JP7376405B2 - Optimization processing device, optimization processing method, and optimization processing program - Google Patents

Description

The present invention relates to an optimization processing device, an optimization processing method, and an optimization processing program that search for an optimal solution to a combinatorial optimization problem.

Conventionally, mathematical optimization techniques have been applied to combinatorial optimization problems such as production planning and delivery planning. For example, Japanese Patent Application Laid-open No. 2017-120561 (Patent Document 1) describes a “logistics planning device for formulating a logistics plan from receiving to delivery of goods in a storage area, A logistics model construction means for constructing a logistics model that is a mathematical model obtained by modeling transport equipment that handles transported goods in a transported goods storage area, transported goods, and logistics planning policy, and a logistics model constructed by the logistics model construction means. The present invention is characterized by comprising: a logistics planning means for drawing up a logistics plan using a mathematical optimization method based on a logistics model; and an output means for outputting the logistics plan drawn up by the logistics planning means. be.

Japanese Patent Application Publication No. 2017-120561

The conventional technology represented by Patent Document 1 has a problem in that modeling is performed manually, which increases costs. It is also assumed that the constraints on optimizing the target problem are possessed as business knowledge or tacit knowledge. Therefore, it cannot be applied to unknown problems that do not have a proven track record.

Therefore, in searching for an optimal solution to a combinatorial optimization problem, the present invention aims to autonomously construct a model and apply techniques applicable to unknown problems.

In order to achieve the above object, one of the typical optimization processing devices, optimization processing methods, and optimization processing programs of the present invention generates a prediction model that predicts the evaluation value of a combination from learning data, and When searching for an optimal solution using a model, the search range is limited based on the distribution of learning data.

According to the present invention, when searching for an optimal solution to a combinatorial optimization problem, a model can be autonomously constructed and applied to an unknown problem.
Problems, configurations, and effects other than those described above will be made clear by the following description of the embodiments.

FIG. 3 is a conceptual diagram of processing by the optimization processing device according to the embodiment. An explanatory diagram of the prediction model and the distribution of training data. An explanatory diagram of a specific example of a combinatorial optimization problem. FIG. 2 is a configuration diagram of an optimization processing device. 5 is a flowchart showing the processing procedure of the optimization processing device. FIG. 3 is an explanatory diagram of the processing procedure of the optimization processing device. A specific example of the learning result display screen. A specific example of the optimal solution search screen. FIG. 7 is an explanatory diagram of a modification of the optimization processing device.

Examples will be described below with reference to the drawings.

FIG. 1 is a conceptual diagram of processing by an optimization processing device according to an embodiment. The optimization processing device according to this embodiment first generates a prediction model from learning data. The learning data is a set of past problems and solutions. A specific example will be described later, but for example, if the problem is the order of operations in a plurality of steps, the solution will be the order (combination) of operations actually performed. For example, deep learning is used to generate the predictive model. A prediction model is a function that calculates a predicted evaluation value from combinations of solution candidates. The predicted evaluation value is an index for relatively evaluating combinations, and is used to compare combinations and search for a more appropriate solution.

When given a problem, the optimization processing device performs optimization processing using the generated prediction model and outputs an optimal solution. Specifically, predicted evaluation values are obtained for combinations as candidate solutions to a given problem, and an optimal solution is obtained by searching for a combination with a higher predicted evaluation value.

Here, the optimization processing device according to this embodiment limits the search range for the optimal solution based on the distribution of learning data. This is because a predictive model generated from learning data can be expected to have high accuracy within the distribution of the learning data, but its accuracy decreases when it deviates from the distribution of the learning data.

FIG. 2 is an explanatory diagram of the prediction model and the distribution of learning data. In FIG. 2, the prediction model is displayed with the z-axis as the prediction evaluation value. Therefore, in the optimization process, the combination that maximizes the value of z (the combination of x and y in FIG. 2) is searched as the optimal solution.

This search is limited to the distribution range of learning data and its vicinity. In FIG. 2, on the curved surface of the prediction model, a range corresponding to the distribution range of the learning data is indicated by surrounding it with a white line. The optimization process can be said to be a process of searching for the maximum value by comparing the values of z in the range surrounded by this white line and its vicinity.

Here, the reason for including the vicinity of the distribution range of learning data in the search range will be explained. Specifically, the search range is larger than the distribution range of the learning data and includes the distribution range of the learning data. Essentially, if training data with a sufficient number and distribution is available, it is possible to generate highly accurate predictive models over a wide range. However, if the number of possible solution combinations is enormous, it becomes impractical to obtain training data with a sufficient number and distribution. In other words, if the solution space is vast, the training data must be a sparse and biased group.

