CN110245818A - Hub location method and apparatus - Google Patents

Abstract

Embodiments of the present invention provide a method and device for selecting a hub location. The method includes: determining the hubness of each pair of nodes in a network; selecting a pair of nodes with the greatest hubness as the only pair of hub nodes in the current network, and setting the current Connect edges between nodes in the network to construct an initial network; each node in the current network includes each hub node and each non-hub node; determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, if the current network hub node If the number of nodes is less than the predetermined number of hub nodes, tree expansion and ring expansion are performed on the current network in turn, and the number of hubs in the current network is increased by one until the predetermined number of hub nodes is reached; the result of the hub location selection corresponding to the current network is output. . The embodiments of the present invention can shorten the solution time and improve the solution accuracy, and provide an efficient solution to the hub location problem in a large-scale network.

Description

Hub site selection method and equipment

technical field

Embodiments of the present invention relate to the technical field of traffic planning, and in particular, to a method and device for selecting a hub location.

Background technique

The problem of hub location exists in many important fields such as transportation and telecommunications. We build hubs in the network to meet the transportation needs of collection, transshipment, and distribution between pairs of nodes. When transporting large flows, economies of scale allow for cost discounts for transport through inter-hub connections.

In the prior art, the hub location result is solved by establishing a single-assignment model or a multiple-assignment model, and assuming that the hub networks of the two models are fully connected; however, in terms of algorithms, precise algorithms (such as Benders Decomposition algorithm) or heuristic algorithm (such as greedy algorithm) to solve the model.

However, although the fully connected allocation model can simplify the problem, the obtained models are far from the actual cases; the Benders decomposition algorithm requires a long solution time, while the greedy algorithm shortens the solution time, but greatly reduces the The quality of understanding; therefore, none of the above solutions can meet the needs.

SUMMARY OF THE INVENTION

Embodiments of the present invention provide a method and device for selecting a hub location, so as to shorten the solution time and improve the accuracy of the solution.

In a first aspect, an embodiment of the present invention provides a method for selecting a hub location, including:

determining the pivotality of each pair of nodes in the network; wherein the pivotality is inversely proportional to the total cost of building each pair of nodes as the only pair of pivot nodes in the network;

Select the pair of nodes with the greatest pivotality as the only pair of pivot nodes in the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest to construct an initial network; where each node in the current network Including each hub node and each non-hub node;

Determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, then perform tree expansion and ring expansion on the current network in turn, so that the total cost of the current network is the lowest , and add one to the number of hubs in the current network until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; output the result of the hub location selection corresponding to the current network.

In a second aspect, an embodiment of the present invention provides a hub site selection device, including:

a determining module, configured to determine the pivotality of each pair of nodes in the network; wherein, the pivotality is inversely proportional to the total cost of constructing each pair of nodes as the only pair of pivot nodes in the network;

The building module is used to select the pair of nodes with the greatest pivotality as the only pair of pivotal nodes of the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest to construct the initial network; Each node in the current network includes each hub node and each non-hub node;

The first processing module is used to determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, perform tree expansion and ring expansion in sequence on the current network to The total cost of the current network is minimized, and the number of hubs in the current network is increased by one until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; the result of the hub location selection corresponding to the current network is output.

In a third aspect, an embodiment of the present invention provides a hub address selection device, including: at least one processor and a memory;

the memory stores computer-executable instructions;

The at least one processor executes computer-implemented instructions stored in the memory to cause the at least one processor to perform the pivot addressing method described in the first aspect and various possible designs of the first aspect above.

In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, where computer-executable instructions are stored in the computer-readable storage medium, and when a processor executes the computer-executable instructions, the first aspect and the first Aspects of the various possible designs described for the hub site selection method.

In the method and device for selecting a hub location provided by this embodiment, the method calculates the hubness of each pair of nodes in the network, and selects a pair of nodes with the greatest hubness to construct an initial network with a pair of hub nodes, and the obtained initial network can be It provides a high starting point for quickly obtaining the results of hub location selection; in addition, through the iterative calculation of the initial network, and in each iteration, tree expansion and ring expansion are performed in sequence until the number of predetermined hub nodes is reached, and the output reaches the predetermined hub. The results of the pivot location selection of the network corresponding to the number of nodes can shorten the solution time and improve the solution accuracy, and provide an efficient solution to the pivot location problem in large-scale networks.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

FIG. 1 is a schematic flowchart 1 of a method for selecting a hub location according to an embodiment of the present invention;

Fig. 2 is an embodiment of the present invention providing n node pairs with the highest pivotality and the optimal solution in the case of p∈{2, 3, 4, 5, 6};

3 is a change diagram of a hub network in a tree expansion operation process provided by an embodiment of the present invention;

4 is a change diagram of a hub network during a ring expansion operation provided by an embodiment of the present invention;

FIG. 5 is a second schematic flowchart of a method for selecting a hub location according to another embodiment of the present invention;

Fig. 6 is the solution obtained by the hub location method provided by the embodiment of the present invention in the CAB, AP, and TR data sets for different network scales n∈{25, 30, 40, 50, 60, 70, 80, 81} gap;

FIG. 7 shows the hub location method provided by the embodiment of the present invention in the CAB, AP and TR data sets for different network scales n∈{25, 30, 40, 50, 60, 70, 80, 81} and enhanced Benders decomposition algorithm Comparison chart of running time;

8 is a comparison diagram of a pivot location method and an enhanced Benders decomposition algorithm provided by an embodiment of the present invention with respect to memory usage;

FIG. 9 is a schematic structural diagram of a hub site selection device provided by another embodiment of the present invention;

FIG. 10 is a schematic diagram of a hardware structure of a hub location selection device provided by an embodiment of the present invention.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The non-fully connected hub location problem required by the present invention is: considering four types of connecting edges (direct connection between non-hub nodes, collection edge from non-hub node to hub node, transit edge between hub nodes and hub node) In the case of assigning edges to non-hub nodes), establish suitable hubs and links at several nodes in the transportation network to minimize the problem of total cost (fixed construction cost and variable transportation cost). In order to achieve this goal, the embodiment of the present invention proposes the concept of "hubbiness" to evaluate the quality of a node as a hub. The pivotality is not only used to screen the initial network under two nodes, but also serves as a guide for the subsequent network expansion process. Based on this, we design an algorithm to iteratively expand the hub network to solve this hub location problem in a short time.

