indicated by rules C1 and C2, or a logical product (and) between n variables A1 through An as indicated by rules C11 and C21. Or may be defined by a logical sum (OR) between n variables A1 to An as indicated by rules C12 and C22.
Here, since the format of “left side ≦ right side” can be rewritten to the format of “left side ≧ right side” by moving the expression, the format of “left side = right side” and the format of “left side ≧ right side” are exemplified.

In addition to the model variable 11b, the following variables are used in the expansion unit as artificial variables used internally in the calculation process.
The reserved variable “BigM” is a constant sufficiently larger than the model variable 11b.
The reserved variable “SmallM” is a constant that is 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.

Here, paying attention to the first line “C1” in FIG. 7, “[C1M]” is described at the beginning of the “collation part”, and “[C1E]” is described at the beginning of the “expansion part”. is there. These [C1M] and [C1E] are IDs of mathematical expressions that follow and mean M = Matching (collation unit) and E = Expanding (expansion unit) 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 needs to 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 expression 17 of “B + BigM × (1-Conf (A)) ≧ C” using

Focusing on the second row “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, focusing on the fifth row “C12” in FIG. 7, n collating units [C12E1],..., [C12En] are associated with one collating unit [C12]. This means that one model data 11 is expanded into n constraint equations 17.

Here, in the data table of FIG. 7, a rule whose rule ID begins with “C” indicates a rule for establishment 13 c, and a rule whose rule ID begins with “F” indicates a premise rule 13 a.
The rules in the seventh line “F1” and the eighth line “F2” are rules corresponding to the newly introduced binary variable Conf (A). For example, the seventh 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 expressions 17 [F1E1] and [F1E2]. . If ConF (A) is 1, [F1E1] is self-explanatory, and [F1E2] shows that QR ≧ 0, that is, the original equation Q ≧ R holds. If ConF (A) is 0, [F1E2] is self-explanatory, and [F1E1] shows that R ≦ Q holds.

Strictly speaking, when R = Q, ConF (A) can be 0 or 1. However, even though R <Q, ConF (A) is 1 and there are no more severe conditions. If care is taken when creating Equation 17, it will not be a problem.
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) (the coefficient c (A) is an appropriate small positive value). If terms are added artificially, if both hold, ConF (A) = 1 can be obtained.

Similarly, the rule in the eighth line “F2” is expanded into two constraint expressions 17 [F2E1] and [F2E2] when the A element has the form “left side (Q) = right side (R)”. Indicate. It can be seen that when Conf (A) = 1, QR ≧ 0 and QR ≦ 0, and Q = R. When Conf (A) = 0, both equations are self-evident.
Similarly to the rule of “F1”, the rule of “F2” may be Conf (A) = 0 when Q = R. However, by devising the objective function 16, the constraint expression 17 can be strictly limited. Can be applied.

FIG. 8 is a data table that further stores the collation unit of FIG. 7 for each element.
This data table includes, for each collation unit ID, the type of the rule (“establishment” for the establishment rule 13c, “premise” for the premise rule 13a), the A, B, C elements, the B element, and the C element. And a comparison operator indicating a relationship between the two.
The logical product (and) between n variables A1 to An as in rule C11 is abbreviated as “And A (n)”, and the logical sum (OR) between n variables A1 to An as in rule C12. ) Is abbreviated as “OR A (n)”.

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

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

FIG. 11 is a flowchart showing details of the generation processing (S13) of the constraint equation 17.
FIG. 12 is an explanatory diagram showing an example for supplementary explanation of the processing of FIG. Hereinafter, each process of FIG. 11 is demonstrated, referring FIG.
First, a loop (S111 to S116) for selecting the input premise model 11a one by one in order from the top is started, and further, a loop for selecting the premise rules 13a one by one in order from the top (S112 to S115). To start. The process of selecting one by one in order from the top is performed, for example, by setting a selection pointer in the first row of each data table in FIGS. 6 to 8 and setting the selection pointer to the next row every time the loop is completed. It is a process to update.
For example, at reference numeral 311 in 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 compares the selected input premise model 11a with the collation unit of the selected premise rule 13a to determine whether or not they match (S113). For example, the input premise model 11a “W4 ≧ 16” conforms to “Q ≧ R” of the matching 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 adapted 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” is obtained, so that the expanded portion of the premise rule 13a “F1” in FIG. 312).
・ [F1E1] W4-16-BigM × ConF (A) ≦ 0
・ [F1E2] W4-16 + BigM × (1-ConF (A)) ≧ 0
In addition to the processing of S114, when an additional term is specified in the premise rule 13a as in the premise rule 13a "F2" in FIG. 10, the additional term is added to the objective function 16. On the other hand, since the additional rule is not specified for 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 mathematical expression of the input expansion unit. In FIG. 12, the variable name to be generated is “F”. However, when there are a plurality of variables to be generated, it is desirable to add a serial number such as “F001, F002, F003. As a result, a developed expression 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 into the constraint equation 17 has been described above. In the following, in S121 to S127, similarly, a process of applying the establishment rule 13c to the input establishment model 11c and expanding the constraint expression 17 is shown.

