MILP-based ground mobile communication network survivability reconstruction method

Abstract

The invention discloses a ground mobile communication network survivability reconstruction method based on mixed integer linear programming, and belongs to the technical field of communication network optimization and robustness enhancement. The method comprises the steps of 1, defining parameter representation of attribute data of the ground mobile communication network, wherein the parameter representation comprises node distribution, communication radius and the like; 2, based on a k-connected graph theory, constructing a ground mobile communication network survivability reconstruction MILP model, and representing connectivity constraints under dynamic movement of nodes through a network flow model; and step 3, solving the model through a branch and bound algorithm to obtain optimal node coordinate configuration for minimizing the total moving distance of network reconstruction on the premise of satisfying survivability topology reconstruction. The method can break through the limitation that a traditional passive response cannot resist a network fault again, improves the topology robustness after the partition network is recovered, effectively prevents the risk caused by the secondary damage of the network in the future, and can be expanded and applied to the engineering fields of unmanned aerial vehicle cluster communication, emergency disaster relief networks and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of enhancing the resilience of communication networks and dynamic topology optimization, and particularly to a method for reconstructing the survivability of a terrestrial mobile communication network based on MILP. Background Art

[0002] In the construction of smart cities, industrial Internet, and battlefield informatization, as the core carrier of ubiquitous connection, the survivability of terrestrial mobile communication networks is directly related to the reliability of critical mission communication. Such networks need to maintain a stable topological structure under multiple dynamic interferences such as complex electromagnetic environments, random node movements, and sudden link interruptions to ensure high-value services such as real-time data transmission and edge computing collaboration. In the 5G era, the dynamic reconfiguration ability of network nodes has become the core indicator for measuring the resilience of communication systems, restricting the feasibility of emerging scenarios such as Internet of Things perception in smart cities and collaborative operation of industrial robot clusters.

[0003] Existing terrestrial mobile network recovery technologies generally have defects in topological resilience design. The core problem is that the dynamic reconfiguration goal is limited to restoring the single connectivity of the network. Although this paradigm can achieve rapid function reconstruction, the single-connected topology essentially forms a tree structure, and the damage of any non-leaf node will cause the network to be split again, forming a negative cycle of "repair-failure" in scenarios where nodes are prone to continuous failure in a dynamic interference environment. Moreover, due to the lack of pre-set redundant links during the reconfiguration process, the single-connected reconstructed network lacks multi-path fault tolerance when encountering subsequent interferences, and the load pressure on key nodes accumulates exponentially, greatly increasing the risk of cascading failures. This passive response recovery logic fundamentally conflicts with the active survivability requirements of the dynamic environment, and it is neither possible to build a topological resilience reserve to resist multiple faults nor to achieve sustainable network maintenance under energy consumption constraints. Summary of the Invention

[0004] To address the above problems, the present invention proposes a method for reconstructing the survivability of a terrestrial mobile communication network based on mixed integer linear programming (MILP). Based on the k-connected graph and network flow theory, an MILP model for reconstructing the survivability of a terrestrial mobile network is constructed to obtain the optimal reconstructed coordinate configuration of mobile network nodes that meet the k-connected requirements, breaking through the limitation of traditional passive responses that cannot resist network failures again, improving the topological robustness after the recovery of the partitioned network, effectively preventing risks brought by future network disruptions, and improving the theoretical completeness and engineering applicability of the recovery strategy for terrestrial mobile communication networks in fault-prone environments.

[0005] A method for reconstructing the survivability of a terrestrial mobile communication network based on MILP includes the following steps (taking k = 2 as an example):

[0006] Step 1: Define the parameter representation of the attribute data of the terrestrial mobile communication network;

[0007] Specifically: Set the set of mobile nodes that make up the ground communication network as V, where i is the serial number of the node and i = 1, 2, …, |V|, and the set of communication links between any two mobile nodes as E. The two-dimensional coordinates of mobile node i before reconstruction are (x i , y i ). The maximum transmission radius of the signal for mobile node communication is R. The source node of the network flow is s1, the backup source node is s2, M is a large number such as 9999, and S is a small number such as 0.0001.

