JP5612817B2 - Method, computer system and computer program for determining delivery routes of multiple vehicles - Google Patents

Description

  The present invention relates to a method, an apparatus, and a program for obtaining a delivery route for delivering an article to a plurality of points by a vehicle. More specifically, the present invention relates to a method for obtaining a solution with a smaller number of vehicles by performing a local search method from the viewpoint of variations in the number of vehicles and the operation rate between vehicles.

  Various solutions have been proposed for the delivery route problem. For example, there are a genetic algorithm method (Patent Documents 1 and 4), a nearest neighbor method (Patent Document 2), a clustering method (Patent Document 3), and the like.

  In the delivery route problem, the most important purpose is to reduce the number of vehicles. If the number of vehicles is the same, the next most important purpose is to shorten the travel distance (or travel time). These two objectives are often in a trade-off relationship that cannot be achieved simultaneously. For example, in the case of vehicles capable of loading up to three articles at six delivery points arranged as shown in FIG. 1 and delivering articles one by one from a central base, the route of (B) is 2 vehicles. Therefore, it can be said that it is better than the route of (A), but if only the travel distance is viewed, it can be seen that (A) is shorter and is a better route.

  In the above example, FIG. 2 shows a list of all the solutions and a plot of the number of vehicles and the travel distance. The solution marked with Δ corresponds to the route (A), and the solution marked with ○ corresponds to the route (B). The former is a solution obtained by performing a local search in the direction of shortening the travel distance from a predetermined initial solution, and is the most excellent solution in terms of travel distance. However, the number of vehicles is inferior to the latter.

In order to deal with this problem, there is known a method that allows a solution obtained by a local search to be updated in a direction that deteriorates a predetermined evaluation value. One of them is tabu search (Non-Patent Document 1). The tabu search is a method for searching for an optimal solution without stagnation of the search by not performing an operation in the tabu list when the evaluation value transits to a nearby delivery route. However, no means for directing to reduce the number of vehicles is taken, and the number of vehicles is searched in a random direction. Even if a solution with a reduced number of vehicles is found, it is only a coincidence. The same applies to Patent Documents 1, 2, and 4. In addition, the clustering method (Patent Document 3) is limited to application to a case where delivery points are geographically organized to some extent.
JP 2001-2334113 A JP 2001-283136 A JP 2003-26335 A JP 2005-43974 A I. H. Osman, “Metastrately simulated annealing and tab search algorithms for the vehicle routing probe”, Anals of Operations Research, Vol. 41, pp. 421-451, 1993.

  Therefore, the present invention provides a method for obtaining a solution with a reduced number of vehicles, which is the most important object in the delivery route problem.

That is, the present invention is the following method.
A method of creating a delivery plan in which a plurality of vehicles deliver articles from a certain base to a plurality of delivery points by a computer having storage means,
For a solution set (N (S)) consisting of neighboring solutions of a given current solution S, the local search is repeated until the given termination condition is reached, and the S is updated to obtain the optimal solution S ^best . Including the step of seeking
In the local search, a step of searching for a solution having the smallest number of vehicles, and when there are a plurality of solutions having the smallest number of vehicles, the plurality of solutions are defined for each vehicle defined by the following equation (1). And a step of searching for a solution having the smallest index β (t) indicating a small variation between vehicles of the evaluation value B _k (t) (tεN (S)) defined by the following formula (2). A method characterized by that.
B _k (t) = Σ _{iεC k} (t) p _i / M (1)

β (t) = 1- _{Σkεσ (t)} B _k (t) ^m / | σ (t) | (2)

here,
p _i : given feature quantity of each delivery point i M: upper limit value of feature quantity at delivery point visited by one vehicle or total sum of feature quantities over all vehicles σ (t): vehicle used in solution t Set of
| σ (t) |: Total number of vehicles used in solution t C _k (t): Set of delivery points visited by vehicle kεσ (t)

  The present invention is characterized in that the delivery route problem is directed such as allocating luggage so that the number of vehicles is reduced. As a result, the problem with each of the above conventional methods imposed on the traveling salesman problem with restrictions on loading capacity and operating time frame, that is, even if the route is short, the number of vehicles increases as a result of less loading of each vehicle. To solve the problem.