Table 1: Parameters in the non-fully connected hub location problem

Table 2: Decision variables in non-fully connected hub location problem

In the non-fully connected hub location problem, there are four types of connecting edges (direct connection edges between non-hub nodes, collection edges from non-hub nodes to hub nodes, transit edges between hub nodes, and distribution edges from hub nodes to non-hub nodes). ) are represented by the symbols 0, 1, 2, and 3, respectively. Among them, the collection edge and the distribution edge are collectively referred to as the access edge. Based on a series of parameters (Table 1) and decision variables (Table 2), the problem we are trying to solve can be modeled as follows:

in The objective function (1) is to find the optimal cost network structure under the appropriate hubs, edges and corresponding traffic flows. By constraint (2), each OD (origin-destination, origin-destination) pair must use one of the four types of connections to serve the traffic flow therebetween. Constraint (3) The flow conservation equation through the pivot node m. Constraints (4-6) ensure that each hub node can only be connected by access edges and hub edges. Constraints (7-9) ensure the feasibility of the traffic flow path (only the established links can transport traffic). Finally, constraint (10) limits the number of hubs to p.

The following uses specific embodiments to describe the hub location method provided by the embodiments of the present invention.

FIG. 1 is a schematic flowchart 1 of a method for selecting a hub location according to an embodiment of the present invention. As shown in Figure 1, the method includes:

S101. Determine the pivotality of each pair of nodes in the network, wherein the pivotality is inversely proportional to the total cost of constructing each pair of nodes as the only pair of pivot nodes in the network.

Optionally, this embodiment proposes a quality evaluation parameter for a node pair in the network, which is named "hubbiness". For a given pair of nodes (k,m), the value of hubbi ^km is the inverse of the total cost approximation when k and m are the only two hubs in the network.

The algorithm simulates the establishment of hubs on node k and node m, as well as the decision on the construction of directly connected edges and access edges. Starting from a fully connected configuration, we design a greedy search algorithm. First, the direct-connected edges are arranged in ascending order based on the transportation demand (it is less likely to establish direct-connected edges between pairs of non-hub nodes with low transportation demand). For each directly-connected edge, if the total cost is reduced after removal, The removal operation is performed; the access edges are sorted in descending order based on the distance (non-hub nodes are less likely to be connected to distant hubs), and for each access edge, if the total cost is reduced after removal, the removal is performed. Operation; finally, we try to greedily replace the hub endpoint of each access edge with other unconnected hub nodes (alternative hubs are sorted in ascending order based on the distance from the non-hub node).

The pivotality of the node pair $(k,m)$ is defined as follows:

where TC ^km is the total cost in the resulting final configuration. The node pair with the highest pivotality and its corresponding final configuration is taken as the solution for the case of p=2. Referring to FIG. 2 , FIG. 2 is an optimal solution in the case of n node pairs with the highest pivotality and p∈{2, 3, 4, 5, 6} provided by an embodiment of the present invention.

Optionally, the pseudocode for determining the pivotality of each pair of nodes in the network may be:

S102: Select a pair of nodes with the greatest pivotality as the only pair of pivot nodes in the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest, to construct an initial network; Each node includes each hub node and each non-hub node.

Optionally, design an initial network for the two-hub case. Calculate its pivotality for each pair of nodes in the network, i.e. the inverse of the approximation of the total cost in the case of only building the pivot on these two nodes. Select the pair of nodes (k, m) with the highest pivotality, and let k-m and m-k be the only pivot edges. Directly connecting edges between non-hub nodes and connecting edges between hub nodes and non-hub nodes are configured according to the network generated when calculating the hubness.

S103. Determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, perform tree expansion and ring expansion on the current network in turn, so that the total number of the current network The cost is the lowest, and the number of hubs in the current network is increased by one until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; the result of the hub location selection corresponding to the current network is output.

Optionally, this step aims to obtain an initial solution for the p>2 case by means of two network design patterns (Tree-Extension and Cycle-Extension).

First, the steps of tree expansion are introduced. For a given network of p hubs, tree expansion replaces one of the hubs and creates another hub to efficiently branch off the hub network.

Let Nei ^h denote the set of adjacent hubs of hub h, we sort all non-hub nodes in ascending order based on the hubness deviation relative to hub h (see formula (12) for the definition of this parameter), and select the top cn nodes to add The upper node h itself forms a set. Experiments show is sufficient to obtain an excellent solution.

Referring to FIG. 3, FIG. 3 is a change diagram of a hub network during a tree expansion operation according to an embodiment of the present invention. Specific steps can include:

Step S1031. In the initial network of Fig. 3(1), for each hub edge l, we select two hub nodes h ₁ and h ₂ (these two nodes may be the same).

Step S1032, if the node pair (h ₁ , h ₂ ) has not appeared (the nodes that have appeared will be recorded in the set G), for For each _{node s1} and each non _{- hub} node _s2 in Edges s ₂ -h ₂ , h ₂ -s ₂ (Figure 3(3)), and initialize the directly connected edge and the access room.

