CN115102894A - Directional blocking-oriented traffic network key node selection method - Google Patents
Directional blocking-oriented traffic network key node selection method Download PDFInfo
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Abstract
The invention discloses a traffic network key node selection method facing directional blocking, which comprises the following steps: extracting a traffic target subnet facing directional blocking; establishing a traffic target selection model facing directional blocking; solving a traffic target selection model by a heuristic search algorithm based on the cost-to-efficiency ratio; a target selection sequence is obtained. According to the starting point and the end point in the traffic network, the communication paths among the nodes, the path lengths of all the paths and the condition of hitting resources consumed by different nodes, an optimal traffic target node set is selected and destroyed, the aim of consuming the least resources and destroying the whole traffic network is achieved, and therefore the task of directionally blocking the transportation network from the starting point to the end point of an enemy is completed.
Description
Technical Field
The invention belongs to the technical field of transportation, and particularly relates to a method for selecting key nodes of a traffic network for directional blocking.
Background
The transportation network is the important part of war attack since ancient times, and the transportation is not only the material basis for the maneuvering of military strength, but also the central link for the logistics guarantee of military materials. With the continuous development of transportation facilities, the destruction and anti-destruction fight of two enemy parties around a traffic line in the modern war often has important influence on the progress and the outcome of the war. Historically, all wars have been based on transportation, and with the continued development and innovation of transportation vehicles and transportation facilities, the role of transportation in military operations has become increasingly important. During war, the traffic network composed of roads, railways, navigation channels and the like has an important guarantee effect on rapid deployment of military personnel materials, and the destruction of the traffic network is helpful for getting a first opportunity in war, so that traffic targets increasingly become key hit targets in modern war.
In modern economic construction, traffic facilities are also important capital construction facilities which are primarily constructed, with the development of economic construction, traffic networks of main countries or regions are more and more developed, roads are comprehensively staggered, and the number of nodes such as bridges, tunnels, interchange hubs and the like is large. The construction of modern traffic networks is mostly systematic design, destroy a single target node and can not completely reach the purpose of thoroughly blocking the transportation capability of enemy traffic networks, and a plurality of nodes need to be selected for combined attack. Aiming at the combat demand of directionally blocking an enemy transportation network in a war, networked modeling and analysis are carried out on an enemy transportation target system, a target selection method for hitting the enemy transportation target system is researched, and a mission planning technical support is provided for effectively blocking enemy troops and material maneuvering. The problem of quickly selecting key nodes meeting the directional blocking requirement from a large and complex traffic network is a very important technical problem to be solved in the field.
Disclosure of Invention
In view of this, the present invention aims to provide a method for selecting a traffic network key node facing directional blocking, where the known enemy traffic network node distribution information is: the method comprises the steps of determining a target node set by hitting resources consumed by different nodes, determining a starting point and a terminal point in the network, communicating paths among the nodes, path lengths of all the paths, and hitting the resources consumed by different nodes, and directionally blocking the rapid transportation network from the starting point to the terminal point by hitting the target point set with the least resource consumption.
The invention aims to realize the method for selecting the key nodes of the traffic network facing the directional blocking, which comprises the following steps:
step1, extracting a traffic target subnet facing directional blocking;
step2, establishing a traffic target selection model facing directional blocking;
step3, solving a traffic target selection model based on a heuristic search algorithm of the cost-effectiveness ratio;
and 4, obtaining a target selection sequence.
Specifically, the traffic target selection model is as follows:
s.t.
formula (1) is an objective function, and represents the total resource consumption for destroying the target node set, wherein V ═ 1,2, ·, n represents the target node set; x is the number of i If the node i belongs to the V and serves as a striking target, the value is 1, otherwise, the value is 0; c i Representing the resources consumed by the hit node i; z represents the overall resource consumption; constraint (2) ensures that at least one node on each path in the front K short circuit is selected as a hit target, wherein the set K ═ 1,2, ·, K represents the front K short circuit set; a is a ik Indicating whether the kth short contains node i, when a ik When equal to 1, means comprisingWhen a is ik When 0 is equal, V is not included k Representing the kth short circuit containing point set; equation (3) constrains the decision variable x i The value range of (a).