FIG. 3 is a block diagram illustrating an example of computer hardware in which the present invention can be implemented. The computer system (301) includes a CPU (302) and a main memory (303), which are connected to a bus (304). The CPU (302) is preferably based on a 32-bit or 64-bit architecture, such as Intel's Xeon (TM) series, Core (TM) series, Atom (TM) series, Pentium (TM) series, The Celeron (TM) series, the AMD Phenom (TM) series, the Athlon (TM) series, the Turion (TM) series, and the Empron (TM) can be used. A display (306) such as an LCD monitor is connected to the bus (304) via a display controller (305). The display (306) is used to display information about the software running on the computer system (301) with a suitable graphic interface. A hard disk or silicon disk (308) and a CD-ROM, DVD or Blu-ray drive (309) are also connected to the bus (304) via an IDE or SATA controller (307). The CD-ROM, DVD or BD drive (309) is used to introduce a program from the CD-ROM, DVD-ROM or BD to a hard disk or silicon disk (308) as required. Further, a keyboard (311) and a mouse (312) are connected to the bus (304) via a keyboard / mouse controller (110) or a USB controller (not shown).

Hereinafter, the method of the present invention will be described with reference to the flowchart showing the method of the present invention shown in FIG. First, a given initial solution is set as the current solution S and the optimum solution S ^best , and τ representing the number of iterations of the local search is set to 1 (401).

The initial optimal solution S ^best may be a solution obtained by a known method. For example, as shown in FIG. 5, a list in which the distances to all other points are arranged in a short order for each delivery point (hereinafter referred to as “neighbor list”) using delivery point data stored in advance. The initial optimum solution can be generated by searching for an unvisited point closest to a certain point (nearest neighbor method). Here, the distance between each point is calculated | required by the shortest path calculation etc. on a digital road network, and is hold | maintained in the format of the table of a point-to-point. Alternatively, the distance between points may be expressed as an Euclidean distance, and an initial optimal solution may be obtained by a nearest neighbor method or the like using a data structure called a kd tree instead of the neighborhood list. Other initial optimal solution generation methods include an insertion method and a saving method (for example, M. M. Solomon, “Algorithms for the vehicle routing and scheduling programs with time windows constraints,” Operation 35, Operations Re, 35). .2, pp254-265, 1987). In the experiment to be described later, a method is provided in which a certain number of vehicles (25) are prepared, and one of the unvisited points where any vehicle can visit one after another, the points closest to the current position are sequentially visited (parallel nearest neighbors). Method) to obtain an initial optimal solution.

The expression format of the solution t may be arbitrary. For example, in FIG. 6, the solution of the route delivered from the base indicated by □ to the points 1, 2, 5 and the route delivered 4, 6, 3, 7 is set to 0 for convenience. It may be expressed as (0,1,2,5,0,4,6,3,7). Usually, it is expressed as a data structure including information for efficiently calculating the objective function. For example, if the delivery amount to points 1, 2, and 5 is 10, 10, 20, calculate the total delivery amount to that point on the route, 10 for point 1, 20 for point 2, By associating 40 with the point 5, it is possible to know the loading amount of the vehicle only by confirming the total delivery amount associated with the last point 5 in the delivery route.

  Returning to FIG. 4, although not shown in the figure, a solution set N (S) consisting of the S neighboring solutions is stored in advance or obtained by a given method. In order to generate a neighborhood solution, an arbitrary method may be used. For example, as shown in FIG. 7, a method of cutting two sides in a certain route and reconnecting them with two new ones (2-Opt method) ), A path shift method (Path shift method) for putting a delivery place in another route, a path exchange method (Path swap method) for exchanging a delivery place in a route, and the like can be used.

