JPH08286920A - Traveling salesman problem processor - Google Patents

Abstract

PURPOSE: To speedily find a result close to an optimum solution by processing a large scale traveling salesman problem at high speed by finding the solution of the traveling salesman problem at high speed. CONSTITUTION: A traveling salesman problem processor 1A is provided with an entire problem processing means for finding the solution by processing the entire problem while using a parallel processor 2 by preparing an entire problem by dividing a minimum rectangle including an entire city corresponding to the number of cells of the parallel computer 2 based on an applied city coordinate and allocated the divided city to the respective cells, and a partial problem processing means for finding the solution by processing a partial problem while using the parallel computer 2 by preparing that partial problem by further hierarchically dividing the minimum rectangle including the city groups of non-found routes corresponding to the number of cells of the parallel computer 2 and allocating these hierarchical city data to the respective cells when the route of the solution found by the parallel computer 2 does not cover the whole city.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a plurality of processor elements connected in a mesh (hereinafter referred to as "cells").
And a traveling salesman problem processing device capable of solving a traveling salesman problem at high speed using a parallel computer having a communication network connecting them and obtaining an optimum solution.

The traveling salesman problem is a problem of searching for the shortest route among routes that go around a city scattered in a two-dimensional plane. For example, suppose you have multiple jobs, each of which requires some time to prepare for the next job. At this time, considering the preparation time between each work as the distance between cities in the traveling salesman problem,
The combination of jobs that completes all jobs in the shortest time is the same as the optimal solution for the traveling salesman problem.

In the traveling salesman problem, the number of routes that make one round is (N-1)! For N cities. Only exists. Then, as the number of cities is increased, the number of city combinations increases explosively.Therefore, the traveling salesman problem is hierarchized and processed by a parallel computer, which reduces the number of city combinations and speeds up processing. It is necessary to plan.

[0004]

2. Description of the Related Art Conventionally, it has been tried to solve a traveling salesman problem (hereinafter referred to as "TSP") using a computer. This process is to input the city information etc. for solving the TSP to the computer, and to finish the route search process when the shortest route can be searched out of the routes that go around all the cities scattered on the two-dimensional plane. Is.

Various algorithms have been tried for the solution of the TSP, but as the number of cities increases, the combination of cities increases on the order of factorial. For this reason, the amount of calculation becomes enormous, and it has been almost impossible to obtain an optimum solution.

By the way, TSP is a problem which many researchers have tackled as a typical combination problem.
Recently, a method of solving by Hopfield type neural network has been actively studied. Also, a method of hierarchizing and obtaining the solution is being studied.

However, in the Hopfield type neural network, there are cases where the optimum solution is not reached due to a drop to the local minimum value. In addition, in the conventional hierarchical solution method, the accuracy of the solution is deteriorated due to the hierarchical structure. In addition, processing is time consuming due to hierarchization.

[0008]

SUMMARY OF THE INVENTION The above-mentioned conventional device has the following problems. (1): Various algorithms have been tried for the solution of the TSP, but as the number of cities increases, the combination of cities increases in the order of factorial. For this reason, the amount of calculation becomes enormous, and it has been almost impossible to obtain an optimum solution.

(2): For example, in the method of solving the TSP by using the Hopfield type neural network, the optimum solution may not be reached due to a drop to the local minimum value. (3): In addition, in the conventional hierarchical solution method, there are problems that the accuracy of the solution becomes poor and time is taken due to the hierarchical method.

It is an object of the present invention to solve such a conventional problem and to use a parallel computer having a mesh structure so as to obtain a solution of the traveling salesman problem at high speed.

Further, the present invention divides the traveling salesman problem according to the number of cells of a parallel computer having a mesh structure and processes it in a hierarchical manner to process a large-scale traveling salesman problem at high speed and optimize it. The aim is to be able to find a solution that is close to the solution as soon as possible.

[0012]

FIG. 1 is a diagram illustrating the principle of the present invention. In order to solve the above-mentioned problems, the present invention constituted a traveling salesman problem processing device as follows.

