Game optimization method and device for link-based combat network attack and defense strategy

Abstract

The present invention provides a game optimization method and device for link-based combat network attack and defense strategies, the method comprising: constructing a kill net model according to the communication relationship between nodes in the link-based combat network, and obtaining the capability value of the kill net model; constructing an attack and defense game model of both sides of the attack and defense, and obtaining the benefit matrix of both sides of the attack and defense in combination with the capability value of the kill net model; solving the Nash equilibrium solution of the attack and defense game model based on the benefit matrix using a solution method corresponding to the scale of the benefit matrix; optimizing the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution. The present invention can realize accurate attack and defense strategy selection in link-based combat network confrontation.

Description

Technical Field

[0001] The present invention belongs to the technical field of combat networks, and in particular relates to a game optimization method and device for link-based combat network attack and defense strategies. Background Art

[0002] With the advancement of advanced equipment, some high-end equipment also possesses reconnaissance, strike, and communications capabilities, offering significant advantages against lower-end threats. However, this traditional point-to-point strike model, due to the highly integrated nature of its equipment, significantly impacts overall combat capability when facing a near-peer adversary. To address this shortcoming, the US military has proposed the concept of mosaic warfare. The core of mosaic warfare is the construction of a highly resilient kill network with decentralized capabilities. Disrupting and protecting this combat network has become a critical concern for both attackers and defenders. For a near-peer adversary, the composition of the combat network has become transparent thanks to high-precision reconnaissance. The key to achieving maximum gains from the enemy's defense and minimizing losses from its attack requires both attackers and defenders to develop optimized strategies in the war game.

[0003] The current process for selecting optimal attack and defense strategies for combat networks is achieved by establishing separate models for network disruption and defense. Attackers primarily focus on optimizing network disruption strategies, while defenders primarily research defense strategies that enhance network robustness. Disruption strategies are guaranteed to be effective, without considering the possibility that defenders will protect network nodes. In reality, defenders are unlikely to allow attackers to destroy them. Network defense, on the other hand, only considers optimizing the initial network structure, without considering the attacker's behavior. Summary of the Invention

[0004] The present invention provides a game optimization method and device for link-based combat network attack and defense strategies, so as to solve the existing problem of being unable to optimize the attack and defense strategies in link-based combat network confrontation.

[0005] Based on the above-mentioned purpose, an embodiment of the present invention provides a game optimization method for the attack and defense strategy of a link-based combat network, including: constructing a kill net model according to the communication relationship between each node in the link-based combat network, and obtaining the capability value of the kill net model; constructing an attack and defense game model of the attacking and defending parties, and obtaining the benefit matrix of the attacking and defending parties in combination with the capability value of the kill net model; solving the Nash equilibrium solution of the attack and defense game model based on the benefit matrix using a solution method corresponding to the scale of the benefit matrix; and optimizing the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution.

[0006] Optionally, the killnet model is constructed based on the communication relationship between nodes in the link-based combat network, including: based on the reconnaissance-communication-command-communicate-strike kill link in the link-based combat network, reconnaissance, command, and strike are used as nodes of the network, and the communication relationship between reconnaissance, command, and strike is used as the edge of the network to construct the killnet model; the killnet model is represented by a graph G(V, E), wherein the node set V is composed of the reconnaissance equipment set I = {i1, i2, ..., i n}、Command and control equipment set C={c1,c2,...,c m}、Strike equipment set A={a1,a2,...,a k}, the edge set E is composed of the communication equipment set T = IC∪CA, IC is the communication equipment set after the reconnaissance equipment and the command and control equipment, CA is the communication equipment set between the command and control equipment and the attack equipment, i j represents the reconnaissance capability value of the jth reconnaissance node, c j Indicates the capability value of the jth accusation node, a j Indicates the capability value of the j-th attack node.

[0007] Optionally, obtaining the capability value of the killnet model includes: calculating the capability value P(G) of the killnet model by applying the following relationship based on the reconnaissance equipment set, the command and control equipment set, the strike equipment set, and the communication equipment set:

[0008]

[0009] Among them, [I] 1×n is a row vector composed of the capability values ​​of each reconnaissance node, [IC] n×m is the communication capability value between the reconnaissance node and the command node, [C] m×m is a diagonal matrix, and the elements on the diagonal are the capabilities of the accusation nodes, [CA] m×k is the communication capability value between the accusation node and the attack node, [A] k×1 It is a column vector consisting of the ability values ​​of each attack node.

[0010] Optionally, the construction of the attack and defense game model of the attacker and defender, and the acquisition of the profit matrix of the attacker and defender in combination with the capability value of the kill net model, include: initializing the attack strategy set and the defense strategy set of the attack and defense game model; calculating the profit of the attacker and defender under different attack strategy and defense strategy combinations, the profit of the attacker R A (Y, W) satisfies the relationship: The attacker's profit R D (Y, W) satisfies the relationship: Wherein, P(G) is the capability value of the kill net model, is the capability value of the kill net model under attack strategy Y and defense strategy W, The kill net model is a game after a round of attack strategy Y and defense strategy W. The payoffs of the attacker and defender under different combinations of attack and defense strategies are combined to construct the payoff matrix of the attacker and defender.