Step S1033. Starting from this initial network, we design a greedy search algorithm: based on the transportation demand, the direct-connected edges are arranged in ascending order (it is less likely to establish direct-connected edges between pairs of non-hub nodes with small transportation requirements) , for each directly connected edge, if the total cost is reduced after removal, the removal operation is performed; the access edges are sorted in descending order based on distance (non-hub nodes are less likely to be connected to long-distance hubs), for each Access edges, if the total cost is reduced after removal, perform the removal operation; try to greedily replace the hub endpoint of each access edge with other unconnected hub nodes (the alternative hub is based on the distance from the non-hub node. to sort in ascending order).

Step S1034 , when the pivotality is calculated for a pair of nodes, there are only two (unidirectional) pivot edges between the two pivot nodes. But the situation becomes more complicated with more than two pivot edges. In addition, in the above operation, only two-way edges are built between the hubs. If the fixed cost of building hub edges is very expensive, building unidirectional rings in the hub network may be a better option. Therefore, the embodiment of the present invention proposes a sub-operation of tree expansion, which is named "tree-close". After connecting the new hub s ₂ and the hub h ₂ , we greedily establish links between the hub s ₂ and other hubs, as long as the total cost can be reduced (Figure 3(4)).

Optionally, for each discovered hinge ring with reverse hinge edges, we simulate removing all its reverse hinge edges, thus generating a unidirectional hinge ring (Fig. 3(5)). If the total cost is reduced, the removal of the reverse hinge edge is performed. After all one-way loops have been explored, the optimal solution is taken as the solution of the number closure operation.

Optionally, the pseudocode of the tree expansion algorithm can be:

The tree expansion mainly expands the hub network through the two-way connection between the hubs. Although its sub-operation tree closure considers the case of one-way hinge rings, it is only for the special case of generating a new ring from the tree, and cannot cover the process of expanding from a small ring to a large ring. Therefore, the embodiment of the present invention proposes another operation "Cycle-Extension".

Referring to FIG. 4 , FIG. 4 is a change diagram of a hub network during a ring expansion operation according to an embodiment of the present invention. Specific steps can include:

Step S1035, in the initial hub network in Fig. 4(1), for each hub edge h ₁ -h ₂ , we select each endpoint (eg h ₁ ). for collection For each node in (say s ₁ ), the simulation replaces hub h ₁ with node s ₁ (Fig. 4(2)).

Step S1036 , for each hub node s ₂ , simulate a new hub at s ₂ , and replace the connecting edge s ₁ -h ₂ with the hub path s ₁ -s ₂ -h ₂ (Fig. 4(3)).

Step S1037, then we perform a greedy search algorithm similar to that in the process of calculating pivotality for the directly connected edges and the access edges: based on the transportation demand, the directly connected edges are sorted in ascending order (establish a direct connection between pairs of non-hub nodes with small transportation requirements). The possibility of connecting the edges is small), for each directly connected edge, if the total cost is reduced after removal, the removal operation is performed; the access edges are sorted in descending order based on the distance (the possibility that the non-hub node is connected to the distant hub For each access edge, if the total cost is reduced after removal, perform the removal operation; try to greedily replace the hub endpoint of each access edge with other unconnected hub nodes (alternate hubs). In ascending order based on the distance from the non-hub node).

Step S1038 , notice that when the number of hinges is increased, the direction of the hinge edges in the optimal solution may change. Therefore, the present invention attempts to reverse all hub edges and update the total cost (Fig. 4(4)).

After exploring all cases of tree expansion and ring expansion, the solution with the lowest total cost is chosen as the final solution for this step.

The pivot location method provided by this embodiment calculates the pivotality of each pair of nodes in the network, and selects a pair of nodes with the greatest pivotality to construct an initial network with a pair of pivot nodes, and the obtained initial network can quickly obtain the pivot. The location selection result provides a higher starting point; in addition, through the iterative calculation of the initial network, and in each iteration, tree expansion and ring expansion are performed in turn until the predetermined number of hub nodes is reached, and the output when the predetermined number of hub nodes is reached. The results of the hub location selection corresponding to the network can shorten the solution time and improve the solution accuracy, and provide an efficient solution to the hub location problem in large-scale networks.

FIG. 5 is a second schematic flowchart of a method for selecting a hub location according to another embodiment of the present invention. As shown in Figure 5, the method includes:

S501. Determine the pivotality of each pair of nodes in the network; wherein the pivotality is inversely proportional to the total cost of constructing each pair of nodes as the only pair of pivot nodes in the network.

Optionally, in a specific embodiment, this step may specifically include:

S5011. Select any node pair in the pivot node pair to be determined as the only pair of pivot nodes in the current network;

S5012. Fully connect each node in the current network to obtain the direct connection edge, the access edge and the hub edge;

S5013. Determine the total cost under the current network configuration; wherein the total cost includes: the construction cost of the directly connected edge, the access edge, the hub edge and the hub node, and the transportation cost between nodes;

S5014. According to the total cost, process the direct connection edge and the access edge of the current network through a greedy algorithm to reduce the total cost and obtain the target network configuration;

In a specific embodiment, this step may specifically include:

S50141. Arrange the directly connected edges in ascending order according to the transportation demand of each directly connected edge, and perform a removal operation on each of the directly connected edges in sequence according to the ascending order; wherein, the removal operation includes: judging Whether the total cost is reduced after the direct connection edge to be executed is removed, if the total cost is reduced after the direct connection edge to be executed is removed, the directly connected edge to be executed is removed;

S50142. Arrange the access edges in descending order according to the length of each access edge, and perform a removal operation on each access edge in sequence according to the descending order; wherein, the removal operation includes: judging that the access edge to be executed will be removed. Whether the total cost is reduced after the incoming edge is removed, if the total cost is reduced after the to-be-executed access edge is removed, the to-be-executed access edge is removed;

S50143. Perform a hub node replacement operation on each access edge after the removal operation in sequence; the hub node replacement operation includes: according to the distance between each candidate hub node and the non-hub node of the access edge to be executed, replace The candidate hub nodes are arranged in ascending order, and the hub nodes that are to be executed access edges are replaced in sequence according to the ascending order; it is judged whether the total cost is reduced after replacing the hub nodes of the access edges to be executed with the candidate nodes. After the total cost is reduced by replacing the hub node of the access edge to be executed with the candidate node, the hub node of the access edge to be executed is replaced.