As already explained, searching within the distribution range of the learning data is effective for obtaining highly accurate predicted evaluation values. On the other hand, making the search range larger than the distribution range of the learning data indicates that there is a possibility of obtaining an optimal solution that deviates from the distribution range of the learning data. By performing work according to an optimal solution that deviates from the distribution range of learning data and using the work results as new learning data, it is possible to expand the distribution range of learning data. That is, by making the search range larger than the distribution range of learning data, it is possible to expand the distribution range of learning data and mature the prediction model.

FIG. 3 is an explanatory diagram of a specific example of a combinatorial optimization problem. FIG. 3 shows a work order optimization problem that targets multiple processes in a warehouse. Specifically, it targets the work of taking ordered products out of the warehouse, labeling them, sorting them, packaging them, and shipping them.

For example, if the number of orders (the number of orders) is 1000 per day, the number of workers is 500, and the 8-hour working time is divided into hourly time periods, the number of combinations of work orders is , becomes "1000!×500!×8!". As described above, there are a huge number of combinations of work orders, and the optimal work order conditions differ for each process. Specifically, in the case of product labeling, products with the same type of label should be processed in succession, in the case of sorting using automatic transport shelves, products that are likely to be ordered at the same time should be processed in succession, and in the case of packaging, orders with the same packaging method should be processed The conditions for shipping are that orders with close shipping destinations must be consecutive.

If we were to newly consider optimizing such tasks, it would be difficult to perform modeling manually using past information, business knowledge, and tacit knowledge. Furthermore, even if past information is accumulated, it cannot be expected that the same tasks will be performed because there are a huge number of combinations.

The optimization processing device according to the present embodiment can autonomously generate a predictive model for such a problem by machine learning using learning data. As the learning data, for example, the order (combination) of tasks performed in the past is used. Although the learning data is sparse and biased in the solution space, a valid solution can be obtained by limiting the search range based on the distribution range of the learning data. Further, by including the vicinity of the distribution range of the learning data in the search range and adding new work results based on the solution to the learning data, the distribution range of the learning data can be expanded.

FIG. 4 is a configuration diagram of the optimization processing device. As shown in FIG. 4, the optimization processing device 10 includes a CPU (Central Processing Unit) 11, a memory 12, a display section 13, an input section 14, and a storage section 15. The CPU 11 operates as various functional units by loading programs read from an auxiliary storage device (for example, the storage unit 15) onto the memory 12, which is a main storage device, and executing them. FIG. 4 shows a state in which programs operating as the predictive model generation section 21, the distance calculation section 22, the evaluation value prediction section 23, and the search section 24 are expanded in the memory 12.

The display section 13 is an output device such as a liquid crystal panel display, and the input section 14 is an input device such as a keyboard or touch panel. The storage unit 15 is a hard disk drive or the like. The storage unit 15 stores various data and programs, and stores learning data 31 and predictive model data 32 as particularly important data for this embodiment. As already explained, the learning data 31 is data used to generate a predictive model. Prediction model data 32 is data that specifies a prediction model.

The predictive model generation unit 21 is a processing unit that performs deep learning using the learning data 31 and generates a predictive model. The predictive model generation unit 21 stores predictive model data 32 that specifies the generated predictive model in the storage unit 15.

The distance calculation unit 22 is a processing unit that calculates the distance from the distribution of the learning data 31 to the solution candidate data.
The evaluation value prediction unit 23 is a processing unit that reads the prediction model data 32 and uses the prediction model specified by the prediction model data 32 to calculate the predicted evaluation value of the solution candidate data.
The search unit 24 is a processing unit that searches for an optimal solution using the predicted evaluation value. The search unit 24 limits the search range based on the distribution of the learning data 31 when searching for an optimal solution.

Here, learning of the predictive model will be explained. When learning a prediction model from the learning data 31, since the learning data 31 is relatively small, it is difficult to accurately predict the actual index. For example, in the example shown in FIG. 3, even if "the number of products that one worker can process in one hour" is predicted as an actual index, the error will be large.

である。このＰ_ｉｊを用いたランキング学習により予測モデルを生成する。 Therefore, the optimization processing device 10 does not directly predict the actual index, but determines the relative magnitude relationship of the actual index. That is, the optimization processing device 10 reduces errors by converting a regression problem into a ranking problem. The predicted evaluation value is an index for finding a combination that gives a better actual index, and corresponds to the actual index. In this embodiment, it is assumed that the larger the predicted evaluation value, the better the value. If this predicted evaluation value is V(x),
here

It is. A predictive model is generated by ranking learning using this P _ij .

