JP2019008499A - Solution search processing device - Google Patents

Abstract

To facilitate the analysis of a solution process of a constraint satisfying solution by explicitly outputting constraint that causes the decision of a solution of a decision variable and information of other solutions that cause constraint propagation of the solution.SOLUTION: A solution search processing device includes: a search step-classified constraint propagation state extraction unit for calculating a changing selectable domain in selecting a value of a decision variable in each search step; a constraint propagation execution unit for executing constraint propagation; a prediction model learning unit for learning a prediction model with the value selected in each step as teacher data on the basis of a result calculated by the search step-classified constraint propagation state extraction unit, updating the domain according to the selected value, and performing learning; a value prediction unit for predicting a value of a decision variable to be selected by the prediction model, updating the domain according to the value selected by the constraint propagation execution unit, and performing search processing; and a cause explanation unit for outputting information of a selectable domain to be a cause in the case of predicting a value of a specified decision variable.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a solution search processing device, and more particularly to a solution search processing device suitable for analyzing a process for obtaining an optimal solution in a problem of searching for a constraint satisfaction solution by large-scale constraint programming.

  As an application of the problem of searching for a constraint satisfaction solution by constraint programming, there are cases in which resource management and planning operations in industrial fields such as railways, resource allocation, and factory production planning are targeted.

  For example, in the railway operation management business, it is required to run a train based on a predetermined train operation plan (diagram) at normal times. If this happens, the plan must be revised so that there is no hindrance to train operation. In addition to train schedules, plans necessary for rail transport include vehicle operation information that defines a vehicle allocation plan for trains on the diagram and crew operation information that defines a crew allocation plan. In the event that a timetable disruption occurs on the day of operation, the vehicle operation information and the crew operation information are corrected according to the timetable correction.

  In addition, for example, in the resource allocation planning business, it is required to develop a daily plan for allocating resources at the resource allocation location where capacity is limited according to the resource inventory that fluctuates daily due to the receipt and shipment of resources. It is done. At this time, while complying with many restrictions such as restrictions on the processing of resources for shipment at the specified date and time and restrictions on the capacity of the means for moving resources per day, the plan for the previous day However, it is necessary to make a daily plan so as not to change as much as possible.

  In the planning work as described above, a solution to a large-scale constraint satisfaction problem has to be derived, and conventionally it has been performed manually by a skilled operator. However, in recent years, with the retirement of skilled operators, the need to replace the above work with a system has become apparent. In a system that substitutes the work of a skilled operator, it is required to find a practical constraint satisfaction solution within a practical time as much as a plan formulated by the operator.

  Until now, a technique for facilitating the solution of a practical constraint satisfaction solution has been proposed. For example, in Patent Document 1, each time a new request such as a domain change of a decision variable is added by a user, the frequency is the frequency at which the same solution is adopted compared to the solution adopted in past problem solving cases. A technique is described in which an evaluation value of a solution candidate is obtained based on this, and a solution having the highest evaluation value among the fixed constraints and additional requirements is output.

  Non-Patent Document 1 discloses a technique called constraint programming as one of programming paradigms for efficiently performing a tree search.

JP 2003-99259 A

Marc Vilain, Henry Kautz, Constraint Propagation Algorithms for Temporal Reasoning, Aaai, 1986, pp377-382

  The technique described in Patent Literature 1 can output an appropriate solution by comparing the solution inputted in the past problem solving case with the request regarding the change of the domain of the decision variable input by the user. Here, the domain means a range of values that the decision variable can take. Certainly, the technique described in Patent Document 1 is effective because a desired solution is output based on past cases when the full search is completed due to a small-scale constraint satisfaction problem. However, in a large-scale constraint satisfaction problem with a large number of constraints and decision variables, it is difficult to search for a set of constraint satisfaction solutions depending on the problem setting situation. When performing a tree search with decision variables as nodes and decision variable values as edges in a large-scale constraint satisfaction problem, it is impossible to perform a full search within a practical time, and it is possible to search within a practical time. Appropriate search rules need to be set not only according to the domain change of the decision variable but also according to the change in the constraint expression so that the solution can be obtained within the number of search steps.