S5015. Determine the pivotality of the selected node pair according to the total cost under the target network configuration;

S5016. Repeat the above steps until the pivotal determination of all node pairs in the network is completed.

S502. Select a pair of nodes with the greatest pivotality as the only pair of pivot nodes in the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest, to construct an initial network; Each node includes each hub node and each non-hub node;

S503. Determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, perform tree expansion and ring expansion on the current network in turn, so that the total number of the current network The cost is the lowest, and the number of hubs in the current network is increased by one until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; the result of the hub location selection corresponding to the current network is output.

In a specific embodiment, the tree expansion may include:

S5031. Construct a hub edge set of the current network; wherein the hub edge is a bidirectional hub edge;

S5032. Repeat the following steps until each hub edge in the hub edge set is traversed, and output the corresponding hub location result when the total cost is the lowest, as the initial network for subsequent operations:

S5033. Select the first hub node h1 and the second hub node h2 of any hub edge to be tree-expanded in the hub-edge set as the hub node to be tree-expanded;

S5034. Arrange the non-hub nodes in ascending order according to the pivotal deviation of the hub nodes to be expanded in the tree, and select the first cn non-hub nodes in the ascending order to form a second hub together with the hub nodes to be replaced set; wherein, the cn is a positive integer;

S5035. Repeat the following steps until each non-hub node in the second hub combination is traversed:

S5036. Select any non-hub node in the second hub set as the first non-hub node, and another non-hub node as the second non-hub node;

S5037. Swap roles between the first hub node and the first non-hub node, use the second non-hub node as a third hub node, and establish the third hub node and each non-hub node in the current network an access edge between the hub nodes, and establishes a direct connection edge between the first hub node after changing roles and each non-hub node in the current network;

S5038. Determine the total cost of the current network, and process the direct connection edge and the access edge of the current network through a greedy algorithm according to the total cost to reduce the total cost;

S5039: Find the hub rings in the current network, and perform the following steps for each hub ring in turn: remove the reverse hub edge of the hub ring to be executed; if the cost after removal is lower than the total cost before removal, then Remove the reverse pivot edge of the pivot ring to be executed.

In a specific embodiment, the ring expansion may include:

S50310. Construct a hub ring set of the current network; repeat the following steps until each hub ring in the hub ring set is traversed, and output the hub location result corresponding to the lowest total cost as the final hub location result, or As an initial network for subsequent operations:

S50311. Select the first endpoint of any pivot edge in any pivot ring in the pivot ring set as the pivot node to be expanded; wherein any pivot edge is the connection between the first endpoint and the second endpoint side;

S50312. Arrange the non-hub nodes in ascending order according to the pivotal deviation of the hub nodes to be expanded, and select the first dn non-hub nodes in the ascending order to form a third non-hub node together with the hub nodes to be expanded. hub set; wherein, the dn is a positive integer;

S50313. Repeat the following steps until each non-hub node in the second hub set is traversed:

S50314. Select any non-hub node in the second hub set as a third non-hub node, and another non-hub node as a fourth non-hub node;

S50315. Swap roles between the expansion hub node to be looped and the third non-hub node; use the fourth non-hub node as the fourth hub node;

S50316. Replace the pivot edge between the third non-hub node and the second endpoint after the roles are switched with the pivot edge between the fourth pivot node and the second endpoint and the fourth pivot node and the role after switching the hub edge of the third non-hub node;

S50317. Determine the total cost of the current network, and process the directly connected edges and access edges of the current network through a greedy algorithm according to the total cost to reduce the total cost;

S50318. Perform a reverse operation on the hub rings in the current network in sequence; the reverse operation includes: determining whether the total cost of the hub ring after reversal is reduced, and if the total cost is reduced, reverse the hub ring.

S504: Optimizing the hub site selection result through a variable neighborhood search algorithm, and outputting the optimized hub site selection result.

In a specific embodiment, this step may specifically include:

S5041, taking the pivot node of the current network as the initial solution set, and determining the initial cost corresponding to the initial solution set;

S5042, selecting any pivot node in the initial solution set to perform role exchange with any non-pivot node to obtain a neighborhood set;

S5043. Calculate the neighborhood cost corresponding to the neighborhood set, and if the neighborhood cost is less than the initial cost, update the neighborhood set to the initial solution set;

S5044. After repeating the above steps S5041 to S5043 for a predetermined number of times, output the result of the hub location selection corresponding to the current initial solution combination.

In this embodiment, the solution obtained by incremental network design is already very good, and the median and the maximum value of the difference between the solution obtained in the experiment and the optimal solution are 0.37% and over 3%, respectively. Therefore, the embodiments of the present invention use Variable Neighborhood Search (VNS) to explore better solutions based on the solutions obtained by incremental network design. There are three VNS strategies for solving the hub location problem: Sequential strategy (Seq-VNS), nested strategy (Nest-VNS) and mixed strategy (Mix-VNS). Seq-VNS requires the shortest running time but explores the least neighborhoods; Nest-VNS explores a wide range of neighborhoods but its running time is unacceptable; Mix-VNS directly strikes a balance between neighborhood size and running time. Therefore, the embodiment of the present invention adopts Mix-VNS.