ここで

となる。 Next, distance calculation will be explained. First, assuming that the features of the learning data 31 follow a multidimensional Gaussian distribution and estimating the distribution parameters of the learning data 31, the Mahalanobis distance between the features of the specific data and the feature distribution of the learning data 31 is

here

becomes.

λを十分に大きく設定すれば、損失関数は、学習データ分布からのマハラノビス距離がα以下のとき「－Ｖ（ｘ）」となり、それ以外で大きい値を取ることになる。 The optimization processing device 10 determines an optimal solution using the following loss function, with x=(π _θ (t|c), c).

If λ is set sufficiently large, the loss function will be "-V(x)" when the Mahalanobis distance from the training data distribution is less than or equal to α, and will take a large value otherwise.

FIG. 5 is a flowchart showing the processing procedure of the optimization processing device 10. The predictive model generation unit 21 of the optimization processing device 10 first stores the learning data 31 in the storage unit 15 (step S101). The predictive model generation unit 21 generates a predictive model from the learning data 31, and stores predictive model data 32 that specifies the generated predictive model in the storage unit 15 (step S102).

After generating the prediction model, the evaluation value prediction unit 23 determines evaluation target data at a predetermined timing (step S103). The evaluation target data corresponds to one combination as a solution candidate. The evaluation value prediction unit 23 reads the prediction model data 32 and calculates the predicted evaluation value of the evaluation target data using the prediction model specified by the prediction model data 32 (step S104).

The distance calculation unit 22 calculates the Mahalanobis distance from the distribution of the evaluation target data and the learning data 31 (step S105).

The search unit 24 evaluates the loss using a loss function based on the predicted evaluation value and the distance (step S106). After step S106, the search unit 24 determines whether to end the search (step S107). The search is terminated when the optimal solution is identified, or when the search steps (steps S103 to S107) are repeated a predetermined number of times. If the search is not completed (step S107; No), the process moves to step S103, and the next evaluation target data is determined. If the search is finished (step S107), the process moves to step S108, the optimal solution is output, and the process ends.

FIG. 6 is an explanatory diagram of the processing procedure of the optimization processing device 10. In FIG. 6, a predictive model is generated from the learning data and used in the optimization process. In the optimization process, the process of calculating the predicted evaluation value of solution candidate data using a prediction model and the process of calculating the solution candidate data from the predicted evaluation value and distance using an optimization algorithm are repeated to find the optimal solution. ing.

FIG. 7 is a specific example of a learning result display screen. In FIG. 7, a graph is displayed with the x-axis as an actual index (the number of products that one worker can process in one hour) and the y-axis as a predicted evaluation value. It is also possible to display the order of work together with the actual index and predicted evaluation value. in particular,
"Work order: BCA...G
Actual indicator: 55.8
Predicted evaluation value: 933.1”
"Work order: DAE...H
Actual indicator: 55.1
Predicted evaluation value: 905.6”
is displayed.
With this display, the optimization processing device 10 can make the user recognize the combination with the highest predicted evaluation value, the combination with the lowest predicted evaluation value, and the like.

FIG. 8 is a specific example of the optimal solution search screen. FIG. 8 shows how the loss function and distance change with repeated optimization steps. As shown in FIG. 8, the value of the loss function decreases according to the number of optimization steps. This means an improvement in the predicted evaluation value. Similarly, the distance also decreases with the number of optimization steps and approaches the high confidence interval.

Next, a modification of the optimization processing device will be described. FIG. 9 is an explanatory diagram of a modification of the optimization processing device. In FIG. 9, a predictive model generation device 50 and an optimization processing device 60 are connected. The predictive model generation device 50 performs processing to generate a predictive model from learning data.

The optimization processing device 60 stores the prediction model generated by the prediction model generation device 50. Further, the optimization processing device 60 stores distribution data indicating the distribution of learning data as information regarding the learning data.

When given a problem, the optimization processing device 60 refers to the prediction model and distribution data, performs optimization processing within a range limited by the distance from the distribution data, and outputs an optimal solution. Once the work is performed based on this optimal solution, the results of the optimization process and the work results are correlated and accumulated in the work results. If the accumulated work results are provided as additional learning data to the predictive model generation device 50, the predictive model generation device 50 will perform learning again to generate a predictive model with improved accuracy and provide it to the optimization processing device 60. can.

