JP2015038429A - Route search method, route search device, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a route search method or the like capable of creating an appropriate tentative solution by appropriately selecting a seed customer in an insertion method.SOLUTION: When a tentative solution is created by an insertion method, a customer management unit 3 divides a space into a plurality of regions, and a seed customer selection unit 5 selects each seed customer from the customers existing in each of the divided regions. A tentative solution creation unit 7 creates a tentative solution by inserting another customer into a closed circuit between each selected seed customer and a deposit. Thus, customers existing around a certain point are prevented from being intensively selected as a seed customer, and a tentative solution that does not require many executions of the insertion method can be created.

Description

  The present invention relates to a route search method, a route search device, and a program, and more particularly to a route search method that generates a route that satisfies a constraint condition and visits a plurality of customers.

  Currently, the transportation industry has serious problems such as an increase in transportation fuel due to soaring crude oil and a decrease in the number of workers involved in the transportation industry. These problems are expected to be overcome by calculating the optimum transportation route. This is expected to be solved by optimizing the vehicle routing problem (VRP).

  In order to solve the VRP, the inventors have proposed a combination of the insertion method and the two-opt method for the column generation method (see Non-Patent Document 1). This is because the insertion method generates a number of provisional solutions (which are not optimal, but a reasonably good solution that observes the constraints such as the time window), and after improving the provisional solution by the two-opt method, Is searched for the optimal solution in combination with the sequence generation method. Here, the insertion method is a method of inserting the remaining customers using evaluation values with respect to a closed circuit connecting customers called seed customers (see Non-Patent Document 2).

Shinichiro Kakui, 4 others, “Optimization of delivery / collection route problem to reduce logistics costs”, Proceedings of Fire Country Information Symposium 2013, C-5-2, 2013. Mikio Kubo, “Logistics Engineering”, Asakura Shoten, 2003

  However, in the conventional method, seed customers are randomly selected in the insertion method. Therefore, for example, when a plurality of customers existing around a certain point are selected in a concentrated manner, an accurate provisional solution cannot be obtained.

  Therefore, an object of the present invention is to propose a route search method and the like that can appropriately select a seed customer and generate a more appropriate provisional solution.

  According to a first aspect of the present invention, there is provided a route search method for generating a route that satisfies a constraint condition and circulates a plurality of customers, wherein the customer management means groups the plurality of customers into two or more customer groups. Grouping step, seed customer selecting means as seed customers, seed customer selecting step for selecting one or more customers from each customer group, and provisional solution generating means starting point under the constraint A provisional solution generating step of generating a provisional solution by inserting a customer other than the seed customer with respect to the closed circuit connecting the various customers, and a route in which the route generation means circulates the plurality of customers based on the provisional solution Including a path generation step for generating.

  A second aspect of the present invention is the route search method according to claim 1, wherein the customer management unit changes the grouping of the plurality of customers, and the customer group is divided in the grouping step. A group changing step for changing to a different second customer group, and a seed customer selecting step in which the seed customer selecting means selects one or a plurality of customers from each of the second customer groups as a second type customer, The provisional solution generation means generates a second provisional solution by inserting a customer other than the second type customer that satisfies the constraint condition with respect to the closed circuit connecting the start point and each of the second type customers. A provisional solution generation step, wherein in the route generation step, the route generation means converts the route to the plurality of customers into the provisional solution generation step and the second provisional solution generation step. And it generates, based on the provisional solution and the second tentative solutions have been generated had.

  A third aspect of the present invention is a route search method according to the first or second aspect, wherein each customer corresponds to a waypoint on a space or a plane, and the customer management means in the grouping step Divides the space or the plane into a plurality of regions, and each customer group is a group of customers corresponding to waypoints included in each region. In the route generation step, the route generation The route generated by the means reduces the cost of visiting the plurality of customers.

  According to a fourth aspect of the present invention, there is provided a route search apparatus for generating a route that satisfies a constraint condition and circulates a plurality of customers, the customer management means for grouping the plurality of customers into two or more customer groups; A seed customer selecting means for selecting one or a plurality of customers from each customer group as a seed customer, and a customer other than the seed customer for each cycle connecting the start point and the various customers under the constraint conditions And provisional solution generation means for generating a provisional solution and route generation means for generating a route for visiting the plurality of customers based on the provisional solution.

  A fifth aspect of the present invention is a program for realizing a route search method according to any one of the first to third aspects in a computer.