Optionally, the pseudocode of the variable neighborhood algorithm can be:

As shown in the pseudocode above, for the initial solution with the set of hubs H ^o , we generate all sets of hubs at the nested level that differ from H ^o by only one hub, and these sets of hubs are called neighborhoods. Subsequently, other local searches (remove/add direct edges, remove/add/replace access edges, remove/add/replace hub edges) are greedily applied to each neighbor and update the current at each step to get the best solution. If the solution is not improved in a given number of consecutive iterations, the algorithm terminates.

The beneficial effects of the hub location method provided by the embodiment of the present invention are as follows: First, the embodiment of the present invention proposes the concept of "hubbiness" to evaluate the quality of the node pair as a hub, and designs a fast solution Algorithm for the pivotality of all nodes in the network. The pivotality is not only used to screen the initial network under two nodes, but also serves as a guide for the subsequent network expansion process. Secondly, for the high-complexity hub location problem that is not fully connected, traditional algorithms can either provide accurate solutions but require extremely long solution time, or greatly shorten the solution time but sharply deteriorate the quality of the obtained solutions. In the present invention, however, by adopting a series of network design rules, the computational complexity of the problem is greatly reduced, so that a high-quality solution can be obtained in a short time. First, it makes it possible to solve the hub location problem in a larger scale network in a reasonable time (200 node scale problems can be solved in this paper); second, it can be used for timely redesign in special cases network. In addition, compared with the best performing enhanced Benders decomposition in the traditional algorithm, this algorithm uses 2 orders of magnitude less memory than the former (for the case of 80 nodes, the former requires about 150GB of memory, while this algorithm only needs about 1GB) . This makes it possible to solve the hub location problem in a larger network under a limited computing platform.

Referring to FIG. 6, FIG. 6 shows the results of the hub location method provided by the embodiment of the present invention for different network scales n∈{25, 30, 40, 50, 60, 70, 80, 81} in the CAB, AP, and TR data sets. Gap to find the solution. The gap of the obtained solution is the percentage difference between the obtained solution and the optimal solution. For the case of n = 25, 30, the parameters (f, b) ∈ {([2500, 3000, 3500, 3000], [0.08, 0.04, 0.03, 0.04]), ([1000, 1000, 1000, 1000], [0.10, 0.04, 0.02, 0.04])} are used; for n ≥ 40, due to the too long solution time of the exact algorithm (enhanced Benders decomposition) that provides the optimal solution, we only test the second set of cost parameters. The fixed construction cost of the hub in all cases is The number of hubs is set to p=2,3,4,5. The results show that, except for one case under 25 nodes, the solution of all other cases solved by the present invention is less than 1%, and more than 90% of the solutions are optimal.

Referring to FIG. 7, FIG. 7 shows the summation of the hub location method provided by the embodiment of the present invention for different network scales n∈{25, 30, 40, 50, 60, 70, 80, 81} in the CAB, AP, and TR data sets. A comparison graph of the runtime of the enhanced Benders decomposition algorithm. The parameters of fixed and transport costs are set as f = [1000, 1000, 1000, 1000] and b = [0.10, 0.04, 0.02, 0.04], the fixed construction cost of the hub in all cases is The number of hubs is set to p=2,3,4,5. Note that the y-axis is on a log scale. This algorithm and the enhanced Benders decomposition algorithm are represented by a square and a circle respectively, and the fitting curve of the operation time is also given. Experiments show that the algorithm runs 2-3 orders of magnitude faster than the enhanced Benders decomposition algorithm. For one case of the sparring scale, the enhanced Benders decomposition algorithm took 230 hours to get the result, while the present algorithm found the optimal solution in 20 minutes. The fitting curve of the running time shows that the computational complexity of the enhanced Benders decomposition algorithm is O(n ⁶ ) while that of the present algorithm is O(n ⁴ ).

Referring to FIG. 8, FIG. 8 is a comparison diagram of the memory usage of the pivot location method and the enhanced Benders decomposition algorithm provided by the embodiment of the present invention. The parameters for fixed and transport costs are set as f = [1000, 1000, 1000, 1000] and b = [0.10, 0.04, 0.02, 0.04], and the fixed construction cost of the hub in all cases is Figure 8(1) shows the memory usage under the network of different scales in the case of p=2. Note that the y-axis is on a logarithmic scale, and the fitting curves of this algorithm and the enhanced Benders decomposition algorithm are also given, and the corresponding fitting functions are and Figure 8(2) is the evolution of memory usage over time in the TR81 dataset for the case of p=5, noting that both the x- and y-axes are on a logarithmic scale. It can be seen that the enhanced Benders decomposition algorithm requires about 100 times the memory of this algorithm.

Finally, Table 3 presents the results of this algorithm for larger cases. At this scale, other algorithms have been unable to give reasonable solutions in acceptable time. The parameters of fixed and transport costs are set as f = [1000, 1000, 1000, 1000] and b = [0.10, 0.04, 0.02, 0.04], and the fixed construction cost of the hub is f _k ^H = 10 ⁷ in all cases, The number of pivots is set to p=2,3,4,5. It can be seen that the algorithm provides an understanding of the problem of reaching the scale of 200 nodes in 11 hours.

Table 3: Solution of the present invention to large-scale networks

FIG. 9 is a schematic structural diagram of a hub site selection device provided by another embodiment of the present invention. As shown in FIG. 9 , the hub site selection device 90 includes: a determination module 901 , a construction module 902 and a first processing module 903 .