  Further, in constraint programming as described in Non-Patent Document 1, the influence that a domain of a certain decision variable reduces the domain of another decision variable via a constraint expression is specified by an operation called constraint propagation. By constraining propagation, the influence of domains of decision variables via the constraint equation is taken into account, and unnecessary search ranges are cut early, thereby efficiently narrowing search areas. However, even in solution search in constraint programming, efficiency in the depth direction of the search tree has been achieved, but efficiency in the width direction has been achieved, such as which branch is searched preferentially among the branches of the search tree. Absent. Therefore, also in constraint programming, it is necessary to perform a dynamic search in the width direction so that a constraint satisfaction solution can be found within a practical time according to the change of the constraint equation.

  It is an object of the present invention to provide information on constraints that cause determination of a decision variable solution and other solutions that cause constraint propagation of the solution in a large-scale constraint satisfaction problem in which a solution search is performed by constraint programming. It is an object of the present invention to provide a solution search processing device that facilitates the analysis and debugging of the process of finding the constraint satisfaction solution by explicitly outputting.

  The configuration of the solution search processing device of the present invention is preferably a solution search processing device that executes a solution processing of a constraint satisfaction problem, and receives a past output solution as an input, and determines a decision variable at each search step of the solution derivation process. Based on the results calculated by the constraint propagation status extraction unit by search step that calculates selectable domains that change when a value is selected, the constraint propagation execution unit that executes constraint propagation, and the constraint propagation status extraction unit by search step Then, the domain of the decision variable before value selection at each step is input, the prediction model is learned using the value selected at each step as teacher data, and the domain is updated according to the value selected by the constraint propagation execution unit. A prediction model learning unit that repeatedly performs learning, and a prediction model learned by the prediction model learning unit using the domain of selectable decision variables before value selection at each search step as input. A value predicting unit that predicts the value of the decision variable to be selected, updates the domain according to the value selected by the constraint propagation execution unit, and repeatedly executes the search processing for the solution of the decision variable is there.

  Further, in the configuration of the solution search processing device, based on the prediction model learned by the prediction model learning unit, the state of the decision variable to be the cause explanation target is input, and the value of the specified decision variable is predicted A cause explanation section for outputting information on selectable domains causing the cause is provided.

  According to the present invention, in a large-scale constraint satisfaction problem in which a solution search is performed by constraint programming, information on the constraint causing the determination of the solution of the decision variable and other solutions causing the constraint propagation of the solution By explicitly outputting, it is possible to provide a solution search processing device that facilitates the analysis and debugging of the solution process of the constraint satisfaction solution, thereby facilitating the solution.

2 is a hardware / software configuration diagram of a solution search processing device according to Embodiment 1. FIG. It is a figure which shows the whole process outline | summary of the solution search processing apparatus which concerns on Embodiment 1. FIG. It is a flowchart which shows the process of the constraint propagation condition extraction part 120 according to search step. It is a figure which shows an example of the past search solution. It is a figure which shows the search information according to step. It is a matrix showing the value selection situation of each decision variable in search step 2. It is a matrix showing the selectable domain of each decision variable in search step 2. It is a figure which shows the example of the teacher data of a prediction model learning part. It is a flowchart which shows the process of a prediction model learning part. It is a figure explaining the concept of a neural network. It is a flowchart which shows the detailed process of the value estimation part 123 and the constraint propagation execution part 122. It is a figure which shows the example of the matrix showing the value selection condition input as a prediction model. It is a figure which shows the example of the matrix showing the domain condition which can be selected input as a prediction model. It is a figure which shows the example of the matrix showing the decision variable output from a prediction model 5 is a flowchart illustrating detailed processing of a cause explanation unit 124 according to the first embodiment. It is a figure which shows the example of the matrix showing the decision variable output from a prediction model. It is a figure showing value selection situation _{Sk made} into the object of cause explanation. FIG. 18 is a diagram illustrating selectable domain situations _Dk that are output with the matrices of FIGS. 16 and 17 as inputs of the cause explanation unit 124. It is a figure which shows the display of the domain which should be selectable in order to select the value of the decision variable used as the object of cause explanation. FIG. 5 is a hardware / software configuration diagram of a solution search processing device according to a second embodiment. It is a figure which shows the solution search processing apparatus which concerns on Embodiment 2, and the whole outline | summary of a process. 5 is a flowchart showing detailed processing of a constraint propagation execution unit 122. It is a figure which shows the example of the constraint propagation execution result. 10 is a flowchart illustrating detailed processing of a cause explanation unit 124 according to the second embodiment. It is a figure which shows the example of the output screen of a cause description part (the 1). It is a figure which shows the example of the output screen of a cause description part (the 2). It is a figure which shows the example of the output screen of a cause description part (the 3). It is a figure which shows the example of an output of the cause estimation result in railroad operation (the 1). It is a figure which shows the example of an output of the cause estimation result in railroad operation (the 2).