  The present invention may be regarded as a computer-readable recording medium that regularly records the program according to the fifth aspect.

  According to the present invention, the customers are divided into a plurality of groups, and by selecting seed customers from each group, it is possible to prevent the seed customers from being concentrated and selected, and the provisioning method may be performed less frequently. It becomes possible to create a solution.

  Furthermore, according to the second aspect of the present invention, by changing the group and executing the insertion method again, the seed customer is selected based on a new criterion, and the seed customer is prevented from being intensively selected. It becomes possible.

  Furthermore, according to the third aspect of the present invention, VRP is premised on movement in a plane or space, and is suitable for VRP by grouping customers based on area division in this plane or space. It is possible to obtain a provisional solution.

It is a schematic block diagram of the route search apparatus which is an example of embodiment of this invention. It is a flowchart which shows an example of operation | movement of the route search apparatus 1 of FIG. It is a figure which shows an example of the area | region on the plane set by the customer management part 3 of FIG. It is a figure which shows an example of the evaluation value calculation in an insertion method. It is a figure which shows an example of the process in a column production | generation method. It is FIG. 1 which shows an example of the route obtained by experiment. It is FIG. 2 which shows an example of the route obtained by experiment.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to this embodiment.

  FIG. 1 is a schematic block diagram of a route search apparatus which is an example of an embodiment of the present invention. The route search device 1 includes a customer management unit 3 (an example of “customer management unit” in the claims of the present application), a seed customer selection unit 5 (an example of “seed customer selection unit” in the claims of the present application), and a provisional solution generation unit. 7 (an example of “provisional solution generation means” in the claims of the present application), a route generation unit 9 (an example of “route generation means” in the claims of the present application), a control unit 10, a customer storage unit 11, and a constraint condition storage Unit 12, area storage unit 13, seed customer storage unit 15, provisional solution storage unit 17, and route storage unit 19.

  The customer storage unit 11 stores a plurality of customers. In this embodiment, it is assumed that each customer is associated with a point on the plane. A depot exists at a predetermined position on the plane. The depot is the starting point of the route to be searched. For example, when collecting from each customer or delivering to each customer, the depot is a place where packages to be delivered are collected and a place where collected packages are collected.

  The constraint condition storage unit 12 stores constraint conditions. The constraint conditions are, for example, the maximum load capacity of each vehicle, the time window of each customer, and each vehicle. For example, when picking up and delivering goods, it is not possible to place a load exceeding the maximum load capacity of the vehicle. Therefore, on the route to be searched, collection and distribution are performed within a range that does not exceed the maximum load capacity of the vehicle moving on each closed path. In addition, each customer has a delivery time zone. Each vehicle also has a limit on the time it takes to leave the depot and the time it takes to return to the depot. Therefore, on the route to be searched, each vehicle needs to leave the depot at an appropriate time zone, and return to the depot at an appropriate time zone via a time zone in which each customer can be delivered. The constraint condition storage unit 12 stores, as constraint conditions, the maximum load capacity of each vehicle, the time window of each customer, each vehicle, and the like.

  The customer management unit 3 divides the plane into a plurality of regions, and groups the customers stored in the customer storage unit 11 by each region. Moreover, the customer management part 3 changes the grouped customer by changing the divided | segmented area | region. An example of a specific operation will be described with reference to FIG. The area storage unit 13 stores an area set by the customer management unit 3.

  The seed customer selection unit 5 selects one or a plurality of seed customers from each customer group set by the customer management unit 3. Thereby, seed customers can be prevented from concentrating on a specific area. If there are a plurality of provisional solutions, the searched route becomes better. Therefore, the selection of the seed customer is performed a plurality of times. Here, it is desirable to change the number of seed customers selected from each group by selection. This is because, in the insertion method, the number of seed customers is closed, and therefore it is desirable to obtain a provisional solution by changing the number of closed circuits. The seed customer storage unit 15 stores the selected seed customer.

  The provisional solution generation unit 7 generates a provisional solution by inserting a customer other than the seed customer for each cycle connecting the depot and various customers so as to satisfy the constraint condition stored in the constraint condition storage unit 12. Specific operations will be described later. The provisional solution storage unit 17 stores the generated provisional solution.

  The route generation unit 9 generates a route for visiting a plurality of customers based on the provisional solution. Specific operations will be described later. The route storage unit 19 stores the route generated by the route generation unit 9.