Specifically, the heuristic search algorithm based on the hit cost-to-efficiency ratio takes the ratio of the number of times that a node appears in the front k short circuit to the cost consumed for hitting the node as a node importance index, and the cost-to-efficiency ratio RCE of the node i i The calculation formula is as follows:
the heuristic search algorithm specifically comprises the following steps:
step 301: judging whether the set K is empty, if the set K still has feasible paths, selecting the shortest path j in the set K to be belonged to the K, and calculating a node set A contained in the path j j (ii) a If the set K is empty, ending the program;
step 302: set of compute nodes A j The cost-to-efficiency ratio of all nodes in the system is selected, and the node with the highest striking cost-to-efficiency ratio is selected to be i E A j ；
Step 303: judging whether the node i is a starting point or an end point, if so, selecting a node with the cost-effectiveness ratio higher than the second, and judging Step303 again;
step 304: and adding the node i to the most preferred node set, sequentially judging whether all paths in the set K contain the node i, deleting all paths containing the node i, and continuing to Step 301.
Furthermore, the traffic target sub-network is a sub-network formed by paths contained in the first k shortest paths, and the extraction process of the traffic target sub-network comprises the following steps:
step 101: initialization: a starting point s, an end point d, a path length threshold value theta that a feasible path existing in the traffic network cannot exceed, k being 1;
step 102: calculating the shortest path from node s to node d, the length being marked as p k ,k＝1；
Step 103: if p is k Less than a predetermined path lengthAdding the path into a candidate path set forming a required subnet if the threshold value theta is not reached, and ending the program if the threshold value theta is not reached;
step 104: let the k path have Q k A node, sequentially for the i-th 1,2, …, Q on the k-th path k 1 node, assuming point i to point i +1 unreachable, i.e., d iq ＝∞,q＝i+1，d iq Representing the distance from the node i to the node q, calculating the shortest path from the ith node to the end point d, wherein the ith node is called a deviated node, the shortest path from the ith node to the end point d is called a deviated path, and recovering d after the circulation is finished iq And (5) original value.
Step 105: q calculated by Step104 k -1 off-path, available Q k -1 feasible paths from the starting point s to the end point d, and selecting the shortest one of the feasible paths, namely the (k + 1) th shortest path with the length p k+1 Let k be k +1, and return to Step 103.
Drawings
Fig. 1 is a schematic overall flow chart of the embodiment of the present invention.
Detailed Description
The present invention is further described with reference to the drawings, but the present invention is not limited thereto in any way, and any modifications or alterations based on the teaching of the present invention shall fall within the scope of the present invention.
The traffic network is complex and huge, generally comprises roads, bridges, tunnels, hubs, overpasses, intersections and the like, and in order to facilitate problem description modeling and solving, the traffic network is abstracted into a complex network in the embodiment, and is expressed by a directed graph G mathematically. G ═ V, E) where V denotes the set of target nodes in the directed graph, E denotes the set of paths in the directed graph, E ij Representing the path from node i to node j. In actual conditions, paths can be quickly restored when hitting enemies, and hitting difficulty is high, so that the hitting of the nodes is only considered, and all paths connected with the nodes are broken down after the nodes are hit.
As shown in fig. 1, the method for selecting a traffic network key node facing directional blocking includes the following steps:
step1, extracting a traffic target subnet facing directional blocking;
step2, establishing a traffic target selection model facing directional blocking;
step3, solving a traffic target selection model based on a heuristic search algorithm of the cost-effectiveness ratio;
and 4, obtaining a target selection sequence.
When the enemy traffic network is directionally blocked according to the battle mission, if the analysis of the whole traffic system not only wastes time and actual problems, but also generates deviation, the enemy needs to be determined to pass through network sections in the traffic system instead of analyzing the whole traffic system. Therefore, how to extract the possibly utilized sub-networks of the enemies from the huge traffic network is a key basis for selecting the traffic target. The embodiment designs an extraction method of a target subnet of a traffic network system based on a DijkStar algorithm. In the Dijkstra algorithm, it is assumed that each node in the traffic network has a label (d) t ，p t )，d t Is the shortest path length from the starting node s to the node t; p is a radical of t The set of previous points representing the t point in the shortest path from s to t.