  Preferably, O (1) feasibility check is performed prior to creating a neighborhood solution. This is because the number of neighboring solutions is more than the square order of the number of points, and it takes time to perform a local search for all neighboring solutions. The above O (1) is read as order one and means that it can be executed in a constant time regardless of the number of delivery points. In the O (1) feasibility check, a side to be deleted in the route is first determined, and a neighborhood solution is generated by limiting points where the travel distance can be shortened by using the length of the side as a hint. For example, since at least one of the two sides to be exchanged by the 2-opt method is not shortened, the mileage after the exchange is not shortened. Accordingly, as shown in FIG. If the side is determined to be AB, the exchange partner's side should be found by examining only the points inside the circle with the side AB as the radius centered on the point A. In order to obtain a point within a radius centered on each point, it is convenient to use the neighborhood list. In FIG. 8 (1), the points D and E are candidates. Also, with respect to the path shift method, it is possible to limit the neighborhood solution of the search candidate by looking only inside the circle with the radius DE as shown in FIG. In the case of BD> DE and BE> DE, a search is performed centering on point A or C with AB + BC-AC as the radius, and a neighborhood solution is generated (for details, see N. Park, H. Okano and H.). Imai, “A path-exchange-type local search algorithm for vehle routing and it's effective search strategy”, Journal of Operations Research.

A local search is performed for the solution set (405). The present invention is defined by the following formula (2) of the evaluation value B _k (t) for each vehicle, which is defined by the following formula (1) after first comparing the number of vehicles in the local search. It is characterized by searching for a solution having a small index β (t) indicating a small variation between vehicles to be directed and reducing the number of vehicles.
B _k (t) = Σ _{iεC k} (t) p _i / M (1)

β (t) = 1- _{Σkεσ (t)} B _k (t) ^m / | σ (t) | (2)

In the above formula (1), p _i is a given feature quantity of each delivery point i, and this is the upper limit value of the feature quantity at the delivery point visited by one vehicle or the sum of the feature quantities over all vehicles (M ) To obtain an evaluation value B _k (t) representing the operating state of the vehicle, for example, the loading rate. A first example of the feature amount p _i and M, p _i is an approximation of the operating time of the following formula (3), M is the upper limit value of the operating time of the vehicle.
p _i = nn _i + t _i (3)

In Equation (3), nn _i is the average value of the distance to the delivery point closest to the delivery point i and the distance to the second closest delivery point, and t _i is the working time at the delivery point i (package) Unloading etc.). In the second example, _pi is the delivery amount to the delivery point i, and M is the upper limit value of the load amount of the vehicle, that is, the load capacity. In the third example, p _i is a constant assigned to the delivery point i, and M is the upper limit value or the sum. When the constant is 1, M is the total number of points. In the fourth example, p _i is a random number assigned to the delivery point i, and M is a total sum of random numbers over all vehicles. Preferably, p _i is an approximation of the operating time.

Β (t) obtained by the equation (2) is an index representing a small variation in the evaluation value B _k (t) between vehicles. The number of vehicles can be reduced by performing a local search in a direction in which β (t) becomes smaller, that is, in a direction in which variation increases. In the formula (2), the power m of B _k (t) is a numerical value greater than 1, preferably 1.5 to 3, and more preferably 1.5 to 2. Normalize by dividing B _k (t) ^m by the total number of vehicles used in solution t | σ (t) |.

The β (t) is the smoothing of the solution space when applying the local search to the so-called bin packing problem when the feature amount _pi is the delivery amount to i and M is the load capacity. It is the same as that used to do. The bin packing problem is a problem of finding how to pack items in a bin that minimizes the number of bins used. However, the objective function of this problem is the number of bins, and other factors such as the bin filling rate are not considered, so the solution space is flat and local search does not work well. To that end, an index of variability was proposed (for details, see T. Osogami and H. Okano, “Local search algorithms for the bin pouring and the irrestriction to the same relationship”. 29-49, 2003). This indicator decreases in value by moving items from a near empty bin to a full bin when there are near empty and full bins. FIG. 9 shows three ways of packing when there are two bins of capacity 1 and four items of size 0.25. The filling method shown in FIG. 9A is not desirable because it has less variation than the other two filling methods. The filling method in FIG. 9 (2) has a large variation, and if one item is moved, it can be changed to the right filling method. In FIG. 9 (3), one bin is empty, which is most desirable. The present invention achieves a reduction in the number of vehicles by applying this index for the first time in a way that is suitable for the delivery route problem.

