CN110620686B - Routing node selection method based on complex communication network - Google Patents

Routing node selection method based on complex communication network Download PDF

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CN110620686B
CN110620686B CN201910838352.7A CN201910838352A CN110620686B CN 110620686 B CN110620686 B CN 110620686B CN 201910838352 A CN201910838352 A CN 201910838352A CN 110620686 B CN110620686 B CN 110620686B
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communication network
routing
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CN110620686A (en
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赵广社
高雷涛
王鼎衡
陈叶飞
张文慧
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/08—Configuration management of networks or network elements
    • H04L41/0803—Configuration setting
    • H04L41/0823—Configuration setting characterised by the purposes of a change of settings, e.g. optimising configuration for enhancing reliability
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/12—Discovery or management of network topologies
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00—Routing or path finding of packets in data switching networks
    • H04L45/02—Topology update or discovery
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00—Routing or path finding of packets in data switching networks
    • H04L45/12—Shortest path evaluation
    • H04L45/123—Evaluation of link metrics

Abstract

The invention discloses a routing node selection method based on a complex communication network, which comprises the following steps: for any complex communication network with a directed topology structure, the maximum matching algorithm is utilized to obtain the minimum number N which enables the whole network to be controllablelA control source and its position; establishing a dynamic equation of the whole network according to the dynamic characteristics of each node in the network; selecting M routing nodes as external control sources to control the whole network to obtain a control cost model of the whole network; simplifying the control cost model and determining constraint conditions; gradually selecting the routing nodes by using a greedy algorithm until the selection of the M routing nodes is completed; and exchanging a certain routing node with a certain non-routing node by using an exchange algorithm, and further optimizing the selection of the M routing nodes according to the influence of the new routing node combination on the control cost of the whole network. The invention can select different numbers of routing nodes in the complex communication network, so that the control cost of the whole communication network is minimum.

Description

Routing node selection method based on complex communication network
Technical Field
The invention belongs to the field of communication and system control, and particularly relates to a routing node selection method based on a complex communication network.
Background
Complex communication networks are composed of a large number of nodes and intricate communication connections between the nodes. In real life, some complex systems can be modeled into a complex communication network for analysis, such as a common social network, a power network, an aviation network, a biological network, and the like. Analyzing the model of the complex communication network is not only for controlling the whole communication network, but also needs to consider how to select the routing node to realize the minimum control cost of the whole communication network.
At present, the research on the complex communication network focuses on the controllability of the network, but under the controllable condition of the whole network, the transmission of the communication between the network nodes needs the input of an additional control signal, and the control cost is generated. Under the condition that the number of the additional control sources is certain, how to select some nodes in the network nodes as routing nodes to be connected with external control sources to control the whole communication network ensures that the control cost of the whole network is minimum, and the method is a problem with practical application value. For example, in a social network, the spread of public opinions is gradually enlarged under the influence of partial people, if important people spread, the public opinions can be spread quickly, and otherwise the public opinions can be subsided. Meanwhile, in the advertising effect, the maximum benefit is realized by using the minimum cost, and some important individual pronunciations with different influences can be selected; that is, under a certain control cost, the minimum number of important figures are selected for the introduction, so that the labor cost can be reduced and the redundant workload can be eliminated. Therefore, focusing on a controllable complex communication network model, and selecting some routing nodes to realize the minimum control cost; or under the condition of certain cost, the minimum number of the routing nodes is selected, and efficient and economic complex communication network maintenance and management can be realized.
Disclosure of Invention
The invention aims to provide a routing node selection method based on a complex communication network, which aims at the problem of overhigh control cost of the complex communication network in the communication process, provides a greedy algorithm to iteratively select a specific routing node in the communication network based on a mathematical model of a routing node selection strategy, and further optimizes the control cost of the whole communication network to keep a lower level.