(1): In a traveling salesman problem processing apparatus 1A for solving a traveling salesman problem using a parallel computer 2 having a plurality of cells connected in a mesh form and a communication network connecting the cells , The minimum rectangle including all cities based on the given city coordinates is parallel computer 2
According to the number of cells, and the divided urban data is assigned to each cell to create an overall problem. The overall problem is processed by the parallel computer 2 to obtain a solution, and the parallel computer 2 When the route of the solution obtained in step 1 does not go around all cities, the smallest rectangle including the cities of the route not obtained is further divided into layers according to the number of cells of the parallel computer 2, and the layers are divided. Sub-problem processing means for creating a sub-problem by allocating hierarchical city data to each cell, and having the parallel computer 2 process the sub-problem to obtain a solution is provided.

(2): In the traveling salesman problem processing device of (1) above, the sub-problem processing means is based on the patrol route obtained immediately before the sub-problem is created, and Find out to which part of the sub-problem the position of the last visited city is assigned, and set the departure city setting means to set the city assigned to the cell closest to it as the departure city of the sub-problem. I have it.

(3): In the traveling salesman problem processing device of (1) above, the sub-problem processing means is based on the patrol route obtained immediately before the sub-problem is created, and Equipped with arrival city setting means to find out which part of the sub-problem the position of the next visited city is assigned to and set the city assigned to the cell closest to it as the arrival city .

(4): In the traveling salesman problem processing device of (1) above, the sub-problem processing means creates a sub-problem when there is no city at a position corresponding to the departure city or the arrival city, A pseudo city setting means for setting the pseudo city created in a pseudo manner is provided at that position.

(5): In the traveling salesman problem processor of (1) above, when the solution of the subproblem is obtained from the parallel computer 2, it is judged whether or not a pseudo city is included in the route. , If a pseudo city is included, find the route excluding the pseudo city, and incorporate that route into the entire route. If the pseudo city is not included, leave the route as it is as the entire route. It is equipped with a route incorporation processing means.

(6): In the traveling salesman problem processor of (1) above, when the solution of the subproblem is obtained from the parallel computer 2, it is judged whether or not there are overlapping routes in the route. When there is a duplicated route, a route duplication correcting means for correcting the route by shifting the position of the arrival city is provided.

[0019]

The operation of the present invention based on the above construction will be described with reference to FIG. When solving the traveling salesman problem, if all the cities can be assigned to the cells of the parallel computer 2 without overlapping, an optimum solution can be obtained without layering by synchronizing communication between the cells. . However, when the number of cells of the parallel computer 2 is less than the total number of cities, it is possible to hierarchically obtain the one close to the optimum solution by the following procedure.

First, the traveling salesman problem processing apparatus 1A
Is the minimum rectangle containing all cities from the given city coordinates.
By dividing all the cities of the traveling salesman problem into m × n cells of the parallel computer 2 by dividing them into × n,
Create an overall problem (level 1) and send it to the parallel computer 2 to request processing. In this case, the overall problem is the above m × n
The problem is to find the shortest route among the routes that go around all the cities mapped in the cell.

The parallel computer 2 which has received the overall problem,
A process of finding the shortest route among routes that go around the city using m × n cells is performed. Then, when the shortest route is obtained from the routes that go through all the given cities, the route data of the shortest route is returned to the traveling salesman problem processing device 1A.

The traveling salesman problem processing device 1A which has received the response judges whether or not the route obtained by the parallel computer 2 has visited all cities. As a result, when it is determined that the obtained route does not go through all the cities, a new subproblem (level 2) is newly created and the parallel computer 2 is requested to perform a process for obtaining a solution of the subproblem.

The parallel computer 2 which has received the subproblem is
For the subproblem, the process of finding the shortest route among the routes that go around the city is performed. Then, when the shortest route is obtained from the routes that go through all the given cities, the route data of the shortest route is returned to the traveling salesman problem processing device 1A.

The traveling salesman problem processing device 1A which has received the response judges whether or not the route obtained by the parallel computer 2 has visited all cities. As a result, when it is determined that the obtained route does not go through all the cities, a further hierarchical subproblem is created and the parallel computer 2 is requested to perform a process for obtaining a solution of the subproblem. In this way, the hierarchical partial problems are processed until the routes of all cities are obtained.

In this case, the traveling salesman problem processing device 1A determines the position of the visiting city immediately before the representative city in the partial problem as the partial problem based on the traveling route obtained immediately before the partial problem is created. Find out which part of it is assigned, and set the city assigned to the cell closest to it as the departure city of the subproblem.