  Hereinafter, each embodiment according to the present invention will be described with reference to FIGS.

Embodiment 1
Hereinafter, Embodiment 1 of the present invention will be described with reference to FIGS.

First, the hardware / software configuration of the solution search processing apparatus according to the first embodiment will be described with reference to FIG.
The solution search processing device is a device for automatically reallocating vehicles and crew members and resource allocation planning in a railway. As shown in FIG. 1, a display unit 101, an input unit 102, a CPU 103, a communication unit 104, This is realized by a general information processing apparatus including the storage unit 107 and the memory 105. The information processing device used as the hardware of the solution search processing device may be a desktop computer, a laptop computer, a tablet, or a server device. Further, the information processing apparatus of the solution search processing apparatus can communicate with other information processing apparatuses via the network 100.

  The storage unit 107 stores past search information 110, step-by-step search information 111, and current search information 112. The past search information 110 is information including past solutions, constraint equations, and initial states of decision variable domains. The step-specific search information 111 is information indicating a relationship between a selectable domain for each decision variable in each solution search and a value of the decision variable selected for solution derivation at that step. The current search information 112 is information composed of the constraint equation and the initial state of the domain of the decision variable, and is the original data to be solved.

  The memory 105 stores a program 106 for executing each function of the solution search processing device, and the function is realized by being executed by the CPU 103. By executing the program 106, the solution search processing device performs a search step-specific constraint propagation status extraction unit 120, a prediction model learning unit 121, a constraint propagation execution unit 122, a value prediction unit 123, and a cause explanation unit 124. Perform the function.

  Next, an overall outline of the processing of the solution search processing device will be described with reference to FIG.

FIG. 2 is a diagram illustrating an overall outline of processing performed by the solution search processing apparatus according to the first embodiment.
In the solution search processing device, first, the search information 110 for each search step receives the past search information 110, and the value of the decision variable selected for each search step and the selectable domain that changes depending on the selection of the decision variable. And is stored in the step-by-step search information 111. Here, the decision variable is a variable whose value is to be determined as a target of the problem. A domain is a range (definition area) of values that a decision variable can take.

  Next, the predictive model learning unit 121 learns a predictive model of the neural network by using teacher data having the selectable domain in the step-by-step search information 111 as an input and outputting the value of the selected decision variable as an output.

  The constraint propagation execution unit 122 calculates the change of selectable domains of other decision variables that are reduced through the constraint each time a value of the decision variable is selected in each step by constraint propagation. Update selectable domain information. The updated domain information is fed back to the prediction model learning unit 121. As described above, the constraint propagation is an operation for calculating an event in which the domain changes when the value of a certain decision variable is determined and the domain of another decision variable is changed via a constraint equation.

  Next, based on the learned model, the value predicting unit 123 predicts and outputs the value of the decision variable to be selected with the domain that can be selected at each step of the current search as an input. After that, as in the process at the time of learning, the constraint propagation execution unit 122 updates the information of the selectable domain after selecting the value of the decision variable, and the information of the value of the selected decision variable and the updated value after selection Information on selectable domains is fed back to the value prediction unit 123.

  The cause explanation unit 124 receives the neural network prediction model learned by the prediction model learning unit 121, and the value prediction unit estimates the value of the selected decision variable in order to estimate a selectable domain that affects the value prediction. A selectable domain that influences the selection of the value of the decision variable is derived by calculating a weight vector of the selectable domain that is generated when the set value is calculated backward in the network output unit.

  Next, detailed processing of the solution search processing device according to the first embodiment will be described with reference to FIGS. 3 to 19.