The basic process of the algorithm for solving the shortest path from the starting point s to the point t is as follows:
step 1: initialization, setting the starting point as: d s ＝0；p s Is empty;
all remaining points: di ∞, pi undefined;
mark start s, mark k ═ s, and set all other points to unmarked.
Step 2: the distances between all marked points k and other directly connected unmarked points j are checked,
and is set as follows: d j ＝min[d j ，d k +w(k，j)]；
W (k, j) represents the path length from node k to node j.
Step 3: the next node is selected.
And selecting the minimum point i from all unmarked nodes, selecting the point i as one point in the shortest path, and setting the point i as the marked node.
Step 4: and finding the last node of the point i.
Finding the point directly connected with the point i from the marked point set and marking the point as p i 。
Step 5: the inode is marked.
If all points are marked, the algorithm ends. Otherwise, mark k ═ i and go to Step2 to continue.
As can be seen from the steps of the algorithm described above; the key part of the Dijkstra algorithm is to continuously find points closest to a source point from unmarked points, add the points to a marked point set, and update the shortest estimated distance from the rest points in the unmarked point set to a starting point.
In order to extract a target point set which is convenient to select and directionally block to be destroyed, a target subnet needs to be extracted from a traffic network, and the problem is simplified to the blocking of all paths in the target subnet. The traffic target sub-network of the problem is the sub-network formed by the paths contained in the first k shortest paths.
The core of the subnet extraction algorithm is to delete an arc on the existing shortest path of the graph and find a replacement arc, thereby finding the next optional path. The subnet extraction algorithm is actually implemented by adding an extra node and corresponding arc in the shortest path of the directed graph. The algorithm is described as follows:
step 101: initialization: a starting point s, an end point d, a path length threshold value theta that a feasible path existing in the traffic network cannot exceed, k being 1;
step 102: calculating the shortest path from node s to node d, the length being marked as p k ,k＝1；
Step 103: if p is k If the path length is less than the set path length threshold value theta, adding the path into a candidate path set forming the required subnet, otherwise, ending the program;
step 104: let the k path have Q k A node, which is sequentially corresponding to the i-th, 1,2, …, and Q on the k-th path k 1 node, assuming point i to point i +1 unreachable, i.e., d iq ＝∞,q＝i+1，d iq Represents the distance from node i to node qCalculating the shortest path from the ith node to the end point d, wherein the ith node is called a deviation node, the shortest path from the ith node to the end point d is called a deviation path, and recovering d after the circulation is finished iq And (5) original value.
Step 105: q calculated by Step104 k -1 off-path, Q is obtained k -1 feasible paths from the starting point s to the end point d, and selecting the shortest one of the feasible paths, namely the (k + 1) th shortest path with the length p k+1 Let k be k +1, and return to Step 103.
According to the method, the first k shortest circuits meeting the directional blocking target requirement can be obtained under the condition of specifying the required shortest circuit path length. By the method, the target sub-network required by research can be effectively extracted.
And constructing a model and designing a target selection algorithm aiming at the extracted target system subnet. Firstly, a traffic target selection problem and basic assumptions facing directional blocking are introduced, optimization targets and relevant constraints of the problem are analyzed on the basis, and a linear integer programming model of the problem is constructed. And finally, designing two target selection heuristic algorithms based on the node importance and the cost-effectiveness ratio respectively.
The method comprises the steps that a starting point and an end point of a traffic network to be blocked and all paths and nodes between the starting point and the end point are obtained through a traffic target sub-network extraction method; and under the condition that the cost for hitting each node and the time consumed by an enemy passing each section of path are known, the minimized hitting cost is taken as an objective function, and a traffic target selection model facing directional blocking is constructed and established in consideration of the constraint conditions such as the capability of destroying the enemy reaching the end point in the expected time and the like.
In order to facilitate subsequent modeling and analysis solving, the following more general assumptions in complex network analysis are introduced:
the time spent by the enemy through each path is known;
after a certain node is hit, the path connected with the node cannot pass through;
the cost of hitting each node is known and hitting must destroy the node.