Further, it is checked which part of the sub-problem the position of the next visited city of the representative city in the sub-problem is allocated, and the city allocated to the cell closest to the sub-problem arrives at the arrival city. Set to. Furthermore, when creating a subproblem, if there is no city at the position corresponding to the starting city or the arriving city, the pseudo city created pseudo is set at that position.

The traveling salesman problem processing apparatus 1A, which has obtained the solutions to the respective subproblems as described above, judges whether or not a pseudo city is included in the route, and when the pseudo city is included. Performs a process of obtaining a route excluding the pseudo city, incorporating the route into the entire route, and incorporating a route as it is into the entire route when the pseudo city is not included.

In this case, when the solution of the subproblem is obtained from the parallel computer 2, it is judged whether or not there are overlapping routes, and if there are overlapping routes, the position of the arrival city is shifted. To correct the route.

As described above, by using the parallel computer having the mesh structure, the solution of the traveling salesman problem can be obtained at high speed. In addition, by dividing the traveling salesman problem according to the number of cells of a parallel computer with a mesh structure and processing it hierarchically, a large-scale traveling salesman problem can be processed at high speed, and the one close to the optimal solution can be processed as soon as possible. You can ask.

[0030]

Embodiments of the present invention will be described below with reference to the drawings. 2 to 11 are views showing an embodiment of the present invention. 2 to 11, 1 is a host computer,
2 is a parallel computer, 3 is a TSP processor (traveling salesman problem processor), 4 is a storage device, 5 is a cell (processor element), and 6 is a communication network. FIG.
The traveling salesman problem processing apparatus 1A shown in (1) corresponds to the host computer 1.

§1: Description of system configuration of the embodiment ...
See FIG. 2. FIG. 2 is a system configuration diagram of the embodiment. In the embodiment, a system including the host computer 1 and the parallel computer 2 performs a process of obtaining a solution of the traveling salesman problem (hereinafter referred to as "TSP").

In the above system, the host computer 1 has a TSP processing unit 3 for performing various TSP processing,
A storage device 4 for storing various information such as city data necessary for TSP processing is provided. In this case, the storage device 4 stores coordinate data of all cities in advance.

The parallel computer 2 executes the processing of the TSP problem data (entire problem and partial problem) requested by the host computer 1. For example, a plurality of cells (processors) connected in a mesh form (processors). The element) 5 and a communication network 6 connecting these cells 5 are provided.

In the above system, the host computer 1
TSP processing unit 3 creates the TSP problem data, transfers the problem data to the parallel computer 2 having the mesh structure, and
Request SP processing. Then, when the parallel computer 2 analyzes and obtains a solution, the data of the solution (the data of the shortest route that travels between all given cities) is transferred to the host computer 1 to respond. The TSP processing unit 3 obtains the shortest route around all the cities of TSP based on the response from the parallel computer 2.

§2: Description of Processing of Embodiment--See FIG. 3 FIG. 3 is a flowchart of processing of the embodiment. Below, FIG.
The processing of the embodiment (entire processing) will be described based on FIG. Note that S1 to S8 indicate processing steps.

When the solution of TSP is obtained, if all cities can be assigned to the cells 5 of the parallel computer 2 without overlapping, the communication between the cells 5 synchronizes to optimize the TSP without hierarchization. You can get a solution.
However, when the number of cells 5 of the parallel computer 2 is smaller than the total number of cities, the TSP can be hierarchized according to the following procedure to obtain an optimal solution.

First, the TSP processor 3 reads necessary data such as coordinates of all cities from the storage device 4 and stores it in the internal memory (S1) to start the processing. Then, the minimum rectangle including all cities is divided into m × n from the given city coordinates (m, n: any integer), and all TSP cities are mapped to m × n cells of the parallel computer 2 ( S2).

Next, the TSP processing unit 3 creates an overall problem to be solved first from the mapped information (S3),
Send the created question to the parallel computer 2 (S4) T
SP processing (in the route that goes around all given cities,
Request the shortest route). In this case, the overall problem to be solved first is a problem of finding the shortest route among the routes that go through all the cities mapped to the m × n cells (all the cities are treated as m × n cities).