[0008] Step 2: Establish a MILP model for the survivability reconstruction of the ground mobile communication network based on the k - connected graph and network flow theory. With network traffic allocation and the coordinates of the nodes after reconstruction as decision variables, and minimizing the total distance of node movement caused by network reconstruction as the optimization goal, overall network topology reconstruction and network survivability design are coordinated;

[0009] Step 2.1: Define the decision variables for the survivability reconstruction of the ground mobile communication network;

[0010] X i : The x - axis coordinate of mobile node i after reconstruction;

[0011] Y i : The y - axis coordinate of mobile node i after reconstruction;

[0012] d i : The Euclidean distance between the coordinates of mobile node i before and after reconstruction;

[0013] D ij : The Euclidean distance between the coordinates of mobile nodes i and j after reconstruction;

[0014] f h,i,j : The network traffic transmitted from node i to node j when node h fails;

[0015] e ij : A variable of 0 or 1, which is 1 if and only if there is a communication link between node i and node j after network reconstruction, otherwise 0;

[0016] Step 2.2: Establish the objective function for the survivability reconstruction of the ground mobile communication network;

[0017]

[0018] Among them, Total Distance is the established objective function, and d i is the Euclidean distance between the coordinates of mobile node i before and after reconstruction;

[0019] Step 2.3: Establish the constraint for calculating the node movement distance;

[0020]

[0021] Among them, X i and Y i are the decision variables of the x and y axial coordinates after the reconstruction of the mobile node i, respectively;

[0022] Step 2.4: Establish the constraint for calculating the distance between nodes after network reconstruction;

[0023]

[0024] Step 2.5: Establish the communication ability constraint between nodes after network reconstruction;

[0025]

[0026]

[0027] Among them, D ij is the Euclidean distance between node i and node j after network reconstruction;

[0028] Step 2.6: Establish the network invulnerable reconstruction constraint based on k-connected graph;

[0029] Network invulnerable reconstruction constraint when any single node other than the source node s1 fails;

[0030]

[0031]

[0032]

[0033] Network invulnerable reconstruction constraint when the source node s1 fails;

[0034]

[0035]

[0036]

[0037] Flow propagation ability constraint between nodes after network reconstruction;

[0038]

[0039] Step 2.7: Variable value constraint;

[0040]

[0041]

[0042] Step 3: Linearize the modeling of the two-dimensional Euclidean distance based on the tangent plane envelope;

[0043] Step 3.1: Introduce additional parameters;

[0044] δ: The maximum acceptable error percentage value for the linearization of the Euclidean distance;

[0045] n: The number of cutting planes used for the linearization of the Euclidean distance;

[0046] θ: The angle between adjacent cutting planes used for the linearization of the Euclidean distance;

[0047] Step 3.2: Introduce additional decision variables;

[0048] dx: The variable of the x - axis movement distance of node i before and after reconstruction;

[0049] dy: The variable of the y - axis movement distance of node i before and after reconstruction;

[0050] DX: The variable of the x - axis distance between nodes i and j after reconstruction;

[0051] DY: The variable of the y - axis distance between nodes i and j after reconstruction;

[0052] Step 3.3: Use the cutting - plane envelope method to linearly approximate the two - dimensional Euclidean distance;

[0053] Linearize the Euclidean distance of node movement before and after network reconstruction;

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Linearize the Euclidean distance between nodes after network reconstruction;

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] Step 4.4: Constraint on additional parameters and variable values;

[0067] θ = argcos(1 + 4δ + 2δ 2 ) (26)

[0068]

[0069] dx, dy, DX, DY ≥ 0 (28)

[0070] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0071] By introducing a k - connected constraint reconstruction mechanism, the present invention breaks through the topological vulnerability bottleneck of traditional single - connected recovery strategies, actively constructs a network topological structure with redundant path fault - tolerance ability during the reconstruction process, enabling the restored network to maintain global connectivity through preset alternative paths when node failures or link interruptions occur subsequently, effectively avoiding the vicious cycle of "repair - re - breakage". At the same time, the present invention constructs a solvable MILP model based on mathematical programming theory, which can obtain the exact optimal solution of node configuration after network reconstruction, minimize the total moving distance of network reconstruction on the premise of meeting the anti - destruction topological reconstruction, enable the terrestrial mobile communication network to have sustainable anti - destruction ability in high - perturbation scenarios such as disaster rescue and tactical communication, and significantly improve the sustainability of network services in complex dynamic environments. Description of the Drawings Figure 1 is a flowchart of a method for anti - destruction reconstruction of a terrestrial mobile communication network based on MILP according to the present invention. Figure 2 is a schematic diagram of a two - dimensional Euclidean distance tangent - plane envelope linearization method adopted by the present invention. Figure 3 is a schematic diagram for comparing different anti - destruction reconstruction strategies of a terrestrial mobile communication network. Detailed Embodiments

[0072] The present invention will be described in detail below with reference to the drawings and embodiments.