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

For the input establishment model 11c “W4 + 16 = W3”, the comparison operator is “=” and the A element of the If part (the input premise model 11a corresponding to the input establishment model 11c) is a single conditional expression. (And or OR is not set in the logical string of FIG. 6), the establishment rule 13c “C2” is satisfied (reference numeral 322).
When “W4 + 16 = W3” is applied to “B = C”, “(W4 + 16) = B, W3 = C” is obtained, so that the establishment rule application unit 12c is a deployment unit of the establishment rule 13c “C2”. Is generated as indicated by 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 established variable generation unit 14c assigns a unique variable name “F” as indicated by reference numeral 323 based on the variable ConF (A) included in the 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 respective output expressions of the premise variable generation unit 14a and the established variable generation unit 14c. Reference numeral 331 indicates a constraint equation 17 as a result of substituting BigM → 48.
It should be noted that BigM has a case where F = 0 where a term of coefficient × (1-F) exists in constraint equation 17 even if F = 1 where a term of coefficient × F exists in constraint equation 17 However, the minimum value for ensuring that the constraint equation 17 is satisfied is set. That is, the reserved variables BigM and SmallM are only used for the purpose of dividing the case between F = 0 and F = 1.
For example, if the first row of the reference numeral 331 “W4-16-BigM × F ≦ 0” is transformed to F = 1, “W4-16 ≦ BigM” is obtained. In the upper limit value column of the model variable 11b in FIG. 4, since the upper limit value of W4 = 64, “W4-16 ≦ 48 ≦ BigM”. Therefore, if BigM = 48, the original equation always holds when F = 1. In this way, BigM is set.
On the other hand, it is preferable that the coefficient of the additional term of the objective function 16 described in S114 is not affected as much as possible. In this embodiment, it is assumed that 1/100 of the coefficient term of the other 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 is shown in which four constraint equations 17 indicated by reference numeral 331 in FIG. 12 are stored. This data table stores, for each model name, correspondence data between a constraint expression 17 generated from the model data 11 and a generated variable used for the constraint expression 17.
The constraint expression 17 of the data table includes a constraint expression number, a “type” indicating whether the rule 13a or the establishment rule 13c is generated, a model number of the model data 11 (number string in FIG. 6), It consists 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 variable” in the data table includes “original variable” that is a conversion source when the assumption variable generation unit 14 a and the established variable generation unit 14 c convert a variable in the constraint expression 17, and “variable name” that is the conversion destination. It consists of.

FIG. 14 is a display screen diagram of the constraint equation 17.
This display screen diagram shows the display field 232 of the model data 11 that is the generation source of the constraint expression 17, the left side portion indicating the correspondence relationship of the “premise” series, and the right side portion indicating the correspondence relation of the “established” series. And a display field 231 including various buttons.
On the left side of the display column 231, a correspondence relationship between the input premise model 11 a of reference numeral 233 → the applied premise rule 13 a “rule F1” → the two constraint expressions 17 (reference numeral 234) to be generated is shown.
On the right side of the display column 231, a correspondence relationship between the input establishment model 11 c of reference numeral 235 → the applied establishment rule 13 c “rule C 2” → the two constraint expressions 17 (reference numeral 236) to be generated is shown.
In addition, the hierarchical relationship between the input premise model 11a and the input establishment model 11c is also associated with a bidirectional arrow.
By referring to the display field 231, the user can confirm the correspondence between the model data 11 input by the user and the constraint equation 17 generated by the constraint equation generation apparatus 1.