The invention is realized by adopting the following technical scheme:
a routing node selection method based on a complex communication network comprises the following steps:
step 1, obtaining the directed topology connection of the whole communication network and utilizing the maximumThe matching algorithm obtains the minimum number of N that makes the entire network controllablelControl sources and locate their position in the communication network;
step 2, establishing a dynamic equation of the whole complex communication network according to the dynamic characteristics of each node in the communication network;
step 3, for a kinetic equation, taking a control input matrix B as an unknown matrix, and selecting M routing nodes as external control sources to obtain a control cost mathematical model of the whole communication network;
step 4, determining constraint conditions of the control input matrix B according to a kinetic equation and a control cost mathematical model;
step 5, simplifying the control cost model, and minimizing NlUnder the constraint of each control source, gradually completing the selection of M routing nodes by using a greedy algorithm;
and 6, further seeking a better solution of the mathematical model of the control cost by using the switching algorithm, optimizing the selection of the M routing nodes, and traversing all the nodes in the network by using the switching algorithm to obtain the final routing node selection.
The invention is further improved in that in step 1, a minimum number N of the directional communication network is obtained and positioned by using a maximum matching algorithmlThe number of control sources, i.e. control sources, must be greater than or equal to NlTo ensure network controllability.
The invention is further improved in that in step 2, the dynamic characteristics of each node in the network are given according to the specific physical characteristics of the node, and therefore, a dynamic equation of the whole complex communication network is established.
The invention is further improved in that each communication network node is set to be linear dynamic or linear nonlinear dynamic, and a mathematical model of the whole communication network is described as
Figure BDA0002192902390000021
Where X (t) ═ X1(t)，...，xN(t)]TIs the state of N network nodes at time t, A is the connection matrix between NxN dimensional network nodes, where element aijRepresents the connection weight of node i and node j, u (t) ═ u1(t)，...，uN(t)]TIs the control signal applied to the network node by the outside world at time t, B is the N x M dimensional input matrix, M is the number of the outside world control sources, when its element BijA non-zero time indicates that the mth control source has an input signal to the ith node.
The further improvement of the invention is that in step 3, the optimal control input signal u (t) is obtained and is known to be a function of the unknown control input matrix B, the mean square integral of the control input signal is taken as the control cost, M routing nodes are selected as external control sources, and a mathematical model of the control cost of the whole network is constructed.
The invention is further improved in that a control rate design method in an optimal control theory is utilized to construct a mathematical model of the control cost of the whole network
Figure BDA0002192902390000031
Wherein the optimal control rate is
Figure BDA0002192902390000032
Figure BDA0002192902390000033
Is the Larmm matrix of the system, x0Is the initial state of the system; knowing the control rate u (t) as a function of the unknown control input matrix B, obtaining a direct functional relationship between the control cost and the control input matrix B as
Figure BDA0002192902390000034
A further development of the invention consists in determining the control input matrix in step 4
Figure BDA0002192902390000035
The constraint of (2) is: | B | non-conducting phosphor0＝M，Bim∈{0，1}，||.||0L representing a matrix0A norm; if additional control sources m connect node i, B im1, otherwise Bim0; and has rank (b) M to ensure that each control source is connectedDifferent routing nodes.
The invention is further improved in that in step 5, the control cost model of the whole communication network is simplified, the influence of each node as a routing node on the control cost of the communication network is evaluated under the controllable premise of the whole communication network, and a greedy algorithm is utilized to perform N minimumlAnd gradually finishing the selection of the M routing nodes under the constraint of each control source.
The invention is further improved by thatB＝BBTB is the matrix ΛBVector of the principal diagonal,/i(t) is e-AtColumn i elements, further simplifying the control cost model to
Figure BDA0002192902390000036
And which satisfies the constraint ∑ibi＝M，0≤bi＜＜M；
The specific operation of selecting M routing nodes by using a greedy algorithm is as follows:
the method comprises the steps of iteratively selecting a routing node through a greedy algorithm to enable the performance to be optimal, namely the control cost to be minimum, and specifically calculating i-1, 2
Figure BDA0002192902390000041
Selecting a first routing node v1So that the control cost E (b) is minimized; if two or more nodes enable the control cost values to be equally small, one of the nodes is selected as a routing node; in selecting s routing nodes v1,…,vsThen aim at
Figure BDA0002192902390000042
Computing
Figure BDA0002192902390000043
Selecting the v ths+1Routing node causes control cost E (b)s+1And at the minimum, the above process is continued until the selection of the M routing nodes is completed.
