CN110245818A - Hub location method and apparatus - Google Patents
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Abstract
The embodiment of the present invention provides a kind of hub location method and apparatus, this method comprises: determining the pivotability of each pair of node in network；Unique a pair of of hub node of maximum a pair of of the node of pivotability as current network is chosen, and the company side in current network between each node is set, constructs initial network；Wherein each node includes each hub node and each non-hub node in current network；Judge whether hinge number of nodes is equal with predetermined hub node quantity in current network, if the hub node quantity of current network is less than the predetermined hub node quantity, tree expansion is then successively executed to current network and ring is expanded, and the hinge quantity of current network is added one, until reaching the predetermined hub node quantity；Export the corresponding hub location result of current network.The embodiment of the present invention can be realized while shortening the solution time, improves solving precision, provides efficient solution for the hub location problem under large scale network.
Description
Technical field
The present embodiments relate to traffic programme technical field more particularly to a kind of hub location method and apparatus.
Background technique
Hub location problem is present in multiple key areas such as transport and telecommunications.We establish hinge in a network, with full
The transportation demand collected, transport and distributed between podomere point pair.When transporting big flow, the effect of scale economy to pass through pivot
The transport for connecting side between knob generates cost less depreciation.
In the prior art, by establishing single distribution model or overabsorption model, and by the hinge network of two kinds of models
It is assumed to be full connection, to solve hub location result；And in terms of algorithm, mostly using exact algorithm at present, (such as Benders is decomposed
Algorithm) or heuritic approach (such as greedy algorithm) solve the model.
However, though problem, these obtained models and actual case can be simplified using the distribution model connected entirely
Example differs greatly；Benders decomposition algorithm needs longer solution time, though and greedy algorithm shortens and solves the time, it is big
It is big to reduce the quality understood；So above scheme is unable to meet demand.
Summary of the invention
The embodiment of the present invention provides a kind of hub location method and apparatus, and the essence of solution is improved while the time is solved to shorten
Degree.
In a first aspect, the embodiment of the present invention provides a kind of hub location method, comprising:
Determine the pivotability of each pair of node in network；Wherein, the pivotability with by each pair of node build in network only
Totle drilling cost when one a pair of of hub node is inversely proportional；
Unique a pair of of hub node of maximum a pair of of the node of pivotability as current network is chosen, and according to pivotability
Company side in network configuration setting current network when maximum between each node, constructs initial network；It is wherein each in current network
Node includes each hub node and each non-hub node；
Judge whether hinge number of nodes is equal with predetermined hub node quantity in current network, if the hinge of current network
Number of nodes is less than the predetermined hub node quantity, then successively executes tree expansion to current network and ring is expanded, so that currently
The lowest cost of network, and the hinge quantity of current network is added one, until the hub node quantity of current network is equal to institute
State predetermined hub node quantity；Export the corresponding hub location result of current network.
Second aspect, the embodiment of the present invention provide a kind of hub location equipment, comprising:
Determining module, for determining the pivotability of each pair of node in network；Wherein, the pivotability is built with by each pair of node
Totle drilling cost when being set as unique a pair of hub node in network is inversely proportional；
Module is constructed, for choosing unique a pair of of hub node of maximum a pair of of the node of pivotability as current network,
And the company side in network configuration setting current network when according to pivotability maximum between each node, constructs initial network；Its
Each node includes each hub node and each non-hub node in middle current network；
First processing module, for judge in current network hinge number of nodes whether with predetermined hub node quantity phase
Deng, if the hub node quantity of current network be less than the predetermined hub node quantity, to current network successively executes set open up
Exhibition and ring are expanded, so that the lowest cost of current network, and the hinge quantity of current network is added one, until current network
Hub node quantity is equal to the predetermined hub node quantity；Export the corresponding hub location result of current network.
The third aspect, the embodiment of the present invention provide a kind of hub location equipment, comprising: at least one processor and storage
Device；
The memory stores computer executed instructions；
At least one described processor executes the computer executed instructions of memory storage so that it is described at least one
Processor executes hub location method described in the various possible designs of first aspect and first aspect as above.
Fourth aspect, the embodiment of the present invention provide a kind of computer readable storage medium, the computer-readable storage medium
Computer executed instructions are stored in matter, when processor execute the computer executed instructions when, realize first aspect as above with
And hub location method described in the various possible designs of first aspect.
Hub location method and apparatus provided in this embodiment, the hinge that this method passes through each pair of node in calculating network
Property, and select maximum a pair of of initial network of the node building with a pair of of hub node of pivotability, the obtained initial network
It can be for quickly obtaining hub location result provides a higher starting point；In addition, by being iterated to calculate to initial network, and
And tree expansion and ring expansion are successively carried out in each iteration, until reaching predetermined hub node quantity, and exports and reach predetermined
The corresponding hub location of network when hub node quantity improves solving precision as a result, it is possible to while shortening the solution time,
Efficient solution is provided for the hub location problem under large scale network.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the flow diagram one for the hub location method that one embodiment of the invention provides；
Fig. 2 be the highest n node of pivotability that provides of one embodiment of the invention to and p ∈ { 2,3,4,5,6 } in the case of
Optimal solution；
Fig. 3 is the variation diagram that tree provided in an embodiment of the present invention expands hinge network in operating process；
Fig. 4 is the variation diagram that ring provided in an embodiment of the present invention expands hinge network in operating process；
Fig. 5 is the flow diagram two for the hub location method that further embodiment of this invention provides；
Fig. 6 is for hub location method provided in an embodiment of the present invention to heterogeneous networks scale in CAB, AP and TR data set
The gap of lower the acquired solution of n ∈ { 25,30,40,50,60,70,80,81 }；
Fig. 7 is for hub location method provided in an embodiment of the present invention to heterogeneous networks scale in CAB, AP and TR data set
Under n ∈ { 25,30,40,50,60,70,80,81 } and enhancing Benders decomposition algorithm runing time comparison diagram；
Fig. 8 is that hub location method provided in an embodiment of the present invention and enhancing Benders decomposition algorithm are used about memory
The comparison diagram of situation；
Fig. 9 is the structural schematic diagram for the hub location equipment that further embodiment of this invention provides；
Figure 10 is the hardware structural diagram of hub location equipment provided in an embodiment of the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
The required non-full connection hub location problem solved of the invention is: considering four kinds of company sides (between non-hub node
Direct-connected transhipment side and hub node in, non-hub node to hub node when collecting, between hub node is to non-hub node
Distribution side) in the case where, suitable hinge and Lian Bian are established on several nodes in transportation network, to minimize totle drilling cost
The problem of (fixed construction cost and variable transportation cost).In order to realize that this target, the embodiment of the present invention propose " hinge
The concept of property " (hubbiness) carrys out quality of the evaluation node as hinge.Pivotability is used not only for screening under two nodes
Initial network, and guidance is provided as subsequent network expansion process.Based on this, we devise a kind of by repeatedly
In generation, expands the algorithm of hinge network, to solve the problems, such as this hub location in a short time.