Referring to FIG. 4 again, the coefficient a is set to “0” (402). This coefficient represents whether or not β (t) is included in the objective function in the local search. When it is 0, it is not included in the objective function, and when it is 1, it is included in the objective function. As described above, when the current solution S is not updated by the search for the direction in which the number of vehicles and the operation time or the travel distance are shortened (first local search), the search for the direction in which the variation in the load amount between the vehicles is increased. A reduction in the number of vehicles is achieved by performing (second local search). In the aspect shown in FIG. 4, the first local search is performed first and then the second local search is performed. However, the reverse order may be used.

  The coefficient a is set by judging whether the number of iterations τ is strange (403). In the first local search (a = 0) of the first time (τ = 0), β (t) is not included in the objective function. When the first local search is completed and the current solution S is not updated, τ is increased by 1 (412), the result of being determined as an odd number (403), and the coefficient a is set to “1” (404). β (t) is incorporated into the objective function and a second local search is performed (405).

The first (a = 0) and second local search (a = 1) are performed using an objective function represented by the following formula (4).

f (t, a) = (| σ (t) |, aβ (t), _{Σk∈σ (t)} d _k (t)) (4)

Here, parentheses indicate that evaluation is performed in lexicographic order from left to right, and d _k (t) is a solution setting, that is, depending on whether the solution to be obtained is the shortest distance or the shortest time. It represents the travel distance or operating time of the vehicle k at t. For example, if there are two objective function values (A, B) and (C, D), these comparisons in the computer are done as follows:
if (A> C) then assert (A, B)> (C, D)
else if (A <C) then assert (A, B) <(C, D)
else if (B> D) then assert (A, B)> (C, D)
else if (B <D) then assert (A, B) <(C, D)
else assert (A, B) = (C, D)
In Formula (4), when a = 1 (second local search), the total number of vehicles | σ | is compared with β. This is because it has been found that even if the number of vehicles decreases, β increases, that is, there may be a contradiction in the magnitude relationship.

When a = 0 (first local search), a solution with the smallest number of vehicles is searched, and when there are a plurality of solutions with the smallest number of vehicles, the travel distance or operating time of the vehicle among the plurality of solutions. The solution with the smallest sum over all the vehicles is searched (405). In FIG. 4, “arg min” (405) means an argument for obtaining the minimum value. If there are multiple smallest solutions, any one of them may be selected. And the optimal solution S ^best of the solutions S _b the first set obtained, compared in the same manner as described above, when the objective function value of the solution S _b obtained in local search is smaller than the S _b as S ^best Save and update the optimal solution (407).

Next, it is determined whether or not a predetermined end condition is satisfied (408), and if it is satisfied, S ^best is output and the process ends (409). As the termination condition, the upper limit of the number of iterations, the upper limit of the calculation time, the upper limit of the latest number of iterations for which the optimum solution has not been updated, and the like are used. If the termination condition is not satisfied, the solution S _b and the current solution S obtained in the first local search, compared in the same manner as described above (410). If the number of vehicles in the solution S _b is smaller than the number of vehicles in the current solution S, or the total number of vehicles traveling distance or operating time is small even if the number of vehicles is the same (Yes in 410), S _b is saved as the current solution S, the current solution is updated, a neighborhood solution of the new current solution S is read or created (not shown), and the first local search is performed again. Otherwise, the local search iteration number τ is increased by 1 (412), and the second local search is entered.