A determining module 901, configured to determine the pivotality of each pair of nodes in the network; wherein the pivotality is inversely proportional to the total cost of constructing each pair of nodes as the only pair of pivot nodes in the network;

The building module 902 is used to select a pair of nodes with the greatest pivotality as the only pair of pivot nodes of the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest, to construct an initial network; Each node in the current network includes each hub node and each non-hub node;

The first processing module 903 is configured to determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, perform tree expansion and ring expansion in sequence on the current network, The total cost of the current network is minimized, and the number of hubs in the current network is increased by one until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; the result of the hub location selection corresponding to the current network is output.

In the hub location selection device provided by the embodiment of the present invention, the device calculates the hubness of each pair of nodes in the network by determining the module, and selects the pair of nodes with the greatest hubness through the building module to construct an initial network with a pair of hub nodes, and obtains The initial network can provide a high starting point for quickly obtaining the results of the hub location; in addition, the initial network is iteratively calculated by the first processing module, and tree expansion and ring expansion are performed in sequence in each iteration until the predetermined hub is reached The number of nodes, and output the corresponding hub location results when the number of hub nodes reaches a predetermined number, can shorten the solution time, improve the solution accuracy, and provide an efficient solution to the hub location problem in large-scale networks.

Optionally, the hub site selection device 90 further includes: a second processing module 904 .

The second processing module 904 is configured to optimize the hub location selection result through a variable neighborhood search algorithm, and output the optimized hub location result.

Optionally, the determining module 901 is specifically configured to:

Select any node pair in the pivot node pair to be determined as the only pair of pivot nodes in the current network;

Fully connecting each node in the current network to obtain the directly connected edge, the access edge and the hub edge;

Determine the total cost under the current network configuration; wherein the total cost includes: the total cost of the directly connected edge, the access edge and the hub edge, and the total cost of the hub node;

According to the total cost, the direct connection edge and the access edge of the current network are processed through a greedy algorithm to reduce the total cost and obtain the target network configuration;

Determine the pivotality of the selected node pair according to the total cost under the target network configuration;

Repeat the above steps until the pivotal determination of all node pairs in the network is completed.

Optionally, the determining module 901 is specifically configured to:

Perform the removal operation on each directly connected edge of the current network through the greedy algorithm;

Perform the removal operation on each access edge of the current network through a greedy algorithm;

The replacement operation is performed on each access edge of the current network through a greedy algorithm.

Optionally, the determining module 901 is specifically configured to:

According to the size of the transportation demand of each directly connected edge, arrange each directly connected edge in ascending order, and perform a removal operation on each of the directly connected edges in sequence according to the ascending order; wherein, the removal operation includes: judging the Whether the total cost is reduced after the direct-connected edge is removed; if the total cost is reduced after the to-be-executed direct-connected edge is removed, the to-be-executed direct-connected edge is removed;

According to the length of each access edge, the access edges are arranged in descending order, and a removal operation is performed on each access edge in sequence according to the descending order; wherein, the removal operation includes: judging that the access edge to be executed will be removed. Whether the total cost is reduced after the removal, if the total cost is reduced after the access edge to be executed is removed, the access edge to be executed is removed;

Performing a hub node replacement operation on each access edge after the removal operation is performed in sequence; the replacement hub node operation includes: according to the distance between each candidate hub node and the non-hub node of the access edge to be performed, replace each backup node The selected hub nodes are arranged in ascending order, and the hub nodes that are to be executed access edges are replaced in sequence according to the ascending order; it is judged whether the total cost is reduced after replacing the hub nodes of the to-be-executed access edges with the alternative nodes. After the total cost is reduced after the hub node executing the access edge is replaced with the candidate node, the hub node of the to-be-executed access edge is replaced.

Optionally, the first processing module 903 is specifically configured to:

Construct a hub edge set of the current network; wherein the hub edge is a bidirectional hub edge;

Repeat the following steps until each hub edge in the hub edge set is traversed, and output the corresponding hub location result when the total cost is the lowest, as the initial network for subsequent operations:

Selecting the first hub node h1 and the second hub node h2 of any hub edge to be tree-expanded in the hub-edge set as the hub node to be tree-expanded;

Arrange the non-hub nodes in ascending order according to the pivotal deviation of the hub nodes to be expanded in the tree, and select the first cn non-hub nodes in the ascending order to form a second hub set together with the hub nodes to be replaced; Wherein, the cn is a positive integer;

The following steps are repeated until each non-hub node in the second hub combination is traversed:

selecting any non-hub node in the second hub set as the first non-hub node, and another non-hub node as the second non-hub node;

Exchange roles between the first hub node and the first non-hub node, use the second non-hub node as a third hub node, and establish the third hub node and each non-hub node in the current network The access edge between, establishes the direct connection edge between the first hub node after the role change and each non-hub node in the current network;

Determine the total cost of the current network, and process the direct connection edges and access edges of the current network through a greedy algorithm according to the total cost to reduce the total cost;

Find the hub rings in the current network, and perform the following steps for each hub ring in turn: remove the reverse hub edge of the hub ring to be executed; if the cost after removal is lower than the total cost before removal, remove The reverse pivot edge of the pivot ring to be executed.