The parallel computer 2, which has received the above problem, first uses the m × n cells 5 to perform the process of finding the shortest route among the routes that go through all the cities. In this case, there may be a group of cities including a plurality of cities in one cell 5, but the group of cities assigned to one cell is considered as one city (representative city) and the shortest route is obtained. .

Then, when the shortest route is obtained from the routes that go through all the given cities, the data of the shortest route is transferred to the TSP processing unit 3 of the host computer 1 to respond to the request.

When the TSP processor 3 receives the response from the parallel computer 2 (S5), the route data is stored in the storage device 4.
Stored in. Then, the TSP processing unit 3 determines whether the route obtained by the parallel computer 2 has traveled all cities (S6). As a result, when it is determined that the obtained route does not travel all cities, a new partial problem is created (S8), and the process from S4 is repeated.

That is, until the routes of all cities are obtained, the minimum rectangle including the unresolved city groups is j
The operation of re-dividing into xk (j, k: arbitrary integer) and layering is repeated (level 1 → level 2 → level 3).
・ ・). In this way, when the route passing through all the cities is obtained, the data of the route search result is output (displayed, output by printing, etc.) (S7), and the process ends.

In the above processing, the TS which has obtained the solution (obtained shortest path data) of each subproblem from the parallel computer 2
The P processing unit 3 performs processing for incorporating the obtained route into the entire route and stores it in the storage device 4.

As described above, it is possible to obtain a solution of the traveling salesman problem at high speed by using a parallel computer having a mesh structure. In addition, by dividing the traveling salesman problem according to the number of cells of a parallel computer with a mesh structure and processing it hierarchically, a large-scale traveling salesman problem can be processed at high speed, and the one close to the optimal solution can be processed as soon as possible. You can ask.

§3: Description of city data--see FIG. 4 FIG. 4 is an explanatory diagram of city data. The TSP processing unit 3
The TSP processing (processing for obtaining the TSP solution) is performed as described above. In this case, the processing is performed by storing the city data shown in the drawing in the storage device 4.

That is, in the storage device 4 accessed by the TSP processing unit 3, for each city, the city ID (city identification code), the actual coordinates of the city (xy coordinates), and the coordinates of the city in the parallel computer. Data such as (position coordinates of cells), inverse (inverse: last visited city), next (next: next visited city), group (group: same group city), number of cities in same group are stored.

The TSP processor 3 stores the data for each city in the storage device 4, and when receiving the response from the parallel computer 2, performs the TSP processing while updating the city data.
In this case, the TSP processing unit 3 first reads the TSP from the storage device 4.
When reading all city coordinate data of SP, each city has the above-mentioned data structure, all cities belong to the same group as the departure city, and the departure city and the arrival city are considered to be the same. From, the processing is assigned to each cell of the parallel computer 2.

From the problem given by the TSP processor 3, the parallel computer 2 finds the shortest route among the routes that go around all given cities. Since the entire patrol route can be traced by "next" of the city data structure, "next" and "inverse" of the target city are rewritten each time the route is obtained.

When the cities are hierarchized, the groups of cities assigned to the same cell form a group, which is stored as an element called a group of each city. The group is
Rewriting is performed in the target city when it is divided into the parallel computers 2. When the entire route is finally obtained, the element of this group is null in all cities.

Then, new sub-problems are created until the routes of all cities are obtained from the initially obtained patrol route, and sub-routes are obtained in the same manner as the first overall problem. The obtained partial route is incorporated into the entire patrol route.

§4: Explanation of city data at the time of creating a partial problem and after processing of a partial problem ... See FIGS. 5 and 6. FIG. 5 is a diagram showing city data at the time of creating a partial problem, and FIG. 6 is a partial problem. It is the figure which showed the city data after a process.

At the time of TSP processing, the TSP processing section 3 performs processing based on city data in the storage device 4. Then, after requesting the parallel computer 2 to process the first overall problem, if the route that has traveled through all the cities is not found, a process for creating a new partial problem and requesting the route to the parallel computer 2 is performed. Request.

In this case, for example, it is assumed that city data exists as shown in FIG. In this state, the TSP processing unit 3 reads, for example, a group including city IDs = 5, 10, and 7 from the storage device 4 as city data of a partial problem, and creates a partial problem from these city data.