  In the following, details of the processing of the solution search processing device of the present embodiment will be described by taking a daily resource allocation plan as an example. The daily resource allocation plan shall be set as follows.

When resources A, B, C, and D exist, the weight of each resource is set to a, b, c, and d. Indicates whether to allocate resources in area 1 for resources A, B, C, and D when 1 is set for resources A, B, C, and D in area 1 and 0 is not set. The decision variable y _1h (h = 1, 2, 3, 4) is as follows.
y ₁₁ ∈ {0,1}
y ₁₂ ∈ {0,1}
y ₁₃ ∈ {0,1}
y ₁₄ ∈ {0,1}
At this time, as a typical example of the constraint, it is assumed that the capacity constraint regarding the capacity limit z ₁ in the area 1 is determined as follows.
ay ₁₁ + by ₁₂ + cy ₁₃ + dy ₁₄ <z ₁
The other areas 2, 3, and 4 are similarly managed by decision variables y _1h , y _2h , y _3h , and y _4h that indicate whether or not resources are to be allocated.

Further, a decision variable x _h (h = 1, 2, 3, 4) indicating in which area the resources A, B, C, and D are arranged is set, and the area number is a domain as follows.
x ₁ ∈ {1, 2, 3, 4}
x ₂ ∈ {1, 2, 3, 4}
x ₃ ∈ {1, 2, 3, 4}
x ₄ ∈ {1, 2, 3, 4}
For the decision variables y _1h and x _h ,
y _1h = 1
Then x _h = l
This relationship shall be established.

  Hereinafter, detailed processing of each unit will be described using this model.

First, the details of the processing of the search step-specific constraint propagation status extraction unit 120 and the processing of the constraint propagation execution unit 122 will be described with reference to FIGS.
The search information 111 by step is composed of the value selection status of each decision variable at the search step k and selectable domains, and is defined by the following matrix.
S _k : Matrix representing value selection status of each decision variable at search step k D _k : Matrix representing selectable domain of each decision variable at search step k Matrix S _k and D _k are rows whose decision variable x in _h, the column indicates the domain of the decision variables x _h. The initial value of each element in the search step k = 0 of S _k is 0.

For S _k , x _h = l in search step k
It shall select one in the column of the row of domains l decision variable x _h which is a.

For D _k , the initial value of each element at the search step k = 0 is set to 1 in the domain l of the decision variable x _h that can be selected in the initial state of the decision variable, and 0 that is not selectable. It is what. For the search step k ≠ 0, the column of the domain l in the row of the decision variable x _h that has become selectable is updated to 1 due to constraint propagation from other decision variables in the state of S _k , and becomes unselectable. Update the value to 0.

Examples of S _k and D _{k in} the search step 2 are as shown in FIGS. 6 and 7, respectively.

FIG. 4 shows an example of a past decision variable x _h (h = 1, 2, 3, 4). Then, (x ₁ , x ₂ ) = (2, 2) selected from (x ₁ , x ₂ , x ₃ , x ₄ ) = ( ₂ , ₂ , ₄ , ₃ ) shown in FIG. The decision variable value selection situation in the situation is indicated by S ₂ shown in FIG. 6, and the domain that can be selected in the search step k = 2 by constraint propagation is indicated by D ₂ shown in FIG.

Based on the above, the process shown in FIG. 3 will be described. First, the search step-specific constraint propagation status extraction unit 120 acquires past search information 110 by processing, and initializes S _k and D _k (S130). The past search information 110 is information including past solutions, constraint equations, and initial states of decision variable domains. In this initialization, S _k is initialized to a zero matrix, but D _k reflects the initial state of the domain of the decision variable (that is, the domain in which each decision variable can be selected in the initial state).

Next, one value of the decision variable is selected from the obtained solutions, and S _k is updated (S131). Next, based on the updated state of S _k , constraint propagation is performed by the constraint propagation execution unit 122 to update D _k (S 132). Thereafter, it is determined whether the processing of S131 and S132 has been performed up to the last decision variable (S133). If there is a decision variable that has not been implemented (S133: NO), the process proceeds to the next decision variable, and S131, When the process of S132 is repeated and the processes of S131 and S132 are ended up to the final decision variable (S133: YES), as shown in FIG. 5, each step number 141 corresponds to the value selection situation 142. S _k to be performed and D _k corresponding to the selectable domain 143 can be acquired.