[0011] Optionally, the Nash equilibrium solution of the attack and defense game model is solved based on the profit matrix using a solution method corresponding to the scale of the profit matrix, including: when the scale of the profit matrix is ​​2×2, the drawing method or the equal expectation method is used to solve the Nash equilibrium angle; when the scale of the profit matrix is ​​greater than 2×2 and less than a preset scale, the linear programming method is applied to solve the Nash equilibrium solution; when the scale of the profit matrix is ​​greater than or equal to the preset scale, a representative reduction strategy set is found according to the profit matrix, and the Nash equilibrium solution of the entire strategy is calculated based on the reduced strategy set.

[0012] Optionally, the method of finding a representative reduction strategy set based on the payoff matrix and calculating the Nash equilibrium solution of the full strategy based on the reduction strategy set includes: initializing the attack strategy and defense strategy combination according to the payoff matrix; obtaining the optimal reaction strategy set based on the initialized attack strategy and defense strategy combination, and obtaining a sub-equilibrium or reduction strategy set based on the optimal reaction strategy set, wherein the optimal reaction strategy set is a set of optimal reaction pure strategies at each moment, and the optimal reaction pure strategy includes the attack strategy with the maximum payoff for the attacker in the payoff matrix and the defense strategy with the maximum payoff for the defender corresponding to the attack strategy; calculating the first Nash equilibrium solution of the reduction strategy set, and determining whether it is the Nash equilibrium solution of the full strategy; if the first Nash equilibrium solution is not the Nash equilibrium solution of the full strategy, cyclically updating the reduction strategy set according to the first Nash equilibrium solution, and updating the first Nash equilibrium solution based on the updated reduction strategy set until the Nash equilibrium solution of the full strategy is obtained.

[0013] Optionally, calculating the first Nash equilibrium solution of the reduced strategy set and determining whether it is the Nash equilibrium solution of the full strategy includes: applying a linear programming method to solve the first Nash equilibrium solution of the reduced strategy set; calculating the first optimal response pure strategy of the attacker to the mixed defense strategy in the first Nash equilibrium solution and the second optimal response pure strategy of the mixed attack strategy; if the payoff of the combination of the mixed defense strategy and the first optimal response pure strategy is equal to the payoff of the first Nash equilibrium solution, and the payoff of the combination of the mixed attack strategy and the second optimal response pure strategy is equal to the payoff of the first Nash equilibrium solution, then determining that the first Nash equilibrium solution is the Nash equilibrium solution of the full strategy.

[0014] Based on the same inventive concept, an embodiment of the present invention also proposes a game optimization device for a link-based combat network attack and defense strategy, including: a kill net construction unit, used to construct a kill net model according to the communication relationship between each node in the link-based combat network, and obtain the capability value of the kill net model; a benefit matrix acquisition unit, used to construct an attack and defense game model of the attacking and defending parties, and obtain the benefit matrix of the attacking and defending parties in combination with the capability value of the kill net model; a game solving unit, used to solve the Nash equilibrium solution of the attack and defense game model based on the benefit matrix using a solution method corresponding to the scale of the benefit matrix; a strategy optimization unit, used to optimize the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution.

[0015] Based on the same inventive concept, an embodiment of the present invention further proposes an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the aforementioned method when executing the program.

[0016] Based on the same inventive concept, an embodiment of the present invention further proposes a computer storage medium, in which at least one executable instruction is stored, and the executable instruction enables a processor to execute the aforementioned method.

[0017] The beneficial effects of the present invention are as follows: as can be seen from the above description, an embodiment of the present invention provides a game optimization method and device for a link-based combat network attack and defense strategy, the method comprising: constructing a kill net model according to the communication relationship between nodes in the link-based combat network, and obtaining the capability value of the kill net model; constructing an attack and defense game model of both the attacker and defender, and obtaining the benefit matrix of both the attacker and defender in combination with the capability value of the kill net model; solving the Nash equilibrium solution of the attack and defense game model based on the benefit matrix using a solution method corresponding to the scale of the benefit matrix; optimizing the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution, and realizing accurate attack and defense strategy selection in the link-based combat network confrontation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 Schematic diagram of a flow chart of a game optimization method for link-based combat network attack and defense strategies in an embodiment of the present invention;

[0020] Figure 2Schematic diagram of the structure of a link-based combat network in an embodiment of the present invention;

[0021] Figure 3 Schematic diagram of the formation of a killing net model in an embodiment of the present invention;

[0022] Figure 4 This is an example diagram of a kill net in an embodiment of the present invention;

[0023] Figure 5 for Figure 4 Schematic diagram of the edge weights of the kill network in ;

[0024] Figure 6 for Figure 4 Schematic diagram of Nash equilibrium solutions under different attack and defense ratios of nodes in the kill network;

[0025] Figure 7 for Figure 4 Schematic diagram of the attacker's payoff in the unprotected kill net;

[0026] Figure 8 for Figure 4 Schematic diagram of the benefits of the kill net under different cost indicators;

[0027] Figure 9 Schematic diagram of the structure of a game optimization device for link-based combat network attack and defense strategies in an embodiment of the present invention;

[0028] Figure 10 Schematic diagram of an electronic device in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to make the objectives, technical solutions and advantages of the present disclosure more clearly understood, the present disclosure is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0030] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in the embodiments of the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0031] The embodiment of the present invention provides a game optimization method for link-based combat network attack and defense strategies. The game optimization method for link-based combat network attack and defense strategies of the embodiment of the present invention is applied to a server. Figure 1 As shown in Figure 2, the game optimization method for link-based combat network attack and defense strategies includes:

[0032] Step S11: constructing a killnet model according to the communication relationship between nodes in the link-based combat network, and obtaining the capability value of the killnet model.