A further improvement of the invention is that in step 6 the selection of the M routing nodes is further optimized by means of a switching algorithm, by removing N, which makes the entire communication network controllablelA node, will (M-N)l) One of the routing nodes exchanges with one of the (N-M) non-routing nodes, and the change condition of the control cost after the exchange is checked; if all (N-M) N exchanges do not reduce the control cost, the algorithm terminates; if the control cost is reduced, updating a group of routing nodes, and then performing (N-M) times of exchange again to select a new routing node; and traversing all nodes in the network to obtain the final routing node selection.
Compared with the prior art, the invention has the following beneficial effects: because additional control input signals are needed for transmitting information among nodes in a complex communication network, a large amount of control cost is generated, and when the number of additional control sources is certain and the whole communication network is controllable, the control sources are connected with different routing nodes to generate different control costs. Aiming at any directed complex communication network, the invention selects and positions the control sources with the least quantity to ensure the controllability of the whole communication network, and selects some key nodes as routing nodes on the constraint, thereby minimizing the control cost when controlling the whole communication network.
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FIG. 1 is a schematic diagram of a network topology according to the present invention;
FIG. 2 is a schematic diagram of a topology matching algorithm of the present invention; wherein fig. 2(a) - (c) are three simple network topologies, respectively;
FIG. 3 is a flow chart of a routing node selection algorithm process in the present invention;
fig. 4 is a flow chart of the implementation process of the switching algorithm in the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a routing node selection method based on a complex communication network, which comprises the following steps:
step 1, obtaining the directed topology connection of the whole communication network, and obtaining the minimum quantity N which enables the whole network to be controllable by utilizing the maximum matching algorithmlControls the sources and locates their position in the communication network.
When the whole network is uncontrollable, the control cost is infinite, and only when the whole network is controllable, the control cost of the whole network is considered to be significant. Obtaining the minimum number N of the whole network controllable by the maximum matching algorithmlThe number of control sources, i.e. control sources, must be greater than or equal to NlAnd the selection of the M routing nodes is completed under the constraint that the network is controllable.
Taking fig. 1 as an example, for a topological graph of such a directed communication network, the purpose is to mine the routing nodes in this communication network, so that the control cost of the whole communication network is minimized. In the communication network topology, if the directed edge set of the nodes does not have a common head and tail, the nodes are considered to be matched; if the tail of the node has edge matching, the node is considered not to be matched; if all nodes are matched, it is called a perfect match. According to the maximum matching algorithm, if the path is a perfect match, at least one control source is required to control the path; if not, the minimum number of control sources is the number of unmatched nodes. Fig. 2 shows a node matching rule in a communication network, wherein white nodes are unmatched nodes, gray nodes are matched nodes, and all nodes are perfect matches for a ring network. The directed communication network topology of fig. 1 can be decomposed into many simple network topologies such as fig. 2, and then the minimum number N of the entire network can be obtained and positioned according to the maximum matching algorithmlA control source.
The purpose of this step is to obtain and locate the minimum number of N using the maximum matching algorithmlAnd the control source ensures that the whole network is controllable and provides basic guarantee for the selection of subsequent routing nodes. When the whole communication network is not controllable, the control cost is infinite, and only when the whole network is under the controllable condition, the whole network is consideredThe control cost is significant. The routing nodes are at a minimum number NlThe control source is selected under the constraint of the control source so as to reduce the control cost of the whole communication network.
And 2, establishing a dynamic equation of the whole complex communication network according to the dynamic characteristics of each node in the network.
Assuming that each communication network node is linear dynamic or linearized nonlinear dynamic, the dynamic model of the entire network can be described as
Figure BDA0002192902390000061
Where x (t) ═ x1(t)，...，xN(t)]TIs the state of N network nodes at time t, A is the connection matrix between NxN dimensional network nodes, where element aijRepresents the connection weight of node i and node j, u (t) ═ u1(t)，...，uN(t)]TIs the control signal applied to the node by the outside world at the time t, B is an N x M dimensional input matrix, M is the number of the outside world control sources and M > NlWhen element bijNon-zero indicating that the mth control source has an input signal to the ith node, bijA value equal to zero indicates that there is no corresponding input signal.
The method mainly comprises the step of establishing a dynamic model of the whole communication network, and providing support for the optimal controller design of the subsequent steps and a control cost mathematical model of the whole network.