In the second local search, when τ becomes an even number (Yes in 403), the coefficient a becomes 1 (404), β (t) is incorporated in the objective function, and the number of vehicles is first determined in the vicinity of the current solution S. When there are a plurality of solutions with the smallest number of vehicles, a solution with the smallest index β (t) is searched for and a plurality of solutions with the smallest β (t) are found. In some cases, the solutions with the same β (t) are compared with the sum of the travel distance or operation time of the vehicle, and the solution with the smallest sum of travel distance or operation time is searched. The obtained solution S _b, comparing the objective function used in the optimal solution S ^best with the first local search. I.e., solutions S _b is less the number of vehicles than S ^best, even number of vehicles is the same Compares the travel distance and the like is small, and if so, places the S _b and S ^best (407 ). Next, it is determined whether or not a predetermined end condition has been reached (408). If the predetermined end condition has been reached, S ^best is output and the process ends (409). Reached in the case no, the current and solution S solutions S _b obtained are compared using an objective function used in the second local search. That is, when the number of vehicles is smaller, the number of vehicles is the same but the index β (t) is smaller, or the number of vehicles and β (t) are the same, but the sum of travel distance or operating time is smaller than S If the current solution S is updated by S _b (411). Next, a neighborhood set of new current solutions is read or created (not shown), and the second local search is repeated (405). When the current solution S is not updated, τ is incremented by one, a is set to 0 (402), and a first local search is performed. In this way, the first local search and the second local search are alternately repeated until the predetermined end condition is reached, and the optimal solution S ^best with the smallest number of vehicles is obtained.

Example 1
The method of the present invention was applied to randomly generated input data without a time frame. 100 distribution points were placed in a rectangular area with a random uniform distribution, and a base was placed in the center of the rectangular area. The number of packages to be delivered to each delivery point was randomly set from 1 to 10, and the maximum operation time was such that 100 trucks with a sufficiently large capacity could visit 100 points. The initial optimal solution is to prepare 25 vehicles and use the method of visiting the points closest to the current position among the unvisited points that any vehicle can visit (parallel nearest neighbor method) one after another. Asked.

The results are shown in FIG. Each method when the load capacity of the vehicle is changed from W / 5 to W (horizontal axis) assuming that the total amount of the load is W, and in this embodiment, the average value of the load is 5 × 100 = 500. Indicates the average (vertical axis) of the optimal number of vehicles obtained in 10 iterations. In the figure, when only the first local search (a = 0) is performed for LS, TS is a tabu search described later, BP (load) is the vehicle evaluation value as a loading factor, and BP (util) is the vehicle The evaluation value is an approximate value of the operation rate, BP (rand) is a characteristic value of the delivery point, and BP (const) is the characteristic value of the delivery point is a constant (100 in this embodiment). It is. BP (util ^ 3) is an evaluation value of the vehicle, which is an approximate value of the operation rate, and m = 3. In other settings, m = 2. The results of each method when the loading capacity of each vehicle is (W / 5) × 3 are LS = 4.2, TS = 4.0, BP (load) = 3.4, BP (util) = 3. 3, BP (rand) = 3.4, BP (const) = 3.5, BP (util ^ 3) = 3.4.

  The following was found from the above results. When a second local search is performed with the β (t) term in the objective function, a solution with a smaller number of vehicles is obtained compared to the local search or tabu search regardless of the maximum load capacity constraint (horizontal axis). Can do. This also applies to the case where constants or random numbers are used as the feature quantities of the delivery points. Among the feature amounts, when an approximate value of the operation rate is used, a route with a smaller number of vehicles can be obtained.

The tabu search to compare used the method which referred the method of the nonpatent literature 1. FIG. 11 shows the flow. In the figure, b (s, t) represents a point (base) focused on to generate a neighborhood solution tεN (s) from the solution s. The bases that have been searched once are stored in the tabu list, and the bases in the tabu list are removed from the search candidates for the neighborhood solution. In addition, the upper limit value θ of the size of the taboo list is set to 1/10 of the number of points, and the taboo list is initialized if the current solution S is not updated in 10 iterations continuously. In the figure, in the neighborhood search in step 1103, it is determined to avoid the base included in the taboo list. In steps 1104 and 1105, the tabu list is updated. In step 1108, even when neighborhood solutions S _b obtained in the search is not better than the current solution S, while number of iterations is not updated current solutions is continuously within 10 times (step 1111), the motion of "climbing" Continued local search with forgiveness.