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

FIG. 15 is a display screen diagram of the optimal solution output by the solver unit 18. This display screen diagram is displayed after the solution button 239e in FIG. 14 is pressed, and has a result display field 241 and a confirmation button 245.
The result display column 241 includes, for each model variable 11b, a numerical value list column 242 when the objective function 16 is optimized while satisfying the constraint equation 17, and a display column 243 indicating the objective function 16 using the model variable 11b. Is displayed. Further, the result display column 241 also displays a display column 244 indicating that the constraints of the model data 11 are established, and various data indicating the calculation progress (such as whether the value of Conf (A) is 1 or 0). May be.
The result display field 241 allows the user to easily confirm whether 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 diagram of FIG. FIG. 16 shows a case where the solver unit 18 fails to solve the mathematical programming problem that maximizes (optimizes) the objective function 16 while satisfying the constraint equation 17. 14 and 16 correspond to display contents as follows.
Input premise model 11a: code 233 → code 253
A constraint expression 17 generated from the input premise model 11a: code 234 → code 254
Input establishment model 11c: code 235 → code 255
Constraint expression 17 generated from the input establishment model 11c: code 236 → code 256
Here, in FIG. 16, it is assumed that the second term of reference numeral 255 is typed as “160” instead of “16” due to carelessness of the user.

In addition to the display 252 that the display control unit 19 could not find the solution, the display control unit 19 displays an error display 257 that indicates the contradiction between the input premise model 11a and the input establishment model 11c that is the cause, An error display 258 indicating a contradiction with the constraint expression 17 denoted by reference numeral 256 is also displayed. The contradiction is a state where there is no solution that satisfies a plurality of mathematical expressions simultaneously.
As a result, the user can quickly and quickly update the model data 11 by noticing the typo of the input establishment model 11c (reference numeral 255), which is the root cause, rather than correcting the constraint expression 17 of the reference numeral 256 one by one. It can be corrected accurately.

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

FIG. 17 is a configuration diagram of the constraint equation generation apparatus 1. In FIG. 17, a solver control unit 18b and a matching solution list 18c are added to the constraint equation generation apparatus 1 of FIG.
The solver control unit 18 b sets details of the objective function 16 in the solver unit 18 for a mathematical programming problem defined by a combination of the objective function 16 and the constraint expression 17. Details of the objective function 16 are as follows, for example.
A setting of whether the optimal value is the minimum value or the maximum value when finding the variable value of the objective function 16 to be the optimal value (one way).
When the variable value of the objective function 16 is determined so as to be 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 that fall within the predetermined range, a new compatible solution list 18c that stores the set of solutions is prepared.

FIG. 18 is a screen diagram showing a detailed input screen of the objective function 16 by the constraint expression generation device 1 of FIG. This screen diagram shows an input field 261 for a variable name to be optimized as the objective function 16, an input field 262 for a result output condition, an input field 263 for the output number of solution results, and the optimal solution is a minimum value or a maximum value. And an input column 265 for a range of solutions to be output to the matching solution list 18c.
In the result output condition input field 262, a group name is input as a result output condition obtained by grouping combinations of input values in the input fields 263 to 265.
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 type). Therefore, whether the optimum value is the minimum value or the maximum value from the input field 264 of the radio button. Let me select one of these.
When “plural” is selected from the input field 263 of radio buttons, a predetermined range of variable values of the objective function 16 is input from the input field 265.

FIG. 19 is a screen diagram showing a result confirmation screen of the solver unit 18 in accordance with the settings input from the screen diagram of FIG. This screen diagram shows a result output condition display field 271 (corresponding to the input field 262) used in the solving process of the solver unit 18, and a solution range display field 272 (input field) in the result output condition of the display field 271. 265), and as a solution result of the solver unit 18, a result list composed of the model variable 11b of the constraint equation 17 (the value of the discrete variable, the representative value of the real variable) and the variable value of the objective function 16 It has a display column 273 and a display column 274 for the constraint equation 17 used for the solution processing.
In the display column 273, two sets of matching solutions that are variable values (F2 = 60) of the objective function 16 that fit within the range of the display column 272 (range of 25 to 80) are listed as the matching solution list 18c. Yes.
In the display column 271, for example, one result output condition can be selected from a plurality of result output conditions registered in advance through FIG. 18 by a pull-down menu. With the change of 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 apparatus 1 in FIG.
In S <b> 201, the solver unit 18 performs a solution finding process based on the result output condition input in FIG. 18 based on the objective function 16 and the constraint expression 17.
In S <b> 202, the solver unit 18 determines whether “plurality” is selected from the input field 263. If it is No in S202 (if “single” is selected), the solver unit 18 determines the optimum solution obtained in S201 in which the objective function 16 has the minimum value or the maximum value as specified in the input field 264. The information is added to the compatible solution list 18c (S211), and the process proceeds to S212. On the other hand, if Yes in S202, the process proceeds to S203.