When the parallel problem is processed by the parallel computer 2 and the resulting data (data of the partial path) is received, the TSP processor 3 uses the data to store the data in the storage device 4.
Update the city data in. As a result of this processing, as shown in FIG. 6, the contents of the city data change and the entire city patrol route becomes more detailed.

§5: Explanation of TSP processing and hierarchical processing
.. Refer to FIGS. 7 and 8. FIG. 7 is an explanatory diagram of the TSP process, and FIG. 8 is an explanatory diagram of the layering process. In addition, the levels 1 and 2 shown in the figure represent levels of hierarchization. Also, the ● symbol indicates a city.

When performing the TSP processing as described above, the TSP
The processing unit 3 reads necessary data from the storage device 4, divides the minimum rectangle including all cities from the given city coordinates (x, y) into m × n, and divides them into m × n cells of the parallel computer 2. T
Map all SP cities.

Then, first, an overall problem to be solved (see level 1 in the figure) is created and transmitted to the parallel computer 2 to transmit the TSP.
Request processing (processing to find the shortest route among routes that go through all given cities).

The parallel computer 2, which has received the above problem, first uses the m × n cells 5 to perform the process of finding the shortest route among the routes that go around the city. Then, when the shortest route is obtained from the routes that go through all the given cities, the data of the shortest route is transferred to the TSP processing unit 3 of the host computer 1 to respond to the request.

Upon receiving the route data from the parallel computer 2, the TSP processor 3 determines whether the route obtained by the parallel computer 2 has traveled all cities.
As a result, when it is determined that the obtained route does not travel all cities, a new partial problem is created and hierarchization is performed (see level 2 in the figure), and the TSP processing is performed again on the parallel computer 2. Ask. Then, when the response from the parallel computer 2 is received, the TSP processing unit 3 updates the city data. In this way, when the number of cells of the parallel computer 2 is smaller than the total number of cities, the TSP process is hierarchized to find the one close to the optimum solution.

In the above processing, city data (city dat
a) is the x, y coordinate (x, y), for example, (0, 1
0), (3, 5), (2, 12) ... That is, the position where each city exists on the coordinate axis is represented by (x, y) with respect to the x, y coordinates including all cities.

Therefore, the problem data created by the TSP processing unit 3 is also 0 (0, 0, for each city ID 0, 1, 2, ...).
0), 1 (0,1), 2 (0,2) ...

By the way, in the first division of all cities (overall problem), a patrol route in which the starting city and the arrival city are the same is obtained, but in each partial problem when hierarchizing, the starting city and the arrival city are already Set from the route requested.

In this case, the TSP processor 3 determines the position of the visited city immediately before the representative city in the subproblem in the subproblem based on the patrol route obtained just before the subproblem is created. Check if it is assigned to a part,
The city assigned to the cell closest to it is set as the departure city for the subproblem.

Further, it is checked which part of the sub-problem the position of the next visited city of the representative city in the sub-problem is allocated, and the city assigned to the cell closest to the sub-problem arrives at the arrival city. Set to. Furthermore, when creating a subproblem, if there is no city at the position corresponding to the starting city or the arriving city, the pseudo city created pseudo is set at that position.

The solution T of each subproblem is obtained as described above.
The SP processing unit 3 determines whether or not the pseudo city is included in the route, and if the pseudo city is included, obtains a route excluding the pseudo city, and determines the route as the entire route. In addition, if the pseudo city is not included,
The process of incorporating the route as it is into the entire route is performed.

In this case, when the solution of the subproblem is obtained from the parallel computer 2, it is judged whether or not there is an overlapping route among the routes, and if there is an overlapping route, the position of the arrival city is shifted. To correct the route.

By doing so, even in a large-scale problem, a large number of sub-problems corresponding to the problem can be created, and by solving each of them, the entire solution can be obtained.
In addition, each subproblem can search its route independently, except for the solution that first finds the entire traveling route. Therefore, one parallel computer 2 can search for a plurality of subproblems in parallel, and the time for obtaining a solution can be shortened.

§6: Explanation of the partial problem city setting process ...
-Refer to FIG. 9. FIG. 9 is an explanatory diagram of the partial problem city setting process, FIG. A is a diagram showing an example of setting departure, arrival, and pseudo cities, and FIG. B is a diagram showing an example of route duplication correction.