And 3, for the kinetic equation, taking the control input matrix B as an unknown matrix, and selecting M routing nodes as external control sources to obtain a control cost mathematical model of the whole communication network.
According to the description of the communication network dynamic model in the step 2, a mathematical model of the whole network control cost is constructed as
Figure BDA0002192902390000062
Figure BDA0002192902390000063
The optimal control rate is obtained by using a design method for the control rate in the optimal control theory for reference
Figure BDA0002192902390000064
Figure BDA0002192902390000065
Wherein
Figure BDA0002192902390000066
Is the Larmm matrix of the system, x0Is the initial state of the system. The known control rate u (t) is a function of the unknown control input matrix B, which is introduced into the model (t)f) A direct functional relationship between the control cost and the control input matrix B can be obtained as
Figure BDA0002192902390000067
Figure BDA0002192902390000068
The above model is further simplified to
Figure BDA0002192902390000069
Figure BDA00021929023900000610
And 4, determining the constraint condition of the control input matrix B according to the kinetic equation and the control cost mathematical model.
It is noted that the control cost depends on the control input matrix B, which depends on which nodes are connected to the control source. Norm constraints and orthonormal are the two most common constraints, both of which often reflect the measure and requirement for signal energy in the field of signal processing. Since B is an N × M dimensional input matrix (M is the number of external control sources), when its element BijNon-zero indicating that the mth control source has an input signal to the ith node, bijA value equal to zero indicates that there is no corresponding input signal. Therefore, for determining the number M of routing nodes connected to the additional control source, it is necessary to satisfy | B | survival0＝M，Bim∈{0，1}，||.||0L representing a matrix0A norm; if additional control sources m connect node i, B im1, otherwise Bim0; and there is rank (b) M to ensure that each control source connects to a different routing node.
Step 5, simplifying the control cost model at a minimum number NlAnd under the constraint of each control source, gradually finishing the selection of the M routing nodes by using a greedy algorithm.
Further decomposing the control cost model simplified in the step 3, specifically making ΛB＝BBTB is the matrix ΛBVector of the principal diagonal,/i(t) is e-AtElement of column i, the cost model is equivalent to
Figure BDA0002192902390000071
And satisfies the constraint condition ∑ibi＝M，0≤biThe model can evaluate the influence of different nodes as routing nodes on the control cost of the whole network, and meanwhile, the influence on the control cost of the whole communication network can be evaluated by reducing or increasing the number of the routing nodes.
Taking fig. 3 as an example, the specific operations of the routing node selection process are as follows:
step 1 the minimum number of N has been acquired and locatedlAnd (3) ensuring the controllability of the whole network by using control sources (the minimum number of routing nodes), and iteratively selecting one node as a routing node by using a greedy algorithm under the constraint so as to minimize the control cost. Specifically, for i ═ 1, 2.., n, the calculation is performed
Figure BDA0002192902390000072
Selecting a first routing node v1So that the control cost e (b) is minimized. If two or more nodes make the control cost value equally small, one of the nodes is selected as a routing node.
In selecting s routing nodes v1，...，vsThen aim at
Figure BDA0002192902390000073
Computing
Figure BDA0002192902390000074
Selecting the v ths+1Routing node causes control cost E (b)s+1And at the minimum, the above process is continued until the selection of the M routing nodes is completed.
And 6, further seeking a better solution of the mathematical control cost model by using an exchange algorithm, optimizing the selection of the M routing nodes, and traversing all nodes in the network by using the exchange algorithm to obtain the final routing node selection.
For the M routing nodes obtained in step 5, the switching algorithm shown in fig. 4 is implemented, and the specific operations are as follows: removing N controllable by the whole network aiming at the M routing nodes selected in the step 5lA node, will (M-N)l) One of the routing nodes is exchanged with one of the non-routing nodes (N-M), and the change of the control cost after the exchange is checked. If all (N-M) N exchanges do not reduce the control cost, the algorithm terminates; and if the control cost is reduced, updating a group of routing nodes, then carrying out (N-M) times of switching again to select new routing nodes, and traversing all the nodes in the network by using a switching algorithm to obtain the final routing nodes.