Table 1: the non-parameter connected in hub location problem entirely
Table 2: the non-decision variable connected in hub location problem entirely
In non-full connection hub location problem, four kinds of companies while (when direct-connected between non-hub node, non-hub node to pivot
When transhipment of the collection of knob node between, hub node and hub node is to the distribution side of non-hub node) symbol is used respectively
0,1,2,3 indicates.Wherein, collect while and be collectively referred to as when distributing access side.Become based on a series of parameter (table 1) and decision
It measures (table 2), we can carry out following modeling at problem to be solved:
Wherein Objective function (1) is to look for
The network structure of optimal cost under to appropriate hinge, Lian Bian and corresponding traffic flow.By constraint (2), each OD (origin-
Destination, origin-destination) pair between traffic flow therebetween must be all serviced using one of four kinds of company sides.Constraint
(3) pass through the stream conservation equation of hub node m.Constraint (4-6) ensure that each hub node can only be by access side and hinge
Side is connected.Constraint (7-9) ensure that the feasibility of traffic flow path (the company Bian Shangke only built up is with traffic flow).Most
Afterwards, the quantity of constraint (10) limitation hinge is p.
Illustrate hub location method provided in an embodiment of the present invention using specific embodiment below.
Fig. 1 is the flow diagram one of hub location method provided in an embodiment of the present invention.As shown in Figure 1, this method packet
It includes:
S101, the pivotability for determining each pair of node in network；Wherein, the pivotability and each pair of node is built as network
In unique a pair of of hub node when totle drilling cost be inversely proportional.
Optionally, the present embodiment proposes the quality assessment parameter for being directed to nodes pair, is named as " hinge
Property " (hubbiness).The node given for one is to (k, m), the value hubbi of pivotabilitykmBe when k and m be in network only
The inverse of totle drilling cost approximation when two hinges.
Hinge is established in the algorithm simulation on node k and node m, and to the direct-connected decision built while with access.From
One configuration connected entirely is set out, we devise the algorithm of a greedy search.Firstly, based on transportation demand to direct-connected side into
Row ascending order arranges (a possibility that establishing direct-connected side between the small non-hub node pair of transportation demand is smaller), direct-connected to every
Side executes removal operation if totle drilling cost reduces after removing；Descending arrangement (non-hub node is carried out to access side based on distance
A possibility that being connected with remote hinge is smaller), to every access side, if totle drilling cost reduces after removing, execute removal operation；
Finally, we, which attempt the greedy hinge endpoint by every access side, replaces with other hub node (alternative pivots not yet connected
Knob carries out ascending order arrangement based on the distance with the non-hub node).
Definition node is as follows to the pivotability of $ (k, m) $:
Wherein TCkmIt is the totle drilling cost under the final configuration of gained.The highest node pair of pivotability and its corresponding finally match
It sets by as the solution in the case of p=2.Referring to fig. 2, Fig. 2 is the highest n node pair of pivotability that one embodiment of the invention provides
With the optimal solution in the case of p ∈ { 2,3,4,5,6 }.
Optionally, the pseudocode of the pivotability of each pair of node can be in the determining network are as follows:
Unique a pair of of hub node of maximum a pair of of the node of S102, selection pivotability as current network, and according to
Company side in network configuration setting current network when pivotability maximum between each node, constructs initial network；Wherein current net
Each node includes each hub node and each non-hub node in network.
Optionally, initial network is designed for the case where two hinges.Its pivotability is calculated for every a pair of of node in network,
I.e. only in the case that on the two nodes build hinge totle drilling cost approximation inverse.Select highest a pair of of the node of pivotability
(k, m), allow k-m and m-k as only two hinge side.Non- hub node is configured according to network generated when calculating pivotability
Between it is direct-connected while and when access between hub node and non-hub node.
S103, judge whether hinge number of nodes is equal with predetermined hub node quantity in current network, if current network
Hub node quantity be less than the predetermined hub node quantity, then to current network successively executes tree expand and ring expansion, with
Make the lowest cost of current network, and the hinge quantity of current network is added one, until the hub node quantity of current network
Equal to the predetermined hub node quantity；Export the corresponding hub location result of current network.
Optionally, which is intended to through two network design modes (tree expansion (Tree-Extension) and ring expansion
(Cycle-Extension)) initial solution of the situation of p > 2 is obtained.
The step of tree is expanded is introduced first.The network comprising p hinge given for one, tree expand and can replace wherein
One hinge, and a hinge is in addition created, efficiently to establish branch on hinge network.
Enable NeihIndicate the set of the adjacent hinge of hinge h, our hinge sexual deviations based on opposite hinge h be (parameter
Definition is referring to formula (12)) ascending order arrangement is carried out to all non-hub nodes, and select cn wherein forward node plus section
Point h itself forms a set.Experiment showsJust it is enough to obtain outstanding solution.
Referring to Fig. 3, Fig. 3 is the variation diagram that tree provided in an embodiment of the present invention expands hinge network in operating process.Specifically
Step may include:
Step S1031, in the initial network of (1) Fig. 3, for each hinge side l, we select two hub node h1
And h2(the two nodes are likely to be identical).
If step S1032, node is to (h1,h2) there is not (node occurred can be recorded in set G),
ForIn each node s1With each non-hub node s2, we are by hinge h1With node s1Role exchange (Fig. 3
(2)), in node s2It is upper to create a hinge, establish new hinge side s2-h2,h2-s2(Fig. 3 (3)), and to direct-connected side and access
Between initialized.