When the subproblem is subdivided and assigned to each cell of the parallel computer 2, it is necessary to determine the departure city and the arrival city in the subproblem. This is to set and determine an appropriate city from the patrol route that has been obtained just before creating the sub-problem by the following procedure.

(1): The position of the city (immediately visited city) pointed to by the inverse of the representative city of the subproblem (the inverse of the representative city ID in the city data) is mapped to any part of the subproblem. Then, the city assigned to the cell with the shortest distance from that is set as the departure city.

(2): Where in the sub-problem the coordinates of the city (next visiting city) pointed to by "Next" of the representative city of the sub-problem are mapped in the same way as in (1) above. , And set the city corresponding to the cell closest to it as the arrival city.

(3): In the above (1) and (2), when there is no city assigned to the corresponding cell, a pseudo city created in a pseudo manner (a city that does not actually exist) is the departure city. Or set it to the arrival city.

In FIG. 9A, a 4 × 4 configuration (cells vertically 4
The number of cells is 4 and the number of cells is 4 in the horizontal direction). The shaded portions in the figure are cells in which cities exist.
In the figure, the last visited city (inverse city), the next visited city (next city), and the starting city cell (start city c
ell) and a dummy end city cell.

As shown in the figure, the cells to which the starting city and the arriving city are assigned are located on any one of the four sides of the rectangle, although the location depends on the configuration.
However, when viewed from the side of a parallel computer, the pseudo city is no different from the actual city, only the number of partial problem cities is increased.

When the starting city and the arriving city are set as described above, it is possible that both are the same or not. If they are the same, the same route as in the case of first solving the TSP will be obtained. If this is not the case, a non-tour route that has a predetermined departure city and arrival city around the sub-problem city is determined, although it is strictly different from the original TSP.

For example, as shown in FIG. 9B, when the departure city and the arrival city are the same and the routes overlap, the position of the cell is moved and the process is repeated. If the starting city and the arriving city overlap, the route may remain circulated internally, so a solution cannot be obtained. Therefore, the pseudo city is set as the arrival city so that the departure city and the arrival city do not overlap with each other and the processing is redone.

§7: Description of detail of city patrol route and hierarchization of route search ... See FIG. 10. FIG. 10 is an explanatory diagram of detail of city patrol route and hierarchization of route search. The TSP processing unit 3 incorporates the partial route obtained as described above into the entire patrol route. At this time, if a pseudo city is included, it is incorporated in a form excluding it. For example, assume that a pseudo city with a city ID of “100” is included.

At this time, the TSP processor 3 "100 → 2 →
If "5" is incorporated into the entire patrol route "0 → 5", the patrol route becomes "0 → 2 → 5" (each numeral indicates a city ID, and an arrow indicates the route).

Further, in the case of the partial patrol route, if the routes overlap (see FIG. 9B), the patrol route which is the solution of all cities becomes long, so the solution of the partial problem was obtained. Later, the location of the arrival city was shifted and the processing was redone.

In this way, the entire traveling route is refined every time the partial route from the parallel computer 2 is received, and finally, the elements are included in the data structure of each city from the entire starting city. You will be able to get a patrol route of the cities connected by "Next".

FIG. 10 shows a state as a result of actually performing the TSP processing, and shows a state in which hierarchization is advanced in the process of obtaining a solution and the traveling route is being refined.
In this city data, the depth of the hierarchy is 3 (level 1
~ Level 3), and the number of partial problems is 5. Also,
It took about 1 second to find the solution.

§8: Explanation of solution of city patrol route ... Fig. 1
See FIG. 1. FIG. 11 is a diagram showing a solution of a city patrol route, FIG. A is a coordinate of a city, and FIG. 11 is a diagram showing a solution of a city patrol route.

In the example shown in FIG. 11, 100 cities are targeted, and the city patrol route is actually obtained for these 100 cities. In this case, the depth of the hierarchy is 4,
The number of partial problems was 34, and the total execution time was about 13 seconds. When the Manhattan length was compared for the distance, the error was about 20% from the substantially optimum solution obtained by the simulated annealing method.

(Other Embodiments) The embodiments have been described above, but the present invention can also be implemented as follows. (1): In addition to the method described in the above embodiment, the setting method of the pseudo city may be set as follows.