Example 2
Next, an instance of Solomon that is widely used as a test instance with a time frame (for details, see MM Solomon, “Algorithms for the vehicle routing and scheduling programs with time windows constraints,” Operation 35, Research 35, Operations 35). 2, pp.254-265, 1987) to compare the method of the present invention with the above tabu search. There are 100 points. There are six classes of instances of Solomon (random point placement, clustered point placement, etc.). One problem in each class, starting from the initial solution with 25 vehicles, as in Example 1, and the solution and convergence obtained by running up to 100 seconds on a ThinkPad X32 (Intel Pentium M 1.8GHz CPU) Is shown in Table 1 and FIGS.

＊１：http://w.cba.neu.edu/~msolomon/heuristi.htmを参照されたい。

Ｒ２０１及びＲＣ２０１は、車両の積載容量が十分大きいため、最大稼動時間の制約が利いて経路長が制限されるインスタンスである。Ｒ２０１は地点の配置がランダムで、ＲＣ２０１は地点がランダムな配置とクラスタ化された配置の混合になっている。これら２つのインスタンスについて、本発明の方法とＴＳの差が顕著であり、本発明の方法における第２局所探索の効果が大きいことが分かった。

* 1: Refer to http://w.cba.neu.edu/~msolomon/heuristi.htm.

R201 and RC201 are instances in which the path length is limited due to the limitation of the maximum operation time because the vehicle loading capacity is sufficiently large. R201 has a random arrangement of points, and RC201 is a mixture of a random arrangement of points and a clustered arrangement. Regarding these two instances, the difference between the method of the present invention and TS is remarkable, and it was found that the effect of the second local search in the method of the present invention is large.

  R101 and RC101 have a longer maximum operating time than R201 and RC201. Similarly, R101 is also restricted in the maximum operation time and the path length is limited. The RC 101 has strong restrictions on both the maximum operating time and the load capacity, and the path length is limited by any of the restrictions. R101 has a random arrangement of points, and RC101 is a mixture of a random arrangement of points and a clustered arrangement. For these instances as well, the method of the present invention found a solution for fewer vehicles than TS.

  C101 and C201 are clustered point arrangements, where C101 is an instance with a long maximum operating time and C201 is a short instance. The restrictions on both the maximum operating time and the load capacity are strong, and the path length is limited by either restriction. In C101, the optimum solution was obtained by either method, but in C201, the method of the present invention found a solution having a smaller number of vehicles than TS.

The method of the present invention is effective in finding solutions with a reduced number of vehicles in various types of delivery route problems.

It is explanatory drawing which shows an example of the relationship between a delivery route and the number of vehicles. It is the graph which plotted the solution in the example shown in FIG. 1 about the number of vehicles and the travel distance. FIG. 11 is a block diagram illustrating an example of computer hardware in which the present invention can be implemented. 3 is a flowchart illustrating the method of the present invention. It is explanatory drawing which shows the example of the structure of a neighborhood list. It is explanatory drawing which illustrates the solution of a delivery route. It is explanatory drawing which shows the production | generation method of a neighborhood solution. It is explanatory drawing which shows the method of O (1) feasibility check. It is explanatory drawing which shows (beta) (t) in the different solution in a bin packing problem. 3 is a graph showing the results of Example 1. 5 is a flowchart of tabu search used in Examples 1 and 2. In Example 2, it is a graph which shows the result about instance C101. In Example 2, it is a graph which shows the result about instance C201. In Example 2, it is a graph which shows the result about instance R101. In Example 2, it is a graph which shows the result about instance R201. In Example 2, it is a graph which shows the result about instance RC101. In Example 2, it is a graph which shows the result about instance RC201.