Step S1033, from this initial network, we devise the algorithm of a greedy search: being needed based on transport
It asks and is carrying out ascending order arrangement (a possibility that when establishing direct-connected between the small non-hub node pair of transportation demand is smaller) to direct-connected,
To every direct-connected side, if totle drilling cost reduces after removing, removal operation is executed；Descending arrangement is carried out to access side based on distance
(a possibility that non-hub node is connected with remote hinge is smaller) if totle drilling cost reduces after removing, holds every access side
Row removes operation；It is (alternative that the greedy hinge endpoint by every access side of trial replaces with the hub node that other are not yet connected
Hinge carries out ascending order arrangement based on the distance with the non-hub node).
Step S1034, when calculating pivotability for a pair of of node, only two between two hub nodes (unidirectional)
Hinge side.But it becomes more complicated more than two hinge sides the case where.In addition, only being had between hinge in aforesaid operations
Two-way side.If the fixed cost for establishing hinge side is very expensive, it can be one more preferable that unidirectional ring is built in hinge network
Selection.Therefore, the embodiment of the present invention proposes the sub-operation that tree is expanded, and is named as " number closure " (Tree-Close).
By new hinge s2With hinge h2After being connected, we are greedy in hinge s2The company of foundation side between other hinges, as long as can reduce
Totle drilling cost (Fig. 3 (4)).
Optionally, for each hinge ring for having reversed hinge side being found, what we simulated remove, and its is all anti-
To hinge side, to generate a unidirectional hinge ring (Fig. 3 (5)).If totle drilling cost reduces, the behaviour on reversed hinge side is removed
Just it is performed.After having explored all unidirectional rings, the optimal solution of gained is just by the solution as several closed procedures.
Optionally, the pseudocode of the tree expandable algorithm can be with are as follows:
Tree, which is expanded, mainly expands hinge network by the two-way Lian Bianlai between hinge.Although its sub-operation tree closure considers
The case where unidirectional hinge ring, but it is just for the special circumstances by setting a newly-generated ring, and cannot include and be opened up from a small ring
Open up the process of big ring.Therefore, the embodiment of the present invention proposes another operation " ring expansion " (Cycle-Extension).
Referring to fig. 4, Fig. 4 is the variation diagram that ring provided in an embodiment of the present invention expands hinge network in operating process.Specifically
Step may include:
Step S1035, in the initial hinge network of Fig. 4 (1), to each hinge side h1-h2On, we select each of which
Endpoint (such as h1).For setIn each node (such as s1), node s is used in simulation1To replace hinge h1(Fig. 4
(2))。
Step S1036, for each hub node s2, simulation in s2A hinge is created, and with hinge path s1-s2-
h2Come the company of replacement side s1-h2(Fig. 4 (3)).
Step S1037, then we to it is direct-connected while and access while executes with calculating pivotability during similar greediness search
Rope algorithm: carrying out ascending order arrangement to direct-connected side based on transportation demand, (foundation is straight between the small non-hub node pair of transportation demand
Even a possibility that side, is smaller), to every direct-connected side, if totle drilling cost reduces after removing, execute removal operation；It is docked based on distance
Enter side and carry out descending arrangement (a possibility that non-hub node is connected with remote hinge is smaller), to every access side, if removing
Totle drilling cost reduces afterwards, then executes removal operation；The hinge endpoint by every access side for attempting greediness replaces with other and not yet connects
The hub node connect (alternative hinge carries out ascending order arrangement based on the distance with the non-hub node).
Step S1038, notice that while increasing hinge number, the direction on hinge side may change in optimal solution.Cause
This, the present invention attempts to carry out all hinge sides reversed and updates totle drilling cost (Fig. 4 (4)).
After having explored all situations that tree is expanded and ring is expanded, the solution of the lowest cost is just selected as this step
Last solution.
Hub location method provided in this embodiment by calculating the pivotability of each pair of node in network, and selects hinge
Property maximum a pair of of node building there is the initial network of a pair of of hub node, the obtained initial network can be quickly to obtain
Hub location result provides a higher starting point；In addition, by being iterated to calculate to initial network, and in each iteration
It successively carries out tree expansion and ring is expanded, when reaching predetermined hub node quantity up to reaching predetermined hub node quantity, and exporting
The corresponding hub location of network as a result, it is possible to shorten solve the time while, improve solving precision, be large scale network under
Hub location problem provide efficient solution.
Fig. 5 is the flow diagram two for the hub location method that further embodiment of this invention provides.As shown in Fig. 5, the party
Method includes:
S501, the pivotability for determining each pair of node in network；Wherein, the pivotability and each pair of node is built as network
In unique a pair of of hub node when totle drilling cost be inversely proportional.
Optionally, in a specific embodiment, which can specifically include:
S5011, pivotability node centering any node to be determined is chosen to unique a pair of of hinge section as current network
Point；
S5012, node each in current network is connected entirely, obtain it is described it is direct-connected in, the access with the pivot
Knob side；
S5013, determine current network configuration under totle drilling cost；Wherein the totle drilling cost includes: the direct-connected side, access
Transportation cost in, hinge between the construction cost and node of hub node；
S5014, according to the totle drilling cost, by greedy algorithm to current network it is direct-connected while and when access handle,
To reduce totle drilling cost, and obtain target network configuration；
In a specific embodiment, which can specifically include:
S50141, the size according to the transportation demand amount on each direct-connected side, each direct-connected side are arranged according to ascending order, and according to institute
It states ascending order and removal operation successively is executed to every direct-connected side；Wherein, the removal operation includes: that judgement moves pending direct-connected side
Except whether rear totle drilling cost reduces, if totle drilling cost reduces after pending direct-connected side is removed, the pending direct-connected side is removed；
S50142, according to it is each access side length, each access side is arranged according to descending, and successively right according to the descending
Every access side, which executes, removes operation；Wherein, removal operation include: judge be by totle drilling cost after the removal of pending access side
No reduction removes the pending access side if totle drilling cost reduces after pending access side is removed；
S50143, replacement hub node operation successively is executed to each access side executed after removing operation；The replacement pivot
Knob nodal operation include: according to each alternative hub node and it is pending access side the distance between non-hub node, will be each standby
It selects hub node to arrange according to ascending order, and successively the hub node on pending access side is once replaced according to the ascending order
Operation；Judge whether totle drilling cost reduces after the pending hub node for accessing side is replaced with alternate node, if connecing pending
The hub node for entering side replaces with totle drilling cost reduction after alternate node, then replaces the hub node on the pending access side
It changes.