  Next, detailed processing of the prediction model learning unit 121 will be described with reference to FIGS.

First, the prediction model learning unit 121 uses the value selection situation S _k and the selectable domain situation D _k created by the constraint propagation situation extraction unit 120 by search step as teacher data for input of prediction model learning from the search information 111 by step. Read (S170). Further, in correspondence to the _{D k-1} of _{S k-1} and selectable domain 162 value selection status 161, the value of the decision variable selected in _{S k,} and extracted as the value selection result 163, the predictive model learning Set as output teacher data. Then, the prediction model is learned by machine learning based on the set teacher data (S171). As an example of the machine learning model, a convolutional neural network that can handle the above data is used. The learned prediction model is output to the value prediction unit 123 and the cause explanation unit 124.

  Here, the convolutional neural network is a neural network having a plurality of convolutional layers (filter units) as intermediate layers. In the filter unit, a filter coefficient (weight vector) is set. The convolution layer performs filtering on the input data. With the above processing, the convolutional neural network inputs two-dimensional data such as image data, performs filtering processing based on the filter coefficient by the intermediate layer, and outputs the identification determination result, the recognition result, and the like by the output layer.

In the neural network according to the present embodiment, as shown in FIG. 10, the value selection status S _k at each node, the selectable domain status D _k , and V _k output as a decision variable are used as teacher data. , Learns the weight at the node. Here, when the matrix representing the weight of S _k is W _k and the matrix representing the weight of D _k is W ′ _k , the following equation is established.
_{V k = S k W k +} D k W 'k
Next, detailed processing of the value prediction unit 123 and the constraint propagation execution unit 122 will be described with reference to FIG.

First, the value predicting unit 123 acquires the current search information 112 and initializes S _k and D _k (S118). Note that the current search information 112 is information including the constraint equation and the initial state of the domain of the decision variable. As for this initialization, S _k is initialized as a zero matrix, and D _k is assumed to reflect the initial state of the domain of the decision variable. Next, the value of the decision variable to be selected is predicted by the weight indicated by the prediction model created by the prediction model learning unit 121 using S _k and D _k as inputs (S181).

Next, the value of the decision variable predicted in S181 is selected, and S _{k + 1} is updated (S182). Next, based on the updated S _{k + 1} , the constraint propagation execution unit 122 executes constraint propagation and updates D _{k + 1} (S183). Next, it is determined whether or not the value has been set up to the last decision variable (S184), and when the value has not been set up to the last decision variable (S184: NO), the process proceeds to the next decision variable. (S185) Hereinafter, S181 to S183 are repeated.

  Next, an example of the input / output result of the process of S181 at the search step k = 1 will be described with reference to FIGS.

Here, when the prediction using the learned prediction model, D _k of the input of the predictive model _12, with S _k in FIG. 13, the output is V _k in FIG. V _k is a matrix serving as an output of the prediction model indicating the value of the decision variable to be selected. When the input of the prediction model is given by D _k in FIG. 12 and S _k in FIG. 13, the matrix V _{k of the} output unit indicating the value of the decision variable to be selected predicted by the learned prediction model is shown in FIG. Thus, like D _k and S _k , the row can be represented by the decision variable and the column can be represented by the domain data table. When a decision variable and its value are selected in descending order of the values of the matrix elements in V _k and a backtracking or the like occurs in the search process, it is necessary to select another decision variable value. The next highest element value of the matrix is selected. In the example shown in FIG. 14, in the search step k = 2, of the value of _{V k,} highest value, row _{x 2,} since the value of the element in 0.7 column 1, as the value of _{x 2,} Domain 1 is preferentially selected.

  Next, detailed processing of the cause explanation unit 124 will be described with reference to FIGS. 15 to 19.

The cause explanation unit 124 obtains an output solution, selects a value of a decision variable to be a cause explanation target for the obtained output solution, and sets a matrix V _k representing the decision variable as an output of the prediction model (S190). ).

Then, the value selection status at the time of searching the value of the selected decision variable in the processing of S190 obtained from the S _k, is set as the input of the predictive model (S191).