Explanation of symbols

301 Computer system 302 CPU
303 Main memory 304 Bus 305 Display controller 306 Display 311 Keyboard

Claims (11)

A method for obtaining delivery routes of a plurality of vehicles by a computer having a storage means,
Create a solution set (N (S)) that is a neighborhood solution of a given current solution S, and repeat the local search for the solution set (N (S)) until a given termination condition is reached. , Updating the current solution S to obtain an optimal solution S ^best ,
In the local search, a step of searching for a solution having the smallest number of vehicles, and when there are a plurality of solutions having the smallest number of vehicles, the plurality of solutions are defined for each vehicle defined by the following equation (1). A step of searching for a solution having the smallest index β (t) indicating a small variation between vehicles of the evaluation value B _k (t) (tεN (S)) defined by the following equation (2) ;
when there are a plurality of solutions having the smallest β (t), a step of searching for a solution having the smallest sum of travel distance or operating time over all vehicles for the plurality of solutions,
B _k (t) = Σ _{iεC k} (t) p _i / M (1)
β (t) = 1- _{Σkεσ (t)} B _k (t) ^m / | σ (t) | (2)
here,
p _i : given feature quantity of each delivery point i M: upper limit value of feature quantity at delivery point visited by one vehicle or total sum of feature quantities over all vehicles σ (t): vehicle used in solution t Set of
| σ (t) |: Total number of vehicles used in solution t C _k (t): Set of delivery points visited by vehicle kεσ (t)
Prior to creating the solution set (N (S)), a feasibility check that can be executed in a constant time regardless of the number of delivery points is performed, and a neighborhood solution is generated after limiting points where the travel distance can be shortened. A method for determining a delivery route for a plurality of vehicles . The step of ^{obtaining the} optimal solution S ^best is a step of repeating the following steps 1) to 9) until a given end condition is reached;
1) A step of performing a first local search for the solution set, and (i) a step of searching for a solution having the smallest number of vehicles,
(Ii) when there are a plurality of solutions having the smallest number of vehicles, a step of searching for a solution having the smallest sum of the traveling distance or operation time of the vehicle over all vehicles among the plurality of solutions;
Performing a first local search comprising:
2) The solution S _b obtained in the first local search has a smaller number of vehicles than the optimum solution S ^best , or the number of vehicles is the same, but the sum of the vehicle travel distance or operation time over all vehicles is If small, updating the optimal solution ^{S best} to save the solution _{S b} as the optimal solution ^{S best,}
3) determining whether or not the end condition is reached, and outputting the S ^best if the end condition is reached;
4) If it is determined not to reach the termination condition in step 3), or less number of vehicles than the first solution S _b is the current solution S obtained in the local search, the vehicle speed is the same If the sum of travel distance or operating time over all the vehicles is small, the solution S _b is saved as the current solution S, the current solution S is updated, and then the step returns to step 1).
5) A step of performing a second local search for a solution set consisting of neighboring solutions of the current solution S in step 1) when the current solution is not updated in step 4). Searching for the smallest number of solutions,
(B) when there are a plurality of solutions having the smallest number of vehicles, a step of searching for a solution having the smallest index β (t) among the plurality of solutions;
(C) when there are a plurality of solutions having the smallest β (t), a step of searching for a solution having the smallest sum of the travel distance or operating time of the vehicle over all the vehicles among the plurality of solutions;
Performing a second local search including:
6) Solution S _b obtained in the second local search, the optimal solution S or less number of vehicles than ^best, if the sum be a number of vehicles are the same over the entire vehicle mileage or operating time is less in stores the solution _{S b} as the optimal solution ^{S best,} updating the optimal solution ^{S best,}
7) determining whether or not the end condition is reached, and outputting the S ^best if the end condition is reached;
8) When it is determined not to reach the termination condition in step 7), or a small number of vehicles than a second solution S _b is the current solution S obtained in the local search, the vehicle speed is the same If the index β (t) is small or the sum of the travel distance or operation time over all vehicles is small even if the number of vehicles and the index β (t) are the same, the S _b Updating the current solution S as a solution S, and performing a second local search again for a solution set consisting of neighboring solutions of the updated current solution S;
9) If S is not updated in step 8), return to step 1) above;
The method of claim 1, wherein: A value the feature amount p _i is defined by the following formula (3),
p _i = nn _i + t _i (3)
(Nn _i : average value of travel time to delivery point closest to delivery point i and travel time to delivery point closest to delivery point t _i : working time at delivery point i)