[0073] A method for anti - destruction reconstruction of a terrestrial mobile communication network based on MILP includes the following steps (taking k = 2 as an example):

[0074] Step 1: Define the parameter representation of the attribute data of the terrestrial mobile communication network;

[0075] Specifically: Set the set of mobile nodes constituting the terrestrial communication network as V, where i is the serial number of the node and i = 1, 2, …, |V|, the set of communication links between any two mobile nodes as E, and the two - dimensional coordinates of mobile node i before reconstruction as (x i , y i) The maximum transmission radius of the signal for mobile node communication is R, the source node of the network flow is s1, the backup source node is s2, M is a large number such as 9999, S is a small number such as 0.0001, δ is the maximum acceptable error percentage value for the linearization of the Euclidean distance, n is the number of cutting planes used for the linearization of the Euclidean distance, and θ is the angle between adjacent cutting planes used for the linearization of the Euclidean distance;

[0076] Step 2: Establish a MILP model for the survivability reconstruction of the terrestrial mobile communication network based on the k-connected graph and network flow theory. Taking the network traffic allocation and the coordinates of the nodes after reconstruction as decision variables, and minimizing the total distance of node movement caused by network reconstruction as the optimization objective, overall network topology reconstruction and network survivability design are coordinated;

[0077] Step 2.1: Define the decision variables for the survivability reconstruction of the terrestrial mobile communication network;

[0078] X i : The x-axis coordinate of mobile node i after reconstruction;

[0079] Y i : The y-axis coordinate of mobile node i after reconstruction;

[0080] d i : The Euclidean distance between the coordinates of mobile node i before and after reconstruction;

[0081] D ij : The Euclidean distance between the coordinates of mobile nodes i and j after reconstruction;

[0082] f h,i,j : The network traffic transmitted from node i to node j when node h fails;

[0083] e ij : A 0 or 1 variable, which is 1 if and only if there is a communication link between node i and node j after network reconstruction, otherwise it is 0;

[0084] dx: The x-axis movement distance variable of mobile node i before and after reconstruction;

[0085] dy: The y-axis movement distance variable of mobile node i before and after reconstruction;

[0086] DX: The x-axis distance variable of mobile nodes i and j after reconstruction;

[0087] DY: The y-axis distance variable of mobile nodes i and j after reconstruction;

[0088] Step 2.2: Establish the objective function for the survivability reconstruction of the terrestrial mobile communication network;

[0089]

[0090] Among them, Total Distance is the established objective function, and d i is the Euclidean distance of the coordinates of the mobile node i before and after reconstruction;

[0091] Step 2.3: Use the tangent plane envelope method to perform a linearized approximation calculation on the node movement distance. The schematic diagram of the linearized approximation method is as Figure 2 shown;

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] θ = argcos(1 + 4δ + 2δ 2 ) (35)

[0098]

[0099] Among them, X i and Y i are the decision variables of the x and y axial coordinates after reconstruction of the mobile node i, respectively, and dx and dy are the x and y axial movement distance variables of the mobile node i before and after reconstruction;

[0100] Step 2.4: Use the tangent plane envelope method to perform a linearized approximation calculation on the distance between nodes after network reconstruction;

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] Among them, DX and DY are the x and y axial distance variables of the mobile nodes i and j after reconstruction, respectively;

[0108] Step 2.5: Establish the communication ability constraint between nodes after network reconstruction;

[0109]

[0110]

[0111] Among them, D ij is the Euclidean distance between node i and node j after network reconstruction;

[0112] Step 2.6: Establish network invulnerable reconstruction constraints based on k-connected graphs;

[0113] Network invulnerable reconstruction constraints when any single node other than the source node s1 fails;

[0114]

[0115]

[0116]

[0117] Network invulnerable reconstruction constraints when the source node s1 fails;

[0118]

[0119]

[0120]

[0121] Constraints on the traffic propagation ability between nodes after network reconstruction;

[0122]

[0123] Step 2.7: Variable value constraints;

[0124]

[0125]

[0126] dx, dy, DX, DY ≥ 0 (54)

[0127] Step 3: Solve the MILP model for invulnerable reconstruction of the terrestrial mobile communication network to obtain the optimal node coordinate configuration that minimizes the total mobile distance of the network reconstruction under the premise of meeting the invulnerable topological reconstruction.

[0128] In this embodiment, the model is solved using the branch and bound algorithm embedded in the commercial MILP solver CPLEX 12.9.0 on the GNU / Linux 4.15.0-142-generic x86_64 operating system, and the gap parameter is set to 10 -5 , and the calculation formula of gap is shown in the following formula:

[0129]

[0130] To demonstrate the superiority of the anti-destruction reconstruction proposed in the present invention, in this embodiment, the MILP model constructed in the present invention is named the anti-destruction reconstruction model 1, abbreviated as model 1, and the traditional reconstruction method of single-connected restoration topology is called the single-connected reconstruction model 2, abbreviated as model 2.