As described above, the optimization processing device according to the present embodiment includes a CPU 11 and a memory 12 that function as a processing unit that performs processing to search for an optimal solution to a combinatorial optimization problem, and a memory 12 that stores information regarding learning data. The storage unit 15 generates a prediction model that predicts the evaluation value of a combination from the learning data, and limits the search range based on the distribution of the learning data when searching for an optimal solution using the prediction model. This allows models to be built autonomously and applied to unknown problems.

Here, it is preferable that the search range is larger than the distribution range of the learning data and includes the distribution range of the learning data. By setting in this way, it is possible to expand the distribution range of learning data and mature the prediction model.

Specifically, the optimization processing device calculates the distance from the distribution of the learning data to the solution candidate data, and sets the range where the distance is less than or equal to the distance threshold as the search range, thereby easily determining the search range. Can be done. Furthermore, an optimal solution can be searched using a loss function based on evaluation values and distances.

Further, by generating a prediction model using ranking learning, the optimization processing device can suppress the influence of errors caused by directly predicting the actual index.
Further, the optimization processing device can improve the accuracy of the prediction model by using the track record of work performed based on the optimal solution as additional learning data.

As a modification, a configuration may be adopted in which the search range is made smaller as learning data is added to approximate the distribution of the learning data (α in the loss function is made smaller). In other words, initially, priority is given to expanding the distribution of learning data by increasing the difference between the search range and the distribution of learning data, and after the distribution range of learning data becomes large enough, the search range is changed to the distribution of learning data. The prediction model can be stabilized by bringing it closer to .

Note that the present invention is not limited to the above-described embodiments, and includes various modifications. For example, the embodiments described above are described in detail to explain the present invention in an easy-to-understand manner, and the present invention is not necessarily limited to having all the configurations described. Furthermore, it is possible not only to delete such a configuration but also to replace or add a configuration.

For example, in the above-mentioned embodiment, the case where the computer operates as the optimization processing device 10 by executing the optimization processing program was explained as an example, but the optimization processing in which various functional units are configured by hardware is explained. It is also possible to implement it as a device.

10, 60: Optimization processing device, 11: CPU, 12: Memory, 13: Display section, 14: Input section, 15: Storage section, 21: Prediction model generation section, 22: Distance calculation section, 23: Evaluation value prediction Section, 24: Search section, 31: Learning data, 32: Prediction model data, 50: Prediction model generation device

Claims (6)

a processing unit that performs processing to search for an optimal solution to a combinatorial optimization problem;
a storage unit that stores information regarding learning data that is a set of past problems and solutions ;
The processing unit includes:
Generate a prediction model that predicts evaluation values of combinations that are candidate solutions by machine learning using the learning data,
When determining the evaluation value for a combination as a candidate solution to a given problem using the prediction model and searching for a combination with a higher evaluation value to find the optimal solution, based on the distribution of the learning data. It limits the search range,
Find the distance from the distribution of the learning data to the solution candidate data, and set the range where the distance is less than or equal to the distance threshold as the search range.
An optimization processing device characterized by: The optimization processing device according to claim 1, wherein the search range is larger than the distribution range of the learning data and includes the distribution range of the learning data. The optimization processing device according to claim 1, wherein the processing unit searches for the optimal solution using a loss function based on the evaluation value and the distance. The optimization processing device according to claim 1, wherein the processing unit generates the prediction model using ranking learning. An optimization processing method for searching for an optimal solution to a combinatorial optimization problem,
The optimization processing device
A predictive model generation step of generating a predictive model that predicts the evaluation value of a combination of solution candidates by machine learning using learning data that is a set of past problems and solutions ;
a search step of determining the evaluation value using the prediction model for a combination as a candidate solution to a given problem , and searching for an optimal solution by searching for a combination with a higher evaluation value;
In the search step, the search range is a range in which the distance from the distribution of the learning data to the solution candidate data is less than or equal to a distance threshold.
An optimization processing method characterized by: An optimization processing program that searches for an optimal solution to a combinatorial optimization problem,
A predictive model generation procedure that generates a predictive model that predicts the evaluation value of a combination of solution candidates by machine learning using learning data that is a set of past problems and solutions ;
causing a computer to execute a search procedure for determining the evaluation value using the prediction model for a combination as a candidate solution to a given problem , and searching for a combination with a higher evaluation value to find an optimal solution ;
In the search procedure, the search range is a range in which the distance from the distribution of the learning data to the solution candidate data is less than or equal to a distance threshold.
An optimization processing program characterized by:

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