The method according to claim 1, wherein M is an upper limit value of an operating time of the vehicle. The feature amount p _i is the delivery amount to the delivery point i, M is the upper limit value of the load of the vehicle, the method according to claim 1 or 2. Wherein a constant feature amount p _i is assigned to the delivery point i, M is the sum or the upper limit value thereof, the method according to claim 1 or 2. The method of claim 5 , wherein the constant is 1 and M is the number of points. Wherein a random number feature amount p _i is assigned to the delivery point i, M is the sum over the entire vehicle random number, The method of claim 1 or 2. Wherein m is a number of 1.5 to 3, any one method according to claim 1-7. Wherein a termination condition calculation time, any one method according to claim 1-8. A computer system for determining a delivery route for a plurality of vehicles ,
Storage means for recording information on bases, delivery points, vehicles and articles;
Current solution storage means for storing the current solution S;
Optimal solution storage means for storing the optimal solution S ^best ;
An initial value setting unit that reads information on a base, a delivery point, a vehicle, and an article from the storage unit, obtains an initial current solution S and an optimal solution S ^best , and writes the initial solution S and the optimal solution storage unit;
Solution set calculation means for obtaining a solution set (N (S)) consisting of neighboring solutions of the current solution S by a given method;
Means for reading each neighborhood solution (t) from the solution set calculation means and performing a first local search,
(I) means for searching for a solution having the smallest number of vehicles than the current solution S;
(Ii) when there are a plurality of solutions having the smallest number of vehicles, a means for searching for a solution having the smallest sum of the traveling distance or operation time of the vehicle over all vehicles among the plurality of solutions;
First local search means including:
Means for performing a second local search for the solution set,
(A) means for searching for a solution having the smallest number of vehicles;
(B) When there are a plurality of solutions having the smallest number of vehicles, the following equation (2) of the evaluation value B _k (t) for each vehicle defined by the following equation (1) among the plurality of solutions. A search means for calculating an index β (t) indicating a small variation between vehicles defined by the above and searching for a solution having the smallest index β (t);
B _k (t) = Σ _{iεC k} (t) p _i / M (1)
β (t) = 1- _{Σkεσ (t)} B _k (t) ^m / | σ (t) | (2)
here,
σ (t): set of vehicles used by solution t
| σ (t) |: Total number of vehicles used in solution t C _k (t): Set of delivery points visited by vehicle kεσ (t) p _i : A given feature quantity of each delivery point i M: The upper limit value of the feature quantity at the delivery point visited by one vehicle or the sum of the feature quantities over all vehicles m is a value greater than m: 1 (c) If there is no solution with a small β (t), β (t Search means for searching for a solution having a smaller sum of vehicle travel distance or operation time among the same solutions;
Second local search means including:
Comparing the solution S _b output from the first or second search means and said S ^best, S _b Do small number of vehicles than S ^best, mileage or operation time even number of vehicles is the same If the sum over all vehicles is small, the optimum solution update means for updating S ^best and simultaneously writing the optimum solution storage means,
After comparing the solutions S _b and S ^best , it is determined whether or not a local search end condition has been reached, and when the end condition has been reached, an end condition determination unit that outputs the S ^best ;
If it does not reach the termination condition, the solution S _b output from the first or second search means in comparison with the current solution S, when S _b is a solution of the first searching means or has less number of vehicles than S, if even number of vehicles is less than or equal the sum of the travel distance or running time, when the S _b is a solution of the second searching means is the vehicle than S Even if the number is small, even if the number of vehicles is the same, the index β (t) is small, or even if the number of vehicles and the index β (t) are the same, the total travel distance or working time over all the vehicles is small A current solution update means for updating S and writing to the current solution storage means,
When the current solution S is not updated, the first local search is switched to the second local search, or the second local search is switched to the first local search, and alternately until the end condition is reached. Local search control means to be performed;
Including
Prior to creating the solution set (N (S)), a feasibility check that can be executed in a constant time regardless of the number of delivery points is performed, and a neighborhood solution is generated after limiting points where the travel distance can be shortened. A computer system for determining delivery routes for multiple vehicles . Claim 1 to perform the steps of the method according to any one of 9 to a computer system, a computer program for determining the delivery route of the plurality of vehicles.

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