In S <b> 203, the solver unit 18 determines whether or not the result obtained in S <b> 201 is within the predetermined range (lower limit value to upper limit value range) input from the input field 265. If No in S203 (if out of 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 constraint equation 17 (for example, “K1 == K1 = 1, K2 = 0, K3 = 0”) that is the combination of the discrete variable values of the optimal solution that is in the range in S203. Constraint equation 17) including “0, K2 = 1, K3 = 1” is added. That is, in the case of the designation to enumerate a plurality of solutions, another solution can be output within the designated solution range by sequentially adding the constraint equation 17 that excludes the set of variables that gives the optimum solution.

In S205, the solver unit 18 adds the optimal solution (solution that fits the range) to the compatible solution list 18c, and returns the process to S201.
In S212, the display control unit 19 displays the result of finding the solution (optimal solution, compatible solution) in the compatible solution list 18c added in S205 and S211 as shown in the display column 273. This makes it possible to enumerate a set of variables that give an optimal solution and a set of variables near the optimal solution.

In addition, this invention is not limited to an above-described Example, Various modifications are included. For example, the above-described embodiments have been described in detail for easy understanding of the present invention, and are not necessarily limited to those having all the configurations described.
Further, a part of the configuration of one embodiment can be replaced with the configuration of another embodiment, and the configuration of another embodiment can be added to the configuration of one embodiment.
Further, it is possible to add, delete, and replace other configurations for a part of the configuration of each embodiment. Each of the above-described configurations, functions, processing units, processing means, and the like may be realized by hardware by designing a part or all of them with, for example, an integrated circuit.
Each of the above-described configurations, functions, and the like may be realized by software by interpreting and executing a program that realizes each function by the processor.

Information such as programs, tables, and files for realizing each function is stored in memory, a hard disk, a recording device such as an SSD (Solid State Drive), an IC (Integrated Circuit) card, an SD card, a DVD (Digital Versatile Disc), etc. Can be placed on any recording medium.
Further, the control lines and information lines indicate what is considered necessary for the explanation, and not all the control lines and information lines on the product are necessarily shown. Actually, it may be considered that almost all the components are connected to each other.
Furthermore, the communication means for connecting the devices is not limited to the wireless LAN, but may be changed to a wired LAN or other communication means.

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

Claims (6)

The model matching knowledge that is read when the model development knowledge defined by the combination of the matching unit and the expansion unit is read from the storage unit and the input model data matches the model verification knowledge that has been read. A rule application unit that generates one or more constraint expressions indicated by the expansion unit corresponding to the above as a constraint equation of a mathematical programming problem expanded from the model data;
A constraint expression generation apparatus, comprising: a display control unit that displays the constraint expression generated by the rule application unit and the model data used to generate the constraint expression in association with each other. The display control unit further displays the model development knowledge applied to the model data in association with each other when the constraint expression and the model data are displayed in association with each other. The constraint expression generation device according to claim 1. The rule applying unit adds an artificial variable value 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 2. The constraint expression generation device according to Item 1. The constraint equation generation apparatus further includes a solver unit that solves the mathematical programming problem based on the constraint equation generated by the rule application unit and the input objective function,
The solver unit has a solution that simultaneously satisfies a plurality of the constraint equations, and when the plurality of constraint equations are in a contradiction relationship, causes the display control unit to display information indicating the conflict relationship. The constraint expression generation device according to any one of claims 1 to 3. The constraint equation generation apparatus further includes a solver unit that solves 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 value of the objective function is within a specified range, and causes the display control unit to display the set of solution results The constraint expression generation device according to any one of claims 1 to 3, wherein The constraint expression generation device includes a rule application unit and a display control unit,
The rule application unit reads model development knowledge defined by a combination of a collation unit and a development unit from a storage unit, and when the input model data conforms to the collation unit of the model development knowledge read Generating one or more constraint expressions indicated by the expansion unit corresponding to the matching collation unit as a constraint equation of a mathematical programming problem expanded from the model data;
The display control unit displays the constraint equation generated by the rule application unit and the model data used for generating the constraint equation in association with each other, and displays the constraint equation.

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