Optionally, the first processing module 903 is specifically configured to:

Construct the hub ring set of the current network; repeat the following steps until each hub ring in the hub ring set is traversed, and output the corresponding hub location result when the total cost is the lowest, as the final hub location result, or as a follow-up The initial network of operations:

Selecting the first endpoint of any pivot edge in any pivot ring in the pivot ring set as the pivot node to be expanded; wherein the any pivot edge is a connecting edge between the first endpoint and the second endpoint;

According to the pivotal deviation of the hub nodes to be expanded, the non-hub nodes are arranged in ascending order, and the first dn non-hub nodes in the ascending order are selected to form a third hub set together with the hub nodes to be expanded. ; wherein, the dn is a positive integer;

The following steps are repeated until each non-hub node in the second hub set is traversed:

selecting any non-hub node in the second hub set as a third non-hub node, and another non-hub node as a fourth non-hub node;

Exchanging roles between the expansion hub node to be looped and the third non-hub node; using the fourth non-hub node as the fourth hub node;

Replacing the pivot edge between the third non-hub node and the second endpoint after changing roles with the pivot edge between the fourth pivot node and the second endpoint and the fourth pivot node and the pivot edge after changing roles The hub edge of the third non-hub node;

Determine the total cost of the current network, and process the direct connection edges and access edges of the current network through a greedy algorithm according to the total cost to reduce the total cost;

A reverse operation is performed on the hub rings in the current network in sequence; the reverse operation includes: determining whether the total cost of the hub ring after reversal is reduced, and if the total cost is reduced, the hub ring is reversed.

Optionally, the second processing module 904 is specifically configured to:

Take the pivot node of the current network as the initial solution set, and determine the initial cost corresponding to the initial solution set;

Selecting any pivot node in the initial solution set to exchange roles with any non-pivot node to obtain a neighborhood set;

Calculate the neighborhood cost corresponding to the neighborhood set, if the neighborhood cost is less than the initial cost, update the neighborhood set to the initial solution set;

After repeating the above steps for a predetermined number of times, output the current initial solution combined with the corresponding hub location result.

The endpoint detection device provided by the embodiment of the present invention can be used to execute the above method embodiments, and its implementation principle and technical effect are similar, and details are not described herein again in this embodiment.

FIG. 10 is a schematic diagram of a hardware structure of a hub location selection device provided by an embodiment of the present invention. As shown in FIG. 10 , the hub address selection device 100 provided in this embodiment includes: at least one processor 1001 and a memory 1002 . The processor 1001 and the memory 1002 are connected through a bus 1003 .

In a specific implementation process, the at least one processor 1001 executes the computer-executed instructions stored in the memory 1002, so that the at least one processor 1001 executes the pivot addressing method performed by the pivot addressing device 100 above.

For the specific implementation process of the processor 1001, reference may be made to the foregoing method embodiments, and the implementation principles and technical effects thereof are similar, and details are not described herein again in this embodiment.

In the above-mentioned embodiment shown in FIG. 10, it should be understood that the processor may be a central processing unit (English: Central Processing Unit, CPU for short), or other general-purpose processors, digital signal processors (English: Digital Signal Processor, referred to as DSP), application specific integrated circuit (English: Application Specific Integrated Circuit, referred to as: ASIC) and the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in conjunction with the invention can be directly embodied as executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

The memory may include high-speed RAM memory, and may also include non-volatile storage NVM, such as at least one disk memory.

The bus may be an industry standard architecture (Industry Standard Architecture, ISA) bus, a Peripheral Component (Peripheral Component, PCI) bus, or an extended industry standard architecture (Extended Industry Standard Architecture, EISA) bus, or the like. The bus can be divided into address bus, data bus, control bus and so on. For convenience of representation, the buses in the drawings of the present application are not limited to only one bus or one type of bus.

The present application also provides a computer-readable storage medium, where computer-executable instructions are stored in the computer-readable storage medium, and when the processor executes the computer-executable instructions, the above-mentioned pivot addressing method performed by the pivot addressing device is implemented.

The present application also provides a computer-readable storage medium, where computer-executable instructions are stored in the computer-readable storage medium, and when the processor executes the computer-executable instructions, the above-mentioned pivot addressing method performed by the pivot addressing device is implemented.

The above-mentioned computer-readable storage medium, the above-mentioned readable storage medium can be realized by any type of volatile or non-volatile storage device or their combination, such as static random access memory (SRAM), electrically erasable Programmable Read Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read Only Memory (PROM), Read Only Memory (ROM), Magnetic Memory, Flash Memory, Magnetic or Optical Disk. A readable storage medium can be any available medium that can be accessed by a general purpose or special purpose computer.

An exemplary readable storage medium is coupled to the processor such that the processor can read information from, and write information to, the readable storage medium. Of course, the readable storage medium can also be an integral part of the processor. The processor and the readable storage medium may be located in application specific integrated circuits (Application Specific Integrated Circuits, ASIC for short). Of course, the processor and the readable storage medium may also exist in the device as discrete components.

Those of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments may be completed by program instructions related to hardware. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the steps including the above method embodiments are executed; and the foregoing storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (10)