Next, in the processing of S192, the value of the matrix V _k representing the decision variable is calculated backward to calculate the value of the selectable domain situation D _k . Finally, in the process of S193, the value of the calculated selectable domain situation _Dk is compared, and a column of elements having a high value of _Dk is extracted as a selectable domain related to the value selection. Output as the cause.

Hereinafter, input / output examples of the cause explanation unit 124 will be described with reference to FIGS. 16 to 19. In the examples of FIGS. 16 and 17, when the cause explanation unit 124 selects 2 for x ₁ , it means that explanation of the cause with 1 selected for x ₂ is performed. The example of FIG. 18 shows an example of a calculation result when the matrix of FIGS. 16 and 17 is used as the input of the cause explanation unit 124, and a selectable domain situation _Dk is obtained by back-calculating the prediction model. In the case of a convolutional neural network, as with the decoding operation used in the auto encoder (GE Hinton, RR Salakhutdinov, Reducing the Dimensionality of Data with Neural Networks, Science, Vol313, 2006, pp504-506), By using the transposed matrix, the selectable domain situation D _k can be calculated back. The value of each element of the selectable domain situation _Dk that is greater than 0 is a domain that should be selectable in order to predict the value of the decision variable that is the subject of the cause explanation. is there. This domain is output as the cause of selection of the value of the decision variable that is the subject of cause explanation.

FIG. 19 shows a domain that should be selectable in order to select the value of the decision variable whose cause is described in the part that is filled in the output screen example. When the x ₁ 2 is selected, for 1 is selected x _2, according to the results of FIG. 18, it is necessary for x ₄ 1 and 3 are selectable, x ₄ It can be seen that the selection of values 1 and 3 is the cause of value selection.

[Embodiment 2]
Hereinafter, Embodiment 2 of the present invention will be described with reference to FIGS.

  In the first embodiment, the cause explanation unit 124 extracts and presents a selectable domain that causes the selection of the value of a specific decision variable. However, in the solution search processing device of this embodiment, an output example of the cause explanation unit In addition to the selectable domains, the constraints and decision variables that have been changed by constraint propagation for the selectable domains and the value selection status thereof are shown.

  First, the hardware / software configuration of the solution search processing apparatus according to the second embodiment and the overall outline of the processing will be described with reference to FIGS. 20 and 21. FIG.

  In the solution search processing device according to the second embodiment, as shown in FIG. 20, in addition to the information stored in the storage unit 107 of the solution search processing device shown in FIG. Stored.

  As shown in FIG. 21, the constraint propagation execution result 113 stores the constraint propagation execution result received from the constraint propagation execution unit 122 and outputs the result to the cause explanation unit 124.

  Next, detailed processing of the solution search processing device according to the second embodiment will be described with reference to FIGS. 22 to 27.

First, details of the detailed processing of the constraint propagation execution unit 122 will be described with reference to FIGS. 22 and 23.
The constraint propagation execution unit 122 first receives the value of the decision variable to be selected from the value prediction unit 123, and executes constraint propagation (S210). Next, the constraint propagation execution unit 122 sets the value of the decision variable selected for each search step as the constraint propagation execution result 113 in the column of the selection status 201 shown in FIG. In the column, the changed constraint is stored in the column of constraint 202, and the decision variable whose selectable domain is changed is stored in the column of decision variable 204 whose selectable domain is changed (S211).

For example, in the example of the constraint propagation execution result 113 shown in FIG. 23, regarding the value selection of the decision variable of x ₁ = 2 in the column of the value selection status 201, D ₁ is added to the column of the corresponding selectable domain 203. X ₂ and x _{4 are} stored in the column of the decision variable 204 that has been stored and the selectable domain has changed. Further, the constraint A is stored in the column of the constraint 202 that caused the constraint propagation corresponding to the decision variable 204 whose domain that can be selected has changed. In the daily resource allocation planning problem, the constraint A stored in the column of the constraint 202 means a constraint related to capacity limitation.

  Note that the correspondence between the value selection status 201 and the constraint 202 can be a one-to-many correspondence, and the correspondence between the constraint 202 and a decision variable whose selectable domain has changed can be a one-to-many correspondence. That is, even if one value is selected in a certain step, there may be a plurality of decision variables whose associated constraints and selectable domains have changed.