S5015, the pivotability that the node pair being selected is determined according to the totle drilling cost under target network configuration；
S5016, above-mentioned steps are repeated, until completing the determination of the pivotability of all nodes pair in network.
Unique a pair of of hub node of maximum a pair of of the node of S502, selection pivotability as current network, and according to
Company side in network configuration setting current network when pivotability maximum between each node, constructs initial network；Wherein current net
Each node includes each hub node and each non-hub node in network；
S503, judge whether hinge number of nodes is equal with predetermined hub node quantity in current network, if current network
Hub node quantity be less than the predetermined hub node quantity, then to current network successively executes tree expand and ring expansion, with
Make the lowest cost of current network, and the hinge quantity of current network is added one, until the hub node quantity of current network
Equal to the predetermined hub node quantity；Export the corresponding hub location result of current network.
In a specific embodiment, the tree is expanded, and may include:
S5031, the hinge line set for constructing current network；Wherein the hinge is while for two-way hinge；
S5032, following steps are repeated, until traversing each hinge side in the hinge line set, and exports assembly
Corresponding hub location when this is minimum is as a result, initial network as subsequent operation:
S5033, the first hub node h1 and second for selecting the hinge side of any expansion to be set in the hinge line set
Hub node h2, as expansion hub node to be set；
S5034, basis carry out ascending order arrangement wait set the hinge sexual deviation for expanding hub node, by each non-hub node, and
The preceding cn non-hub nodes selected in the ascending order arrangement are constructed as the second hinge set with hub node to be replaced jointly；
Wherein, the cn is positive integer；
S5035, following steps are repeated, until traversing the non-hub node of each of the second hinge combination:
S5036, any non-hub node in the second hinge set is selected as the first non-hub node, Ling Yifei
Hub node is as the second non-hub node；
S5037, first hub node and the described first non-hub node are subjected to role exchange, it is non-by described second
Hub node is established in the third hub node and current network between each non-hub node as third hub node
Access side, the direct-connected side in first hub node after establishing changing role and current network between each non-hub node；
S5038, the totle drilling cost for determining current network, and according to the totle drilling cost, by greedy algorithm to current network
It is direct-connected to be handled while with access, to reduce totle drilling cost；
Hinge ring in S5039, lookup current network, and following steps successively are executed to each hinge ring: it removes wait hold
The reversed hinge side of row hinge ring；If the cost after removing is reduced relative to the totle drilling cost before removal, remove described pending
The reversed hinge side of hinge ring.
In a specific embodiment, the ring is expanded, and may include:
S50310, the hinge ring set for constructing current network；Following steps are repeated, until traversing the hinge ring collection
Each hinge ring in conjunction, and export corresponding hub location when the lowest cost as a result, as final hub location as a result, or
Initial network of the person as subsequent operation:
S50311, the first end point for selecting any hinge side in the hinge ring set in any hinge ring are used as to ring
Expand hub node；Wherein any hinge is while for the company of first end point and the second endpoint；
S50312, basis expand the hinge sexual deviation of hub node to ring, and each non-hub node is carried out ascending order arrangement, and
Preceding dn non-hub nodes in the ascending order arrangement are selected, hub node is expanded with to ring, is constructed as third hinge collection jointly
It closes；Wherein, the dn is positive integer；
S50313, following steps are repeated, until traversing the non-hub node of each of the second hinge set:
S50314, any non-hub node in the second hinge set is selected as the non-hub node of third, it is another
Non- hub node is as the 4th non-hub node；
S50315, described hub node and the non-hub node progress role exchange of the third will be expanded to ring；It will be described
4th non-hub node is as the 4th hub node；
S50316, the non-hub node of the third after changing role and the hinge side between the second endpoint are replaced with into institute
The hinge side for stating the 4th hub node and the second endpoint and the non-pivot of the third after the 4th hub node and changing role
The hinge side of knob node；
S50317, the totle drilling cost for determining current network, and according to the totle drilling cost, by greedy algorithm to current network
It is direct-connected to be handled while with access, to reduce totle drilling cost；
S50318, reverse operating successively is executed to the hinge ring in current network；The reverse operating comprises determining that hinge
Whether the totle drilling cost after ring is reversed reduces, if totle drilling cost reduces that hinge ring is reversed.
S504, the hub location result is optimized by variable neighborhood search algorithm, and exports the hinge after optimization
Addressing result.
In a specific embodiment, the step, can specifically include:
S5041, using the hub node of current network as initial solution set, and determine initial solution set it is corresponding initially at
This；
S5042, any hub node selected in the initial solution set carry out role swap with any non-hub node
After obtain Neighbourhood set；
S5043, the corresponding neighborhood cost of Neighbourhood set is calculated, if neighborhood cost is less than initial cost, by Neighbourhood set
Initial solution set is updated；
S5044, after repeating above-mentioned steps S5041 to step S5043 pre-determined number, current initial solution combination pair is exported
The hub location result answered.
It is fine by being incremented by the obtained solution of network design in the present embodiment, solution and optimal solution obtained in experiment
The median and maximum value of difference ratio are respectively 0.37% and more than 3%.Therefore, the embodiment of the present invention uses change neighborhood search
(Variable Neighborhood Search, VNS) comes on the basis of solution obtained by increasing network design to explore preferably solution.