Claims (1)

1. A routing node selection method based on a complex communication network is characterized by comprising the following steps:
step 1, obtaining the directed topology connection of the whole communication network, and obtaining the minimum quantity N which enables the whole network to be controllable by utilizing the maximum matching algorithmlThe number of control sources, i.e. control sources, must be greater than or equal to NlTo ensure network control and to locate their position in the communication network;
step 2, endowing the dynamic characteristics of each node in the communication network according to the specific physical characteristics of the node, and establishing a dynamic equation of the whole complex communication network; setting each communication network node to be linear dynamic or linearizedThe mathematical model of the entire communication network is described as
Figure FDA0002669675750000016
Where x (t) ═ x1(t)，...，xN(t)]TIs the state of N network nodes at time t, A is the connection matrix between NxN dimensional network nodes, where element aijRepresents the connection weight of node i and node j, u (t) ═ u1(t)，...，uN(t)]TIs the control signal applied to the network node by the outside world at time t, B is the N x M dimensional input matrix, M is the number of the outside world control sources, when its element BijA non-zero time indicates that the mth control source has an input signal to the ith node;
step 3, for a kinetic equation, taking a control input matrix B as an unknown matrix, and selecting M routing nodes as external control sources to obtain a control cost mathematical model of the whole communication network; obtaining an optimal control input signal u (t) which is known to be a function of an unknown control input matrix B, taking the mean square integral of the control input signal as control cost, selecting M routing nodes as external control sources, and constructing a mathematical model of the control cost of the whole network; by utilizing a control rate design method in an optimal control theory, a control cost mathematical model of the whole network is constructed as
Figure FDA0002669675750000011
Wherein the optimal control rate is
Figure FDA0002669675750000012
Figure FDA0002669675750000013
Is the Larmm matrix of the system, x0Is the initial state of the system; knowing the control rate u (t) as a function of the unknown control input matrix B, obtaining a direct functional relationship between the control cost and the control input matrix B as
Figure FDA0002669675750000014
Step 4, determining constraint conditions of the control input matrix B according to a kinetic equation and a control cost mathematical model; determining a control input matrix
Figure FDA0002669675750000015
The constraint of (2) is: | B | non-conducting phosphor0＝M，Bim∈{0，1}，||.||0L representing a matrix0A norm; if additional control sources m connect node i, Bim1, otherwise Bim0; and there is rank (b) M to ensure that each control source connects to a different routing node;
step 5, simplifying a control cost model of the whole communication network, evaluating the influence of each node as a routing node on the control cost of the communication network on the premise that the whole communication network is controllable, and utilizing a greedy algorithm to perform minimum quantity NlThe selection of M routing nodes is gradually completed under the constraint of each control source; let ΛB＝BBTB is the matrix ΛBVector of the principal diagonal,/i(t) is e-AtColumn i elements, further simplifying the control cost model to
Figure FDA0002669675750000021
And which satisfies the constraint ∑ibi＝M，0≤bi≤M；
The specific operation of selecting M routing nodes by using a greedy algorithm is as follows:
the method comprises the steps of iteratively selecting a routing node through a greedy algorithm to enable the performance to be optimal, namely the control cost to be minimum, and specifically calculating i-1, 2
Figure FDA0002669675750000022
Selecting a first routing node v1So that the control cost E (b) is minimized; if two or more nodes enable the control cost values to be equally small, one of the nodes is selected as a routing node; in selecting s routing nodes v1，...，vsThen aim at
Figure FDA0002669675750000023
Computing
Figure FDA0002669675750000024
Selecting the v ths+1Routing node causes control cost E (b)s+1At minimum, the above processes are continued until the selection of M routing nodes is completed;
step 6, further seeking a better solution of a mathematical model of the control cost by using an exchange algorithm, optimizing the selection of M routing nodes, and traversing all nodes in the network by using the exchange algorithm to obtain the final routing node selection; the way of further optimizing the selection of the M routing nodes by means of the switching algorithm is to eliminate the N which makes the entire communication network controllablelA node, will (M-N)l) One of the routing nodes exchanges with one of the (N-M) non-routing nodes, and the change condition of the control cost after the exchange is checked; if all (N-M) N exchanges do not reduce the control cost, the algorithm terminates; if the control cost is reduced, updating a group of routing nodes, and then performing (N-M) times of exchange again to select a new routing node; and traversing all nodes in the network to obtain the final routing node selection.
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