  Next, detailed processing of the cause explanation unit 124 of the second embodiment will be described with reference to FIG.

In the description of the present embodiment, differences from FIG. 15 of the first embodiment will be mainly described.
After the process of S192, the cause explanation unit 124 extracts a decision variable corresponding to the selectable domain that causes the value selection from the value of _{Dk in} the input unit of the calculated prediction model (S194). Next, the cause explanation unit 124 extracts a search step in which the selectable domain of the extracted decision variable has changed (S195), extracts the decision variable 204 in which the selectable domain has changed according to the constraint propagation execution result 113, By referring to the constraint described in the constraint 202 column corresponding to the decision variable in which the extracted selectable domain has changed and the value selection status described in the value selection status 201, the reason why the selectable domain has changed is as follows. It outputs (S196).

  Next, a specific example when the detailed processing of the cause explanation unit 124 of the second embodiment is applied to the example of the constraint propagation execution result 113 shown in FIG. 23 will be described with reference to FIGS.

For example, suppose that it is estimated that 1 and 3 were selectable domains for x ₄ as a cause of predicting x ₃ = 4 as shown in FIG. In this case, the decision variable corresponding to a selectable domain that caused is x _4. Here, the constraint propagation in which the selectable domain of x ₄ has changed from the constraint propagation execution result shown in FIG. 23 is before x ₃ = 4, and is due to constraint A when x ₁ = 2 is selected. It can be estimated that.

25 to 27 show examples of output to the screen of the cause estimation result at that time (display unit 101 of the solution search processing device in FIG. 1). In the example of FIG. 25, when the decision variable to be the cause of the cause estimation and its value is x ₃ = 4, the cause constraint is the constraint A described in the column of the constraint 202 in FIG. X ₁ = 2 is displayed in a table format.

  In the example of FIG. 26, the information displayed in FIG. 25 is represented by a tree notation in which selection of a decision variable is represented by a node, which corresponds to selection of a node that is a cause estimation target and a decision variable that is a cause. The nodes to be printed are shown in black. For the node corresponding to the selection of the causal decision variable, the name of the constraint that propagated the constraint that affected the domain of the selectable decision variable is also described. In addition, when the scale of a tree becomes large, the notation of unrelated nodes may be omitted.

  Further, as an output example of the cause estimation result, as shown in FIG. 27, a logic tree focusing only on the relationship between the cause estimation target and the cause may be displayed. In this logic tree, the root of the arrow is the selection of the decision variable causing the cause, and the tip of the arrow indicates the cause estimation target.

[Other Embodiments]
As mentioned above, although each embodiment of this invention was described concretely, this invention is not limited to this, In the range which does not deviate from the summary, various corrections are possible.

  In the second embodiment, as an output example of the cause estimation result, an example is shown in which a search tree as shown in FIG. 25 and a logic tree focusing only on the relationship between the cause estimation object and the cause as shown in FIG. 27 are displayed. Depending on the work screen of the resource allocation task such as the railway operation management task and the resource allocation planning task, the cause variable and the constraint display may be displayed as the resource and resource operation constraint of each task.

  Here, an output example of the cause estimation result in the railway operation will be described with reference to FIGS. 28 and 29.

  In railway terms in railway operation, “vehicle” refers to the hardware of a railway vehicle, and “train” refers to traveling on the diagram (departing from one station at what time and what time to another station) It is a concept that includes (arrival in minutes). Here, consider a solution search processing problem in which a train is a decision variable and a vehicle is a domain. The restrictions are station location and operation time. As an output example of the cause estimation result in the railway operation at this time, as shown in FIG. 28, the cause of the table format and the causal relationship of the result may be shown in comparison, or as shown in FIG. It may be displayed in the form of

In the above embodiment, a convolutional neural network is used as a prediction model for machine learning. However, a decision variable value selection situation S _k and a selectable domain D _k can be set as inputs, and decision variable candidates to be selected are selected. Other models, such as a naive Bayes classifier, may be used as long as they predict.

Further, in the above embodiment, the decision variable value selection status S _k and the selectable domain D _k are assumed as the input of the prediction model for performing machine learning. However, the selectable domain D _{0 in the} initial state is also available. Various variations are possible for the form of selectable domains, such as introducing.