To solve hub location problem, there are three types of the strategies of VNS: strategy (Sequential strategy, Seq-VNS) in succession, nested
Tactful (nested strategy, Nest-VNS) and mixed strategy (mixed strategy, Mix-VNS).Seq-VNS needs
Shortest runing time but the least neighborhood of exploration；Nest-VNS explores large-scale neighborhood but its runing time is unacceptable
's；Mix-VNS has directly reached a balance in neighborhood scale and runing time.Therefore the embodiment of the present invention uses Mix-
VNS。
Optionally, the pseudocode for becoming neighborhood processing can be with are as follows:
As shown in above-mentioned pseudocode, H is combined into for hinge collectionoInitial solution, we nesting level generate and HoOnly one
The different all hinge set of a hinge, these hinge collection are referred to as neighborhood.Then, (removal/addition is straight for other local searches
Lian Bian, removal/addition/replacement access side, removal/addition/replacement hinge side) each neighbours are applied to by greedy, and every
Step updates currently available best solution.If solution is not modified in the subsequent iteration of given quantity, algorithm is terminated.
The beneficial effect of hub location method provided in an embodiment of the present invention is: firstly, the embodiment of the present invention proposes
The concept of " pivotability " (hubbiness) carrys out evaluation node to the quality as hinge property, and devises a kind of rapid solving
Algorithm of all nodes to pivotability in network.Pivotability be used not only for screen two nodes under initial network, and by
Guidance is provided as subsequent network expansion process.Secondly, it is directed to the non-full connection hub location problem of the higher hinge of complexity,
Traditional algorithm or accurate solution can be provided but solution time for needing extremely to grow or be greatly shortened and solve time but institute
The quality that must be solved sharply deteriorates.And in the present invention, by using a series of network design rules, the computation complexity quilt of problem
It substantially reduces, so as in a short time to obtain the solution of high quality.First, this is more extensive to solve within the reasonable time
Hub location problem under network provides possible (the problem of can solving 200 node sizes herein)；Second, this can
For redesigning network in time under special circumstances.In addition, being decomposed with classic enhancing Benders is showed in traditional algorithm
It compares, (for the case of 80 nodes, the former about wants, and 150GB's is interior than the former few memory for using 2 orders of magnitude for this algorithm
It deposits, and this algorithm only needs 1GB or so).This is the hub location solved under more large scale network under limited computing platform
Problem provides possibility.
Referring to Fig. 6, Fig. 6 is for hub location method provided in an embodiment of the present invention to not in CAB, AP and TR data set
With the gap of lower the acquired solution of network size n ∈ { 25,30,40,50,60,70,80,81 }.The gap of the acquired solution is institute
The percentage with optimal solution difference must be solved.For n=25, the case where 30, parameter (f, b) ∈ of two groups of fixations and transportation cost
([2500,3000,3500,3000], [0.08,0.04,0.03,0.04]), ([1000,1000,1000,1000], [0.10,
0.04,0.02,0.04] it) } is used；The case where for n >=40, due to providing exact algorithm (the enhancing Benders of optimal solution
Decompose) too long of solution time, we only test second group of cost parameter.The fixation construction cost of hinge is all under all situations
It isThe number of hinge is arranged to p=2, and 3,4,5.The result shows that in addition to a situation under 25 nodes, this
The solution that invention solves other all cases is both less than 1%, and is optimal more than 90% solution.
Referring to Fig. 7, Fig. 7 is for hub location method provided in an embodiment of the present invention to not in CAB, AP and TR data set
With the comparison under network size n ∈ { 25,30,40,50,60,70,80,81 } with enhancing Benders decomposition algorithm runing time
Figure.Fixed and transportation cost parameter be arranged to f=[1000,1000,1000,1000] and b=[0.10,0.04,0.02,
0.04], the fixation construction cost of hinge is all under all situationsThe number of hinge is arranged to p=2, and 3,4,5.
Notice that y-axis is logarithmic scale.This algorithm and enhancing Benders decomposition algorithm respectively with it is rectangular and it is round indicate, operation time
Matched curve also provide together.Experiment shows this algorithm 2-3 number faster than the speed of service for enhancing Benders decomposition algorithm
Magnitude.For a case of scale of wherein fighting each other, enhance Benders decomposition algorithm need 230 hours obtain as a result, and
This algorithm just had found optimal solution in 20 minutes.The matched curve of runing time shows to enhance the meter of Benders decomposition algorithm
Calculation complexity is O (n6) and this algorithm then be O (n4)。
Referring to Fig. 8, Fig. 8 be hub location method provided in an embodiment of the present invention and enhancing Benders decomposition algorithm about
The comparison diagram of memory service condition.Fixed and transportation cost parameter is arranged to f=[1000,1000,1000,1000] and b
=[0.10,0.04,0.02,0.04], the fixation construction cost of hinge is all under all situationsFig. 8 (1) is p
Memory service condition in the case of=2 under different scales network.Notice that y-axis is logarithmic scale, this algorithm and enhancing Benders
The matched curve of decomposition algorithm is also presented, and corresponding fitting function is respectivelyWith
Fig. 8 (2) is the evolution of memory service condition at any time in TR81 data set in the case of p=5, it is noted that x-axis and y-axis are logarithm
Scale.It can be seen that enhancing Benders decomposition algorithm needs about 100 times of this algorithm of memory.
Finally, giving the result that this algorithm solves more extensive case in table 3.Under this scale, other algorithms are
Reasonable solution can not be provided within the acceptable time.Fixed and transportation cost parameter be arranged to f=[1000,1000,
1000,1000] and b=[0.10,0.04,0.02,0.04], the fixation construction cost of hinge is all f under all situationsk H=
107, the number of hinge is arranged to p=2, and 3,4,5.It can be seen that this algorithm reaches 200 nodes within 11 hours
The problem of scale, provides understanding.
Table 3: solution of the present invention to large scale network
Fig. 9 is the structural schematic diagram for the hub location equipment that further embodiment of this invention provides.As shown in figure 9, the hinge
Addressing equipment 90 comprises determining that module 901, building module 902 and first processing module 903.
Determining module 901, for determining the pivotability of each pair of node in network；Wherein, the pivotability with by each pair of section
Totle drilling cost when point construction is unique a pair of of hub node in network is inversely proportional；
Module 902 is constructed, for choosing unique a pair of of hinge section of maximum a pair of of the node of pivotability as current network
Point, and the company side in network configuration setting current network when according to pivotability maximum between each node, construct initial network；
Wherein each node includes each hub node and each non-hub node in current network；
First processing module 903, for judge in current network hinge number of nodes whether with predetermined hub node quantity
It is equal, if the hub node quantity of current network is less than the predetermined hub node quantity, tree is successively executed to current network
It expands and ring is expanded, so that the lowest cost of current network, and the hinge quantity of current network is added one, until current network
Hub node quantity be equal to the predetermined hub node quantity；Export the corresponding hub location result of current network.