For example, in FIG. 9, the mesh structure 4
It is also possible to adopt a method of limiting to a specific cell such as allocating not only to a side but also to a square cell. Alternatively, a method may be adopted in which, without placing a pseudo city, a cell that is closest to a sub-problem among the actually existing cities is assigned to a cell to which the city is assigned.

(2): The structure of the city data is not limited to that described in the above embodiment, and can be implemented by any data structure including the same data as in the above embodiment. (3): The storage device for storing the city data can be implemented by any storage device such as a magnetic disk device, a magneto-optical disk device, a magnetic tape device, and a semiconductor storage device. When performing the TSP processing, necessary data is transferred from the storage device to an internal work memory for processing, and stored in the storage device when the processing is completed.

(4): Since each subproblem (processing after the hierarchical level 2) can independently search its path, one parallel computer processes a plurality of subproblems in parallel (partial processing). Parallel processing of problems). By doing so, the time for obtaining the TSP solution can be further shortened.

[0088]

As described above, the present invention has the following effects. (1): Even for a large-scale traveling salesman problem, a solution that incorporates hierarchies can be used to quickly find a solution. Further, by requesting a parallel computer having a mesh structure to process the divided subproblems, it is possible to shorten the time for obtaining a solution.

(2): By dividing the traveling salesman problem according to the number of cells of a parallel computer having a mesh structure and processing the layers in a hierarchical manner, a large-scale traveling salesman problem is processed at high speed to obtain an optimal solution. You can ask for something close to you as soon as possible. Further, in the processing of the partial problem, the departure city and the arrival city are set, but when each of the cities does not exist at a predetermined position, the pseudo city is set, so that the processing can be efficiently performed.

(3): Since each subproblem (processing after the hierarchical level 2) can independently search its path, one parallel computer can process a plurality of subproblems in parallel. If this is the case, the time for obtaining the TSP solution can be further shortened.

In addition to the above effects, the following effects are obtained corresponding to each claim. (4): In claim 1, the minimum rectangle including all cities is divided according to the number of cells of the parallel computer based on the given city coordinates.
The whole problem is created by assigning this divided city data to each cell, and the whole problem is processed by a parallel computer to obtain a solution, and the route of the solution obtained by the parallel computer is used for all cities. If it is not a round trip, the smallest rectangle containing the cities of the routes that have not been obtained is further divided into layers according to the number of cells in the parallel computer, and this divided and hierarchized city data is assigned to each cell. The sub-problem processing means is provided for creating a sub-problem and causing the parallel computer to process the sub-problem to obtain a solution.

Therefore, the solution of the traveling salesman problem can be obtained at high speed by using the parallel computer having the mesh structure and performing the hierarchical sub-problems in parallel processing. In addition, by dividing the traveling salesman problem according to the number of cells of a parallel computer with a mesh structure and processing it hierarchically, a large-scale traveling salesman problem can be processed at high speed, and the one close to the optimal solution can be processed as soon as possible. You can ask.

(5) In claim 2, the subproblem processing means determines the position of the visited city immediately before the representative city in the subproblem based on the patrol route obtained just before the subproblem is created. It is provided with a departure city setting means for checking which part of the problem is assigned and setting the city assigned to the cell closest to it as the departure city of the partial problem. Therefore, the process of setting the departure city can be reliably performed when the partial problem is processed, and the TSP process can be efficiently performed.

(6) In claim 3, the subproblem processing means determines the position of the next visited city of the representative city in the subproblem based on the patrol route obtained immediately before creating the subproblem. An arrival city setting means is provided for checking which part of the problem is assigned and setting the city assigned to the cell closest to it as the arrival city. Therefore, the arrival city setting process can be reliably performed when the partial problem is processed, and the TSP process can be efficiently performed.

(7): In claim 4, the sub-problem processing means, when creating a sub-problem, if there is no city at the position corresponding to the departure city or the arrival city, creates the pseudo problem at that position. A pseudo city setting means for setting a pseudo city is provided.

Therefore, even if the departure city or the arrival city is not in the predetermined position, the departure city and the arrival city can be set surely by the pseudo city, and the TSP processing for the partial problem can be efficiently performed.