  The control unit 10 controls the operation of the route search device 1.

  Next, the operation of the route search device 1 in FIG. 1 will be described with reference to FIG. FIG. 2 is a flowchart showing an example of the operation of the route search apparatus 1 of FIG.

  First, the customer management unit 3 divides the plane into a plurality of areas and sets the areas (step ST1). An example will be described with reference to FIG. In FIG. 3, as indicated by the solid line 23, a case where the depot 21 is divided into four regions is shown. Group customers that exist in each area.

  Subsequently, the seed customer selecting unit 5 selects a seed customer from each customer group (step ST2). In FIG. 3, it is assumed that one seed customer is selected from each region and four seed customers 25, 27, 29, and 31 are selected.

  Subsequently, the provisional solution generation unit 7 inserts a customer other than the seed customer using the evaluation value for each cycle connecting the depot and various customers so as to satisfy the constraint condition, and generates a provisional solution ( Step ST3). An example of the process will be described.

The evaluation value Δ used is calculated by the equation (1). Here, d _ji is a distance between a customer i and a customer j on a certain route. As shown in FIG. 4, the evaluation value Δ ^k _ij passes from customer i to customer j as shown in (b) instead of going directly from customer i to customer j as shown in (a). Thus, the increase in the distance when the customer j is reached is evaluated. The provisional solution generation unit 7 inserts each customer in a place where the evaluation value Δ is the smallest among those that can satisfy the constraint conditions. When calculating the evaluation value, a large value may be given to those that cannot comply with the constraint condition, and the evaluation value may be inserted into a place where Δ is the smallest as a whole.

  The provisional solution created only by the insertion method may include many routes that have room for improvement, such as an intersection on the route. Therefore, the provisional solution generation unit 7 improves the provisional solution by using the two-opt method. The two-opt method is a method of eliminating the intersection of branches existing on the route.

  It is assumed that a route between the customer i and the customer j and a route between the customer k and the customer l exist in a certain cycle. The provisional solution generation unit 7 determines that the routes intersect when the formula (2) is established between the customers i and j and the customers k and l. When it is determined that there is a crossing point, the route between the customers i and j and the customer k and l is connected to the route between the customers i and k and the customers j and l. At this time, if the time window cannot be protected by removing the intersection, the intersection is not deleted.

  The control unit 10 determines whether or not the provisional solution generation process has been performed a predetermined number of times under the same region division (step ST4). If the predetermined number of times has not been performed, the process returns to step ST2. It is desirable that the seed customer selection unit 5 selects seed customers by changing the number to be selected from each customer group. The insertion method can create only the number of seed customers due to the nature of the algorithm. Therefore, various forms of provisional solutions can be created by increasing or decreasing the number of seed customers.

  When the predetermined number of times has been performed, the customer management unit 3 changes the area (step ST5). In the present embodiment, it is assumed that the area is changed by rotating as shown by the broken line 33 in FIG. As a result, seed customers 25 and 27 previously belonged to different groups and were selected from different groups, but after the change, the seed customers 25 and 27 are selected from the same group. When selecting seed customers one by one, they are not selected at the same time. As described above, various variations of provisional solutions can be obtained by changing the region. As described above, the customer management unit 3 may change the region by setting at least one of the regions to be radial with the depot 21 as the center and changing this position by rotation or the like.

  Subsequently, the control unit 10 determines whether or not the region has been changed a predetermined number of times (step ST6). If the area has not been changed a predetermined number of times, the process returns to step ST2, and the seed customer selecting unit 5 selects a seed customer based on the newly set area (step ST2), and the provisional solution generating unit 7 Generates a provisional solution by the insertion method and the two-opt method (step ST3). Thus, a plurality of provisional solutions are obtained by repeating a predetermined number of times.

  The path generation unit 9 searches for an optimal solution using a column generation method for a plurality of provisional solutions. The column generation method searches for an optimal solution by combining individual routes of provisional solutions. FIG. 5 shows an example of processing by the column generation method. It is assumed that provisional solutions 51 and 53 are obtained. Here, by combining the closed path 55 in the provisional solution 51 and the closed path 57 in the provisional solution 53, a route 59 having a lower cost such as a moving distance than the provisional solutions 51 and 53 can be obtained. In the column generation method, the solution becomes better as the number of combination candidates increases. Therefore, it is desirable to create multiple provisional solutions. The route generation unit 9 selects, as a final route, a route with a low cost such as the shortest travel distance.