In the traffic node target selection problem, the problem factor mainly comprises k short-circuit target sub-networks, wherein the sub-networks comprise nodes and select hit target nodes. The embodiment mainly performs definition and constraint analysis on three factors, and defines the optimization target of the model.
(1) k short-circuited target subnetwork
And after a traffic system network model is built, calculating and extracting a k short circuit target sub-network. The set of target nodes in the sub-network is denoted as V ═ {1,2, ·, n };
(2) sub-network comprising nodes
Counting target nodes in the extracted sub-network;
(3) selecting a target node of a strike
Selecting a target node needing to be struck through calculation;
(4) optimizing an objective
And the resource consumption for destroying the target node is minimized.
Through the problem description, the parameters and decision variables used in the modeling process are summarized as follows:
the traffic target selection optimization problem facing the directional blocking is to select a target node set capable of cutting off all k short circuits between a starting point and a terminal point, and to minimize the overall resource consumption for destroying all nodes in the set, wherein a mathematical model is as follows:
s.t.
equation (1) is an objective function, representing the overall resource consumption for destroying the target node combination. Constraint (2) ensures that at least one node on each k short is selected as a hit target; the constraint (3) represents the value range of the decision variable.
Aiming at the problem of traffic target selection facing directional blocking, a corresponding heuristic algorithm is designed based on two different node importance degree calculation methods. According to the embodiment, through research, it is found that generally, selecting hit target nodes according to the degree (out degree and in degree) sorting of the nodes cannot select the target node which most effectively blocks the first K shortest circuits, and therefore, the sum of the occurrence times of the nodes in the first K shortest circuits is calculated as the importance degree of the node to sort and select the target. Through experiments, the target node selected by the method can be effectively blocked off the enemy traffic network.
Degree is a basic term describing a network graph and is also an important concept describing the properties of a single node. The network graph is composed of a plurality of nodes and a plurality of edges connecting the nodes, and the number of the edges connected by each node is the degree of the node. When the degree is used as an index of the importance of a node of a traffic network, the more roads connecting the node, the higher the importance of the node. But the importance of a single node defined by the method cannot well reflect the importance of the node in utilizing the traffic network in the process of enemy directional maneuver.
The embodiment provides a heuristic search algorithm based on Node Importance (NI), which takes the sum of k short-circuit times before a Node appears as a Node importance index of the method, and solves a target selection set in a traffic network model based on the importance.
Node I Importance (NIi) is defined as follows:
equation (4) indicates that the more K shorts share a node, the more this node is for blocking enemies from A to BIt is important. By statistical value NI i The ranking of the node importance degree is used as the ranking of the node importance degree in the traffic network, so that a basis is provided for the selection of the directional blocking target node.
On the basis of the node importance, a heuristic search algorithm based on a Ratio of Cost and Efficiency (RCE) is further provided, the product of the total number of times of short circuits of the node appearing before k times and the Cost consumed by attacking the node is taken as a node importance index of the method, and a target selection set in a traffic network model is solved on the basis of the importance.
Define node i hit cost-to-efficiency Ratio (RCEi) as follows:
in practical situations, the method also needs to define a cost set C according to the strike cost of different nodes i And selecting a striking target point set by calculating the cost-to-efficiency ratio of each target point and sorting.
The method takes the sequencing of the statistical values RCE as the sequencing of the importance degree of the nodes in the traffic network, thereby providing a basis for the selection of the directional blocking target nodes. The method specifically comprises the following steps:
step 301: judging whether the set K is empty, if feasible paths still exist in the set K, selecting the shortest path j in the set K to be belonged to the K, and calculating a node set A contained in the path j j (ii) a If the set K is empty, ending the program;
step 302: set of compute nodes A j The cost-to-efficiency ratios of all nodes in the system are selected, and the node i belonging to the A with the highest striking cost-to-efficiency ratio is selected j ；
Step 303: judging whether the node i is a starting point or an end point, if so, selecting a node with the cost-effectiveness ratio higher than the second, and judging Step303 again;
step 304: adding the node i to the bestpoint set, sequentially judging whether all paths in the set K contain the node i, deleting all paths containing the node i, and continuing to Step 301;
the bestpoint collection is a search result.