[0131] To facilitate the representation of the model results, several symbols are introduced in this embodiment to represent the results of each model: the optimal objective function value obtained by the model, that is, the total moving distance of node reconstruction, is represented by TTD, and the corresponding calculation time is represented by CT;

[0132] To facilitate the quantification of model differences, this embodiment introduces the index of the total moving distance difference of node reconstruction, represented by D TDD as shown in the following formula:

[0133]

[0134] Ten test instances of a certain terrestrial mobile communication network are selected to test and verify the MILP model constructed in the present invention. It is set that there are 10 mobile nodes in the network, the maximum transmission radius of the signal between nodes is 10, M is 999, S is 0.001, and the maximum acceptable error percentage value of the linearization of the two-dimensional Euclidean distance is 0.1%;

[0135] The experimental results are shown in Table 1. The anti-destruction reconstruction model can obtain the optimal node anti-destruction coordinate configuration that minimizes the total moving distance of network reconstruction when the relative error percentage of the linearization of the two-dimensional Euclidean distance does not exceed 0.1%. From the perspective of the solution efficiency, for all test instances, both reconstruction models can obtain the optimal solution within 11 seconds; from the perspective of the total moving distance of reconstruction, the robust reconstruction strategy involved in the present invention requires more TDD than the traditional single-connected reconstruction strategy. The average value of the D TDD index is 76.87%, but the topological structure obtained by model 1 has better robustness than the topological structure obtained by model 2 and can resist possible future network failures, such as Figure 3 shown;

[0136] Table 1 Comparison of the results of the two models

[0137] From the above comparison results, it can be seen that the anti-destruction reconstruction method of the terrestrial mobile communication network designed in the present invention exhibits good robustness in the face of a network failure again, breaking through the limitation that the traditional passive response, such as the single-connected reconstruction strategy, cannot resist network failures again, and improving the theoretical completeness and engineering applicability of the terrestrial mobile communication network restoration strategy for fault-prone environments.

Claims

1. A terrestrial mobile communication network survivability reconstruction method based on MILP; comprising the following steps: (1) Define the parameter representation of terrestrial mobile communication network attribute data; Suppose the set of mobile nodes constituting the ground communication network is V, i is the node number and i = 1, 2, ..., |V|, the set of communication links between any two mobile nodes is E, and the two-dimensional coordinates of mobile node i before reconstruction are (x i ,y i ), the maximum transmission radius of the signal of the mobile node communication is R, the source node of the network flow is s1, the backup source node is s2, M is a large number such as 9999, S is a small number such as 0.0001, δ is the maximum acceptable error percentage value of the Euclidean distance linearization, n is the number of cutting planes used in the Euclidean distance linearization, and θ is the angle between adjacent cutting planes used in the Euclidean distance linearization; (2) A MILP model for the survivability reconstruction of ground mobile communication networks based on k-connected graphs and network flow theory is established. The network traffic distribution and the node coordinates after reconstruction are used as decision variables, and the total distance of node movement caused by network reconstruction is minimized as the optimization goal. The network topology reconstruction and network survivability design are coordinated. The specific methods are as follows: (2.1) Define variable X i Represents the x-axis coordinate of mobile node i after reconstruction; define variable Y i Represents the y-axis coordinate of the mobile node i after reconstruction; define the variable d i represents the Euclidean distance between the coordinates of mobile node i before and after reconstruction; define variable D ij represents the Euclidean distance between the reconstructed coordinates of mobile nodes i and j; define f h,i,j represents the network traffic transmitted from node i to node j when node h fails; define e ij represents a 0 or 1 variable, which is 1 if and only if there is a communication link between node i and node j after network reconstruction, otherwise it is 0; define variable dx to represent the x-axis moving distance of mobile node i before and after reconstruction; define variable dy to represent the y-axis moving distance of mobile node i before and after reconstruction; variable DX represents the x-axis distance between mobile nodes i and j after reconstruction; variable DY represents the y-axis distance between mobile nodes i and j after reconstruction; (2.2) Establish the objective function of the survivability reconstruction of the ground mobile communication network: (2.3) The tangent plane envelope method is used to perform linear approximate calculation of the node movement distance: θ=argcos(1+4δ+2δ 2 ) (2.4) The tangent plane envelope method is used to perform linear approximate calculation of the distance between nodes after network reconstruction: (2.5) Establish the communication capacity constraints between nodes after network reconstruction: (2.6) Establish network anti-destruction reconstruction constraints based on k-connected graph: (2.7) Variable value constraints: dx,dy,DX,DY≥0 (3) The MILP model of terrestrial mobile communication network survivability reconstruction is solved by the branch and bound algorithm, and the optimal node coordinate configuration that minimizes the total moving distance of network reconstruction under the premise of satisfying survivability topological reconstruction is obtained. This breaks through the limitation that traditional passive response cannot resist network failure again, improves the topological robustness of the partitioned network after recovery, and effectively prevents the risks brought by secondary network damage in the future.

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