Hub location equipment provided in an embodiment of the present invention, the equipment calculate each pair of node in network by determining module
Pivotability, and select maximum a pair of of the node of pivotability to construct the initial network with a pair of of hub node by building module,
The obtained initial network can be for quickly obtaining hub location result provides a higher starting point；In addition, passing through at first
Reason module iterates to calculate initial network, and successively carries out tree expansion and ring expansion in each iteration, until reaching pre-
Determine hub node quantity, and exports the corresponding hub location of network when reaching predetermined hub node quantity as a result, it is possible to contracting
While the short solution time, solving precision is improved, provides efficient solution party for the hub location problem under large scale network
Case.
Optionally, hub location equipment 90 further include: Second processing module 904.
Second processing module 904, for being optimized by variable neighborhood search algorithm to the hub location result, and it is defeated
Hub location result after optimizing out.
Optionally, the determining module 901, is specifically used for:
Pivotability node centering any node to be determined is chosen to unique a pair of of hub node as current network；
Node each in current network is connected entirely, obtain it is described it is direct-connected in, the access with the hinge side；
Determine the totle drilling cost under current network configuration；Wherein the totle drilling cost include: it is described it is direct-connected while, access while and hinge
The totle drilling cost on side and the totle drilling cost of hub node；
According to the totle drilling cost, the direct-connected of current network is handled while with access by greedy algorithm, to reduce
Totle drilling cost, and obtain target network configuration；
The pivotability for the node pair being selected is determined according to the totle drilling cost under target network configuration；
Above-mentioned steps are repeated, until completing the determination of the pivotability of all nodes pair in network.
Optionally, the determining module 901, is specifically used for:
It is executed by each direct-connected side of the greedy algorithm to current network and removes operation；
It is executed by each access side of the greedy algorithm to current network and removes operation；
Replacement operation is executed by each access side of the greedy algorithm to current network.
Optionally, the determining module 901, is specifically used for:
According to the size of the transportation demand amount on each direct-connected side, each direct-connected side is arranged according to ascending order, and according to the ascending order
Successively every direct-connected side is executed and removes operation；Wherein, the removal operation includes: total after judgement removes pending direct-connected side
Whether cost reduces, if totle drilling cost reduces after pending direct-connected side is removed, the pending direct-connected side is removed；
According to the length on each access side, each access side is arranged according to descending, and successively every is connect according to the descending
Enter side and executes removal operation；Wherein, the removal operation includes: to judge whether drop totle drilling cost after the removal of pending access side
It is low, if totle drilling cost reduces after pending access side is removed, the pending access side is removed；
Replacement hub node operation successively is executed to each access side executed after removing operation；The replacement hub node behaviour
Work includes: according to the distance between the non-hub node of each alternative hub node and pending access side, by each alternative hinge section
Point is arranged according to ascending order, and successively carries out replacement operation to the hub node on pending access side according to the ascending order；Sentence
Whether totle drilling cost reduces after the disconnected hub node by pending access side replaces with alternate node, if by the pivot on pending access side
Totle drilling cost reduces after knob node replaces with alternate node, then is replaced the hub node on the pending access side.
Optionally, the first processing module 903, is specifically used for:
Construct the hinge line set of current network；Wherein the hinge is while for two-way hinge；
Following steps are repeated, until traversing each hinge side in the hinge line set, and export the lowest cost
When corresponding hub location as a result, initial network as subsequent operation:
Select the first hub node h1 and the second hinge section on the hinge side of any expansion to be set in the hinge line set
Point h2, as expansion hub node to be set；
According to wait set the hinge sexual deviation for expanding hub node, each non-hub node is subjected to ascending order arrangement, and selected institute
The preceding cn non-hub nodes stated in ascending order arrangement are constructed as the second hinge set with hub node to be replaced jointly；Wherein,
The cn is positive integer；
Following steps are repeated, until traversing the non-hub node of each of the second hinge combination:
Any non-hub node in the second hinge set is selected as the first non-hub node, another non-hinge section
Point is used as the second non-hub node；
First hub node and the described first non-hub node are subjected to role exchange, by the described second non-hinge section
Point is used as third hub node, and establishes the access in the third hub node and current network between each non-hub node
Side, the direct-connected side in first hub node after establishing changing role and current network between each non-hub node；
The totle drilling cost of current network is determined, and according to the totle drilling cost, by greedy algorithm to the direct-connected side of current network
It is handled with access side, to reduce totle drilling cost；
The hinge ring in current network is searched, and following steps successively are executed to each hinge ring: removing pending hinge
The reversed hinge side of ring；If the cost after removing is reduced relative to the totle drilling cost before removal, the pending hinge ring is removed
Reversed hinge side.
Optionally, the first processing module 903, is specifically used for:
Construct the hinge ring set of current network；Following steps are repeated, until traversing in the hinge ring set
Each hinge ring, and corresponding hub location when the lowest cost is exported as a result, as final hub location as a result, conduct
The initial network of subsequent operation:
The first end point for selecting any hinge side in the hinge ring set in any hinge ring, which is used as, expands pivot to ring
Knob node；Wherein any hinge is while for the company of first end point and the second endpoint；
According to the hinge sexual deviation for expanding hub node to ring, each non-hub node is subjected to ascending order arrangement, and selected institute
Preceding dn non-hub nodes in ascending order arrangement are stated, hub node is expanded with to ring, is constructed as third hinge set jointly；Its
In, the dn is positive integer；
Following steps are repeated, until traversing the non-hub node of each of the second hinge set:
Any non-hub node in the second hinge set is selected as the non-hub node of third, another non-hinge section
Point is used as the 4th non-hub node；
Described hub node will be expanded to ring and the non-hub node of the third carries out role exchange；By the 4th non-pivot
Knob node is as the 4th hub node；
The non-hub node of the third after changing role and the hinge side between the second endpoint are replaced with the described 4th
The hinge side and the 4th hub node of hub node and the second endpoint and the non-hub node of the third after changing role
Hinge side；
The totle drilling cost of current network is determined, and according to the totle drilling cost, by greedy algorithm to the direct-connected side of current network
It is handled with access side, to reduce totle drilling cost；
Reverse operating successively is executed to the hinge ring in current network；The reverse operating comprises determining that hinge ring is reversed
Whether totle drilling cost afterwards reduces, if totle drilling cost reduces that hinge ring is reversed.