As can be seen from the summary and the embodiments of the present invention, the problem of directional blocking of a traffic network in the present embodiment refers to known enemy traffic network node distribution information: under the conditions of starting point and end point, communication paths among nodes, path length of each path and the consumption of resources of different nodes in the network, an optimal traffic target node set is selected and destroyed, and the aim of consuming the least resources and destroying the whole traffic network is achieved, so that the task of directionally blocking the transportation network from the starting point to the end point of an enemy is completed.
Claims (4)
1. The method for selecting the key nodes of the traffic network facing the directional blocking is characterized by comprising the following steps:
step1, extracting a traffic target subnet facing directional blocking;
step2, establishing a traffic target selection model facing directional blocking;
step3, solving a traffic target selection model based on a heuristic search algorithm of cost-effectiveness ratio;
and 4, obtaining a target selection sequence.
2. The method for selecting key nodes of a traffic network facing directional blocking according to claim 1, wherein the traffic target selection model is as follows:
s.t.
equation (1) is an objective function, representing the maximumThe overall resource consumption of the target node set is destroyed in a small mode, wherein V & ltgt1, 2 & gtis & ltcng & gtand n & ltcng & gt represents the target node set; x is a radical of a fluorine atom i If the node i belongs to the V and serves as a striking target, the value is 1, otherwise, the value is 0; c i Representing the resources consumed by the hit node i; z represents the overall resource consumption; constraint (2) ensures that at least one node on each path in the front K short circuit is selected as the hit target, wherein the set K ═ 1,2, ·, K } represents the front K short circuit set; a is ik Indicating whether the kth short contains node i, when a ik When equal to 1, means comprising, when a ik When 0 is equal, V is not included k Representing the kth short circuit containing point set; equation (3) constrains the decision variable x i The value range of (a).
3. The method for selecting key nodes of traffic network facing directional blocking according to claim 2, wherein the heuristic search algorithm based on the cost-to-effectiveness ratio takes the ratio of the number of times that a node appears in the front k short circuit to the cost consumed for hitting the node as a node importance index, and the cost-to-effectiveness ratio RCE of a node i i The calculation formula is as follows:
the heuristic search algorithm specifically comprises the following steps:
step 301: judging whether the set K is empty, if the set K still has feasible paths, selecting the shortest path j in the set K to be belonged to the K, and calculating a node set A contained in the path j j (ii) a If the set K is empty, ending the program;
step 302: set of compute nodes A j The cost-to-efficiency ratios of all nodes in the system are selected, and the node i belonging to the A with the highest striking cost-to-efficiency ratio is selected j ；
Step 303: judging whether the node i is a starting point or an end point, if so, selecting a node with the cost efficiency higher than the second highest, and judging Step303 again;
step 304: and adding the node i to the most preferred node set, sequentially judging whether all paths in the set K contain the node i, deleting all paths containing the node i, and continuing to Step 301.
4. The method for selecting the key nodes of the traffic network facing the directional blocking according to claim 1, wherein the traffic target sub-network is a sub-network formed by the first k shortest paths, and the extraction process of the traffic target sub-network comprises the following steps:
step 101: initialization: a starting point s, an end point d, a route length threshold value theta which is not exceeded by a feasible route existing in the traffic network, wherein k is 1;
step 102: calculating the shortest path from node s to node d, the length being marked as p k ,k＝1；
Step 103: if p is k If the path length is smaller than the set path length threshold value theta, adding the path into a candidate path set forming a required subnet, otherwise, ending the program;
step 104: let the k path have Q k A node, which is sequentially corresponding to the i-th, 1,2, …, and Q on the k-th path k 1 node, assuming point i to point i +1 unreachable, i.e., d iq ＝∞,q＝i+1，d iq Representing the distance from the node i to the node q, calculating the shortest path from the ith node to the end point d, wherein the ith node is called a deviated node, the shortest path from the ith node to the end point d is called a deviated path, and recovering d after the circulation is finished iq And (4) the original value.
Step 105: q calculated by Step104 k -1 off-path, Q is obtained k -1 feasible paths from the starting point s to the end point d, and selecting the shortest one of the feasible paths, namely the (k + 1) th shortest path with the length p k+1 Let k be k +1, and return to Step 103.
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