(8) In claim 5, when the solution of the subproblem is obtained from the parallel computer, it is judged whether or not a pseudo city is included in the route, and the pseudo city is included. Is equipped with route incorporation processing means that finds a route excluding the pseudo city, incorporates the route into the entire route, and, if the pseudo city is not included, incorporates the route as it is into the overall route. .

Therefore, every time a partial route is received from the parallel computer, the entire traveling route is refined, so that the entire route can be sequentially and reliably obtained. Moreover, since the route excluding the pseudo city is incorporated into the entire route, an accurate route can be obtained.

(9): In claim 6, when the solution of the subproblem is obtained from the parallel computer, it is judged whether or not there is an overlapping route in the route, and when the overlapping route is present, A route duplication correcting means for correcting the route by shifting the position of the arrival city is provided. Therefore, an accurate route is always required.

[Brief description of drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is a system configuration diagram of an embodiment.

FIG. 3 is a processing flowchart of an embodiment.

FIG. 4 is an explanatory diagram of city data according to the embodiment.

FIG. 5 is a diagram showing city data at the time of creating a partial problem in the example.

FIG. 6 is a diagram showing city data after partial problem processing in the embodiment.

FIG. 7 is an explanatory diagram of TSP processing in the embodiment.

FIG. 8 is an explanatory diagram of layering processing according to the embodiment.

FIG. 9 is an explanatory diagram of city setting processing of a partial problem in the embodiment.

FIG. 10 is an explanatory diagram of detailing of city tour routes and hierarchization of route search according to the embodiment.

FIG. 11 is a diagram showing a solution of a city patrol route in an example.

[Explanation of symbols]

 1 Host Computer 2 Parallel Computer 3 TSP Processor 4 Storage Device 5 Cell (Processor Element) 6 Communication Network

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Kaoru Kawamura 1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture, Fujitsu Limited (72) Inventor, Yue Inada 1015, Kamedotaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture, Fujitsu Limited ( 72) Inventor Hideki Miwatari 1015 Kamiodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture, Fujitsu Limited

Claims (6)

[Claims] 1. A traveling salesman problem processing apparatus for obtaining a solution of a traveling salesman problem using a parallel computer having a plurality of cells connected in a mesh shape and a communication network in which each cell is connected. Based on the city coordinates, divide the smallest rectangle containing all cities according to the number of cells in the parallel computer, assign the divided city data to each cell to create an overall problem, and let the parallel computer process the overall problem. When the route of the solution obtained by the parallel computer and the route of the solution obtained by the parallel computer do not go around the entire city, the minimum rectangle containing the cities of the route not obtained is determined according to the number of cells of the parallel computer. Create a subproblem by assigning the divided and hierarchized city data to each cell, and let the parallel computer process the subproblem to solve. TSP processing apparatus characterized by comprising a subproblem processing means for calculating. 2. The sub-problem processing means determines the position of the visiting city immediately before the representative city in the sub-problem based on the patrol route obtained until immediately before the sub-problem is created. 2. The circuit according to claim 1, further comprising a departure city setting means for determining whether or not a city assigned to a cell closest to the cell is set as a departure city of the partial problem. Salesman problem processor. 3. The sub-problem processing means determines which part of the sub-problem the position of the next visited city of the representative city in the sub-problem is based on the patrol route obtained immediately before the sub-problem is created. 2. The traveling salesman problem according to claim 1, further comprising arrival city setting means for checking whether or not the cell is assigned to the cell, and setting the city assigned to the cell closest to it as the arrival city. Processing equipment. 4. The sub-problem processing means, when creating a sub-problem, if there is no city at a position corresponding to a departure city or an arrival city, sets a pseudo city that has been pseudo created at that position. The traveling salesman problem processing device according to claim 1, further comprising city setting means. 5. When a solution of a subproblem is obtained from the parallel computer, it is judged whether or not a pseudo city is included in the route, and when the pseudo city is included, the pseudo city is selected. Claimed to have a route incorporation processing means for obtaining the excluded route, incorporating the route into the entire route, and incorporating the route as it is into the overall route when the pseudo city is not included. The traveling salesman problem processing device according to item 1. 6. When a solution of the subproblem is obtained from the parallel computer, it is judged whether or not there is an overlapping route among the routes, and if there is an overlapping route, the position of the arrival city is shifted. The traveling salesman problem processing device according to claim 1, further comprising route duplication correcting means for correcting the route.