1. A hub site selection method, characterized in that, comprising: determining the pivotality of each pair of nodes in the network; wherein the pivotality is inversely proportional to the total cost of building each pair of nodes as the only pair of pivot nodes in the network; Select the pair of nodes with the greatest pivotality as the only pair of pivot nodes in the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest to construct an initial network; where each node in the current network Including each hub node and each non-hub node; Determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, then perform tree expansion and ring expansion on the current network in turn, so that the total cost of the current network is the lowest , and add one to the number of hubs in the current network until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; output the result of the hub location selection corresponding to the current network. 2. The method according to claim 1, wherein the method further comprises: The hub site selection result is optimized through a variable neighborhood search algorithm, and the optimized hub site selection result is output. 3 . The method according to claim 1 , wherein the connecting edges between the non-hub nodes are direct connecting edges, the connecting edges between the pivot nodes and the non-hub nodes are access edges, and the connecting edges between the hub nodes are access edges. 4 . The edge is a hub edge; the determination of the hubness of each pair of nodes in the network includes: Select any node pair in the pivot node pair to be determined as the only pair of pivot nodes in the current network; Fully connecting each node in the current network to obtain the directly connected edge, the access edge and the hub edge; Determine the total cost under the current network configuration; wherein the total cost includes: the construction cost of the directly connected edge, the access edge, the hub edge and the hub node, and the transportation cost between nodes; According to the total cost, the direct connection edge and the access edge of the current network are processed through a greedy algorithm to reduce the total cost and obtain the target network configuration; Determine the pivotality of the selected node pair according to the total cost under the target network configuration; Repeat the above steps until the pivotal determination of all node pairs in the network is completed. 4. The method according to claim 3, wherein the processing of the direct connection edge and the access edge of the current network by a greedy algorithm comprises: Perform the removal operation on each directly connected edge of the current network through the greedy algorithm; Perform the removal operation on each access edge of the current network through a greedy algorithm; The replacement operation is performed on each access edge of the current network through a greedy algorithm. 5. The method of claim 1, wherein the tree expansion comprises: Construct a hub edge set of the current network; wherein the hub edge is a bidirectional hub edge; Repeat the following steps until each hub edge in the hub edge set is traversed, and output the corresponding hub location result when the total cost is the lowest, as the initial network for subsequent operations: Selecting the first hub node h1 and the second hub node h2 of any hub edge to be tree-expanded in the hub-edge set as the hub node to be tree-expanded; Arrange the non-hub nodes in ascending order according to the pivotal deviation of the hub nodes to be expanded in the tree, and select the first cn non-hub nodes in the ascending order to form a second hub set together with the hub nodes to be replaced; Wherein, the cn is a positive integer; The following steps are repeated until each non-hub node in the second hub combination is traversed: selecting any non-hub node in the second hub set as the first non-hub node, and another non-hub node as the second non-hub node; Exchange roles between the first hub node and the first non-hub node, use the second non-hub node as a third hub node, and establish the third hub node and each non-hub node in the current network The access edge between, establishes the direct connection edge between the first hub node after the role change and each non-hub node in the current network; Determine the total cost of the current network, and process the direct connection edges and access edges of the current network through a greedy algorithm according to the total cost to reduce the total cost; Find the hub rings in the current network, and perform the following steps for each hub ring in turn: remove the reverse hub edge of the hub ring to be executed; if the cost after removal is lower than the total cost before removal, remove The reverse pivot edge of the pivot ring to be executed. 6. The method of claim 1, wherein the ring expansion comprises: Construct the hub ring set of the current network; repeat the following steps until each hub ring in the hub ring set is traversed, and output the corresponding hub location result when the total cost is the lowest, as the final hub location result, or as a follow-up The initial network of operations: Selecting the first endpoint of any pivot edge in any pivot ring in the pivot ring set as the pivot node to be expanded; wherein the any pivot edge is a connecting edge between the first endpoint and the second endpoint; According to the pivotal deviation of the hub nodes to be expanded, the non-hub nodes are arranged in ascending order, and the first dn non-hub nodes in the ascending order are selected to form a third hub set together with the hub nodes to be expanded. ; wherein, the dn is a positive integer; The following steps are repeated until each non-hub node in the second hub set is traversed: selecting any non-hub node in the second hub set as a third non-hub node, and another non-hub node as a fourth non-hub node; Exchanging roles between the expansion hub node to be looped and the third non-hub node; using the fourth non-hub node as the fourth hub node; Replacing the pivot edge between the third non-hub node and the second endpoint after changing roles with the pivot edge between the fourth pivot node and the second endpoint and the fourth pivot node and the pivot edge after changing roles The hub edge of the third non-hub node; Determine the total cost of the current network, and process the direct connection edges and access edges of the current network through a greedy algorithm according to the total cost to reduce the total cost; A reverse operation is performed on the hub rings in the current network in sequence; the reverse operation includes: determining whether the total cost of the hub ring after reversal is reduced, and if the total cost is reduced, the hub ring is reversed. 7. The method according to any one of claims 2-6, wherein the said hub location selection result is optimized by a variable neighborhood search algorithm, and the optimized hub location result is output, comprising: Take the pivot node of the current network as the initial solution set, and determine the initial cost corresponding to the initial solution set; Selecting any pivot node in the initial solution set to exchange roles with any non-pivot node to obtain a neighborhood set; Calculate the neighborhood cost corresponding to the neighborhood set, if the neighborhood cost is less than the initial cost, update the neighborhood set to the initial solution set; After repeating the above steps for a predetermined number of times, output the current initial solution combined with the corresponding hub location result. 8. A hub site selection equipment, characterized in that, comprising: a determining module, configured to determine the pivotality of each pair of nodes in the network; wherein, the pivotality is inversely proportional to the total cost of constructing each pair of nodes as the only pair of pivot nodes in the network; The building module is used to select the pair of nodes with the greatest pivotality as the only pair of pivotal nodes of the current network, and set the edges between the nodes in the current network according to the network configuration when the pivotality is the greatest to construct the initial network; Each node in the current network includes each hub node and each non-hub node; The first processing module is used to determine whether the number of hub nodes in the current network is equal to the predetermined number of hub nodes, and if the number of hub nodes in the current network is less than the predetermined number of hub nodes, perform tree expansion and ring expansion in sequence on the current network to The total cost of the current network is minimized, and the number of hubs in the current network is increased by one until the number of hub nodes in the current network is equal to the predetermined number of hub nodes; the result of the hub location selection corresponding to the current network is output. 9. A hub location selection device, comprising: at least one processor and a memory; the memory stores computer-executable instructions; The at least one processor executes the computer-executable instructions stored in the memory to cause the at least one processor to perform the pivot addressing method of any one of claims 1-7. 10. A computer-readable storage medium, characterized in that, computer-executable instructions are stored in the computer-readable storage medium, and when a processor executes the computer-executable instructions, the method as claimed in any one of claims 1 to 7 is implemented. The hub site selection method described above.