  Subsequently, the experiment will be described. Hereinafter, setting a region and selecting a seed customer is referred to as a proposed method, and selecting at random is referred to as a conventional method. First, we compare the calculation time and the total travel distance of the proposed method and the conventional method. Next, in order to verify the usefulness of the proposed method, an experiment using a benchmark (see http://web.cba.neu.edu/~msolomon/problems.htm) is performed. The CPU of the used PC is ES-2620 2.00 GHz, memory 64 GB, OS is Windows (registered trademark) 7, and programming language is C.

  Table 1 compares the calculation time of the proposed method and the conventional method. The calculation time is the result when the number of iterations of the insertion method is changed until the change in the solution of the proposed method and the conventional method converges within 1% according to the customer distribution. Table 1 confirms that the proposed method is faster. This is because the provisional solution used for the column generation method can be reduced by appropriately selecting seed customers.

  Table 2 shows a comparison of dispersion of the total travel distance when the number of trials is five. It was confirmed that the proposed method had a smaller variance than the conventional method and derived a stable solution. This is thought to be because the selection of seed customers was made more evenly.

  Next, in order to confirm the usefulness of the proposed method, we conduct experiments using four benchmarks with different numbers of customers. The closer the experimental result is to the benchmark test solution, the more the optimal solution can be evaluated.

  Table 3 shows the result of the shortest total travel distance among the 10 experiments. 6 and 7 show examples of routes. From Table 3, it can be said that the proposed method was able to derive the optimum solution. Specifically, it can be said that the route of FIG. The route in FIG. 7 has a total mileage of about 0.6% longer than the benchmark solution. For example, it is expected to improve the provisional solution by improving the quality of the provisional solution using another local search method such as the or-opt method.

  DESCRIPTION OF SYMBOLS 1 Route search device, 3 Customer management part, 5 types customer selection part, 7 Provisional solution generation part, 9 Path generation part, 10 Control part, 11 Customer memory part, 12 Restriction condition memory part, 13 Area | region storage part, 15 kinds customer Storage unit, 17 provisional solution storage unit, 19 route storage unit, 21 depot, 23 area division, 25, 27, 29, 31 type customer, 33 area division, 41 depot, 43, 45, 47 customer, 51, 53 provisional solution , 55,57 closed, 59 route

Claims (5)

A route search method for generating a route that satisfies a constraint condition and visits a plurality of customers,
A grouping step in which customer management means groups the plurality of customers into two or more customer groups;
A seed customer selecting means for selecting one or a plurality of customers from each of the customer groups as a seed customer;
A provisional solution generating step for generating a provisional solution by inserting a customer other than the seed customer with respect to a closed circuit connecting the start point and the various customers under the restriction condition;
A route search method including a route generation step in which a route generation means generates a route for visiting the plurality of customers based on the provisional solution. A group change step in which the customer management means changes the grouping of the plurality of customers to a second customer group different from the customer group divided in the grouping step;
A seed customer selecting step in which the seed customer selecting means selects one or a plurality of customers from each of the second customer groups as a second seed customer;
The provisional solution generation means generates a second provisional solution by inserting a customer other than the second type customer that satisfies the constraint condition with respect to the closed circuit connecting the start point and each of the second type customers. Including a provisional solution generation step,
In the route generation step, the route generation means determines a route for traveling the plurality of customers based on the provisional solution and the second provisional solution generated in the provisional solution generation step and the second provisional solution generation step. The route search method according to claim 1, wherein the route search method is generated. Each customer corresponds to a waypoint in space or plane,
In the grouping step, the customer management means divides the space or the plane into a plurality of regions, and each customer group is a group of customers corresponding to waypoints included in each region. ,
The route search method according to claim 1 or 2, wherein, in the route generation step, the route generated by the route generation means reduces the cost of visiting the plurality of customers. A route search device that generates a route that satisfies a constraint condition and visits a plurality of customers,
Customer management means for grouping the plurality of customers into two or more customer groups;
Seed customer selecting means for selecting one or more customers from each customer group as seed customers;
Provisional solution generating means for generating a provisional solution by inserting a customer other than the seed customer for each cycle connecting the start point and the various customers under the constraint condition;
A route search device comprising route generation means for generating a route for visiting the plurality of customers based on the provisional solution.   The program for implement | achieving the route search method in any one of Claim 1 to 3 in a computer.