Optionally, the Second processing module 904, is specifically used for:
Using the hub node of current network as initial solution set, and determine the corresponding initial cost of initial solution set；
It selectes after any hub node in the initial solution set carries out role swap with any non-hub node and obtains
Neighbourhood set；
The corresponding neighborhood cost of Neighbourhood set is calculated, if neighborhood cost is less than initial cost, by Neighbourhood set to initial
Solution set is updated；
After repeating above-mentioned steps pre-determined number, current initial solution is exported in conjunction with corresponding hub location result.
End-point detection equipment provided in an embodiment of the present invention, can be used for executing above-mentioned embodiment of the method, realization principle
Similar with technical effect, details are not described herein again for the present embodiment.
Figure 10 is the hardware structural diagram of hub location equipment provided in an embodiment of the present invention.As shown in Figure 10, this reality
The hub location equipment 100 for applying example offer includes: at least one processor 1001 and memory 1002.Wherein, processor 1001,
Memory 1002 is connected by bus 1003.
During specific implementation, at least one processor 1001 executes the computer that the memory 1002 stores and executes
Instruction, so that at least one processor 1001 executes hub location method performed by hub location equipment 100 as above.
The specific implementation process of processor 1001 can be found in above method embodiment, implementing principle and technical effect class
Seemingly, details are not described herein again for the present embodiment.
In above-mentioned embodiment shown in Fig. 10, it should be appreciated that processor can be central processing unit (English:
Central Processing Unit, referred to as: CPU), can also be other general processors, digital signal processor (English:
Digital Signal Processor, referred to as: DSP), specific integrated circuit (English: Application Specific
Integrated Circuit, referred to as: ASIC) etc..General processor can be microprocessor or the processor is also possible to
Any conventional processor etc..Hardware processor can be embodied directly in conjunction with the step of invention disclosed method to have executed
At, or in processor hardware and software module combination execute completion.
Memory may include high speed RAM memory, it is also possible to and it further include non-volatile memories NVM, for example, at least one
Magnetic disk storage.
Bus can be industry standard architecture (Industry Standard Architecture, ISA) bus, outer
Portion's apparatus interconnection (Peripheral Component, PCI) bus or extended industry-standard architecture (Extended
Industry Standard Architecture, EISA) bus etc..Bus can be divided into address bus, data/address bus, control
Bus etc..For convenient for indicating, the bus in illustrations does not limit only a bus or a type of bus.
The application also provides a kind of computer readable storage medium, and calculating is stored in the computer readable storage medium
Machine executes instruction, and when processor executes the computer executed instructions, realizes the hinge choosing that hub location equipment as above executes
Location method.
The application also provides a kind of computer readable storage medium, and calculating is stored in the computer readable storage medium
Machine executes instruction, and when processor executes the computer executed instructions, realizes the hinge choosing that hub location equipment as above executes
Location method.
Above-mentioned computer readable storage medium, above-mentioned readable storage medium storing program for executing can be by any kind of volatibility or non-
Volatile storage devices or their combination realize that, such as static random access memory (SRAM), electrically erasable is only
It reads memory (EEPROM), Erasable Programmable Read Only Memory EPROM (EPROM), programmable read only memory (PROM) is read-only to deposit
Reservoir (ROM), magnetic memory, flash memory, disk or CD.Readable storage medium storing program for executing can be general or specialized computer capacity
Any usable medium enough accessed.
A kind of illustrative readable storage medium storing program for executing is coupled to processor, to enable a processor to from the readable storage medium storing program for executing
Information is read, and information can be written to the readable storage medium storing program for executing.Certainly, readable storage medium storing program for executing is also possible to the composition portion of processor
Point.Processor and readable storage medium storing program for executing can be located at specific integrated circuit (Application Specific Integrated
Circuits, referred to as: ASIC) in.Certainly, processor and readable storage medium storing program for executing can also be used as discrete assembly and be present in equipment
In.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above-mentioned each method embodiment can lead to
The relevant hardware of program instruction is crossed to complete.Program above-mentioned can be stored in a computer readable storage medium.The journey
When being executed, execution includes the steps that above-mentioned each method embodiment to sequence；And storage medium above-mentioned include: ROM, RAM, magnetic disk or
The various media that can store program code such as person's CD.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (10)
1. a kind of hub location method characterized by comprising
Determine the pivotability of each pair of node in network；Wherein, the pivotability and to build each pair of node be in network unique one
Totle drilling cost when to hub node is inversely proportional；
Unique a pair of of hub node of maximum a pair of of the node of pivotability as current network is chosen, and according to pivotability maximum
When network configuration setting current network in company side between each node, construct initial network；Wherein each node in current network
Including each hub node and each non-hub node；
Judge whether hinge number of nodes is equal with predetermined hub node quantity in current network, if the hub node of current network
Quantity is less than the predetermined hub node quantity, then successively executes tree expansion to current network and ring is expanded, so that current network
The lowest cost, and the hinge quantity of current network is added one, until the hub node quantity of current network be equal to it is described pre-
Determine hub node quantity；Export the corresponding hub location result of current network.
2. the method according to claim 1, wherein the method also includes:
The hub location result is optimized by variable neighborhood search algorithm, and exports the hub location result after optimization.
3. the method according to claim 1, wherein the company between non-hub node is while to be direct-connected, hinge section
Lian Bianwei hinge side of company while for access, between hub node between point and non-hub node；It is every in the determining network
To the pivotability of node, comprising:
Pivotability node centering any node to be determined is chosen to unique a pair of of hub node as current network；
Node each in current network is connected entirely, obtain it is described it is direct-connected in, the access with the hinge side；
Determine the totle drilling cost under current network configuration；Wherein the totle drilling cost include: it is described it is direct-connected while, access while, hinge side and
Transportation cost between the construction cost and node of hub node；
According to the totle drilling cost, the direct-connected of current network is handled while with access by greedy algorithm, to reduce assembly
This, and obtain target network configuration；
The pivotability for the node pair being selected is determined according to the totle drilling cost under target network configuration；
Above-mentioned steps are repeated, until completing the determination of the pivotability of all nodes pair in network.