In the above embodiment, for the selectable domain D _k , in order to reflect the number of branches that may be followed in the course of the tree search, if the search step k ≠ 0, other decision variables in the state of S _k Although the domain l column in the row of the decision variable x _h that can be selected is updated to 1 and the one that cannot be selected is updated to 0 by the constraint propagation from the above, it is not necessary to limit to this example. For example, the domain l of the row of the decision variable x _h that can be selected by the constraint propagation from the decision variable including the self in the state of S _k by removing the restriction of constraint propagation from another decision variable It may be possible to update the column of 1 to 1 and to update the value that has become unselectable to 0, and even if the value of the searched decision variable is selectable, it is expressed by a value such as 0 to -1. Also good.

  In the above embodiment, the cause explanation unit 124 is used when the solution is calculated. However, even when the solution is not calculated and the solution search progresses halfway, the cause explanation unit 124 is used as the debugger. The cause of the value of the decision variable selected during the solution search may be explained.

[Summary]
As is clear from the above embodiments, according to the present invention, in the large-scale constraint satisfaction problem in which solution search is performed by constraint programming, the influence of not only the decision variable but also the change of the constraint equation is grasped. Explicitly indicate the constraints that cause the decision variable and other decision variables so that the decision variable value to be selected dynamically can be changed to facilitate the solution of the constraint satisfaction solution desired in practice. Accordingly, it is possible to provide a tool for explicitly displaying information for facilitating problem solving to a problem solver by giving means for debugging and problem solving suggestions.

DESCRIPTION OF SYMBOLS 100 ... Network 101 ... Display part 102 ... Input part 103 ... CPU
104 ... Communication unit 105 ... Memory 106 ... Program 107 ... Storage unit 110 ... Past search information 111 ... Step-specific search information 112 ... Current search information 113 ... Constraint propagation execution result 120 ... Search step-specific constraint propagation status extraction unit 121 ... Prediction model learning unit 122 ... constraint propagation execution unit 123 ... value prediction unit 124 ... cause explanation unit

Claims (8)

A solution search processing device that executes a solution process for a constraint satisfaction problem,
Constraint propagation state extraction unit for each search step that takes a past output solution as an input and calculates a selectable domain that changes when selecting the value of the decision variable in each search step of the solution derivation process;
Based on the results calculated by the constraint propagation execution unit that executes constraint propagation and the constraint propagation status extraction unit by search step, the value of the decision variable before the value selection at each step is input, and the value selected at each step A prediction model learning unit that learns the prediction model as teacher data, updates the domain according to the value selected by the constraint propagation execution unit, and repeatedly executes the learning,
The domain of selectable decision variables before value selection in each search step is used as an input, the value of the decision variable to be selected in the prediction model learned in the prediction model learning unit is predicted, and the value selected by the constraint propagation execution unit And a value prediction unit that updates the domain in response and repeatedly executes the search process for the solution of the decision variable.   Furthermore, based on the prediction model learned by the prediction model learning unit, the state of the decision variable that is the target of the cause explanation is input, and information on selectable domains that cause the value of the specified decision variable is predicted. The solution search processing apparatus according to claim 1, further comprising a cause explanation unit for outputting. The predictive model learning unit and the value predicting unit perform machine learning based on a machine learning model that predicts a candidate of a decision variable to be selected using a value selection situation of a decision variable and a selectable domain as an input. The solution search processing device according to claim 1. 4. The solution search processing device according to claim 3, wherein the machine learning model is a convolutional neural network.   The cause explanation unit presents values and constraints of other decision variables that cause the value of the specific decision variable to be predicted by the value prediction unit for the value of the decision variable selected during the calculated solution or solution search The solution search processing device according to claim 1, wherein:   6. The value of the decision variable specified by the value prediction unit, the value of the other decision variable that causes the prediction, and the constraint are displayed on a tree in which selection of the decision variable is expressed by a node. The solution search processing device described.   The value of the decision variable identified by the value prediction unit, the value and constraint of the other decision variable that causes the prediction, and the cause that predicted the value of the decision variable and the result are displayed on the logic tree. The solution search processing device according to claim 5, wherein:   6. The solution search processing device according to claim 5, wherein a cause and a result are displayed on a diagram with a vehicle as a decision variable and a train as a domain.

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