4. according to the method described in claim 3, it is characterized in that, it is described by greedy algorithm to the direct-connected side of current network and
Access side is handled, comprising:
It is executed by each direct-connected side of the greedy algorithm to current network and removes operation；
It is executed by each access side of the greedy algorithm to current network and removes operation；
Replacement operation is executed by each access side of the greedy algorithm to current network.
5. the method according to claim 1, wherein the tree is expanded, comprising:
Construct the hinge line set of current network；Wherein the hinge is while for two-way hinge；
Following steps are repeated, until traverse each hinge side in the hinge line set, and when exporting the lowest cost pair
The hub location answered is as a result, initial network as subsequent operation:
The first hub node h1 and the second hub node h2 on the hinge side of any expansion to be set in the hinge line set are selected,
As expansion hub node to be set；
According to wait set the hinge sexual deviation for expanding hub node, each non-hub node is subjected to ascending order arrangement, and select the liter
Preceding cn non-hub nodes in sequence arrangement are constructed as the second hinge set with hub node to be replaced jointly；Wherein, described
Cn is positive integer；
Following steps are repeated, until traversing the non-hub node of each of the second hinge combination:
Any non-hub node in the second hinge set is selected as the first non-hub node, another non-hub node is made
For the second non-hub node；
First hub node and the described first non-hub node are subjected to role exchange, the described second non-hub node is made
For third hub node, and the access side in the third hub node and current network between each non-hub node is established, built
Direct-connected side in first hub node and current network after vertical changing role between each non-hub node；
It determines the totle drilling cost of current network, and according to the totle drilling cost, to the direct-connected side of current network and is connect by greedy algorithm
Enter side to be handled, to reduce totle drilling cost；
The hinge ring in current network is searched, and following steps successively are executed to each hinge ring: removing pending hinge ring
Reversed hinge side；If the cost after removing is reduced relative to the totle drilling cost before removal, the anti-of the pending hinge ring is removed
To hinge side.
6. the method according to claim 1, wherein the ring is expanded, comprising:
Construct the hinge ring set of current network；Following steps are repeated, until traversing each of described hinge ring set
Hinge ring, and corresponding hub location when the lowest cost is exported as a result, as final hub location as a result, as subsequent
The initial network of operation:
The first end point for selecting any hinge side in the hinge ring set in any hinge ring, which is used as, expands hinge section to ring
Point；Wherein any hinge is while for the company of first end point and the second endpoint；
According to the hinge sexual deviation for expanding hub node to ring, each non-hub node is subjected to ascending order arrangement, and select the liter
Preceding dn non-hub nodes in sequence arrangement, expand hub node with to ring, are constructed as third hinge set jointly；Wherein, institute
Stating dn is positive integer；
Following steps are repeated, until traversing the non-hub node of each of the second hinge set:
Any non-hub node in the second hinge set is selected as the non-hub node of third, another non-hub node is made
For the 4th non-hub node；
Described hub node will be expanded to ring and the non-hub node of the third carries out role exchange；By the described 4th non-hinge section
Point is used as the 4th hub node；
The non-hub node of the third after changing role and the hinge side between the second endpoint are replaced with into the 4th hinge
The hinge side and the 4th hub node of node and the second endpoint and the pivot of the non-hub node of the third after changing role
Knob side；
It determines the totle drilling cost of current network, and according to the totle drilling cost, to the direct-connected side of current network and is connect by greedy algorithm
Enter side to be handled, to reduce totle drilling cost；
Reverse operating successively is executed to the hinge ring in current network；After the reverse operating comprises determining that hinge ring is reversed
Whether totle drilling cost reduces, if totle drilling cost reduces that hinge ring is reversed.
7. according to the described in any item methods of claim 2-6, which is characterized in that it is described by variable neighborhood search algorithm to described
Hub location result optimizes, and exports the hub location result after optimization, comprising:
Using the hub node of current network as initial solution set, and determine the corresponding initial cost of initial solution set；
Neighborhood is obtained after selecting any hub node in the initial solution set and any non-hub node progress role swap
Set；
The corresponding neighborhood cost of Neighbourhood set is calculated, if neighborhood cost is less than initial cost, by Neighbourhood set to initial disaggregation
Conjunction is updated；
After repeating above-mentioned steps pre-determined number, current initial solution is exported in conjunction with corresponding hub location result.
8. a kind of hub location equipment characterized by comprising
Determining module, for determining the pivotability of each pair of node in network；Wherein, the pivotability is with by the construction of each pair of node
Totle drilling cost in network when unique a pair of hub node is inversely proportional；
Module is constructed, for choosing unique a pair of of hub node of maximum a pair of of the node of pivotability as current network, and
Company side in network configuration setting current network when according to pivotability maximum between each node, constructs initial network；Wherein when
Each node includes each hub node and each non-hub node in preceding network；
First processing module, for judging whether hinge number of nodes is equal with predetermined hub node quantity in current network, if
The hub node quantity of current network is less than the predetermined hub node quantity, then tree expansion and ring are successively executed to current network
It expands, so that the lowest cost of current network, and the hinge quantity of current network is added one, until the hinge section of current network
Point quantity is equal to the predetermined hub node quantity；Export the corresponding hub location result of current network.
9. a kind of hub location equipment characterized by comprising at least one processor and memory；
The memory stores computer executed instructions；
At least one described processor executes the computer executed instructions of the memory storage, so that at least one described processing
Device executes hub location method as described in any one of claim 1 to 7.
10. a kind of computer readable storage medium, which is characterized in that be stored with computer in the computer readable storage medium
It executes instruction, when processor executes the computer executed instructions, realizes hinge as described in any one of claim 1 to 7
Site selecting method.
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| CN112330011A (en) * | 2020-11-02 | 2021-02-05 | 杭州五代通信与大数据研究院 | ICT infrastructure site selection method based on variable neighborhood search |
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