[0033] like Figure 2 As shown in the figure, based on the combat network, the kill chain, consisting of six stages: discovery, positioning, tracking, targeting, engagement, and assessment, is transformed into a kill web formed by reconnaissance, communication, command and control, and strike equipment. This not only improves inter-service and inter-equipment coordination and combat mission execution efficiency, but also effectively increases mission success when facing enemy attacks due to the complementary relationships between equipment within the kill web. The weapon and equipment system can form a kill web through command and communication relationships. This kill web can be represented by a simple graph G(V, E), where V is the set of nodes in the graph, representing the equipment in the kill web, and E is the set of edges in the graph, representing the relationships between the equipment. During combat operations, effectively dismantling the enemy kill web and reducing its combat effectiveness can be translated into the problem of dismantling the kill web. However, defenders cannot allow attackers to destroy their network, so network defense is highly likely to render the attack ineffective. This attack-defense process can be represented by a game model. According to game theory, the Nash equilibrium of a game model is the solution that stabilizes the game.

[0034] In an embodiment of the present invention, the killnet model is constructed based on the reconnaissance-communication-command-communication-strike kill link in the link-based combat network, with reconnaissance, command, and strike as network nodes and the communication relationships between reconnaissance, command, and strike as network edges; Figure 3 As shown, the kill network model is represented by a graph G(V, E), where the node set V is composed of the reconnaissance equipment set I = {i1, i2, ..., i n}、Command and control equipment set C={c1,c2,...,c m}、Strike equipment set A={a1,a2,...,a k}, the edge set E is composed of the communication equipment set T = IC∪CA, IC is the communication equipment set after the reconnaissance equipment and the command and control equipment, CA is the communication equipment set between the command and control equipment and the attack equipment, i j represents the reconnaissance capability value of the jth reconnaissance node, c j Indicates the capability value of the jth accusation node, a jIndicates the capability value of the j-th attack node.

[0035] The capability value P(G) of the killnet model is calculated based on the reconnaissance equipment set, the command and control equipment set, the strike equipment set, and the communication equipment set using the following relationship:

[0036]

[0037] Among them, [I] 1×n is a row vector composed of the capability values ​​of each reconnaissance node, [IC] n×m is the communication capability value between the reconnaissance node and the command node, [C] m×m is a diagonal matrix, and the elements on the diagonal are the capabilities of the accusation nodes, [CA] m×k is the communication capability value between the accusation node and the attack node, [A] k×1 It is a column vector consisting of the ability values ​​of each attack node.

[0038] The capability value of the kill web model defined above is the sum of the capability values ​​of all kill chains in this kill web model that include reconnaissance-communication-command-control-communication-strike.

[0039] Step S12: constructing an attack and defense game model for both the attacker and defender, and obtaining a profit matrix for both the attacker and defender in combination with the capability value of the kill net model.

[0040] In the embodiment of the present invention, an attack-defense game model is constructed based on the following assumptions: (1) There is only one attacker and one defender, and both the attacker and the defender have complete information about the combat network. In other words, both the attacker and the defender have complete knowledge of the topological structure, node performance, and connection relationship between nodes of the combat network. In addition, both the attacker and the defender have complete information about the game process, that is, both the attacker and the defender know each other's strategy set and have complete knowledge of their own and the opponent's benefits under each strategy. (2) All attack and defense behaviors are only targeted at the edges representing the communication equipment in the combat network. The attacker selects some of the edges in the graph to attack, and the defender selects some of the edges in the graph to defend. If the edge fails, the nodes at both ends of the edge are not affected, but the kill chain to which the edge belongs will fail. If the attacker chooses to attack the edge and the defender does not defend, the edge fails; if the attacker chooses to attack the edge and the defender chooses to defend, the edge continues to be effective. (3) The game is played for only one round. After the attacker and the defender give their strategy sets, the benefits under the strategies are calculated to generate a benefit matrix; the equilibrium strategy can be calculated based on the benefit matrix. (4) The attacker has the same attack cost for each edge, and the defender has the same defense cost for each edge. However, the costs for the attacker and defender for the same edge are not necessarily the same.

[0041] In step S12, optionally, the attack strategy set and the defense strategy set of the attack and defense game model are initialized first. Let the cost of the attack and defense link be 1, and the attacker's available resources be n a , the defender's available resources are n d , then the number of attacks on the edge is n a , the number of defenses is n d . Let Y = [y1, y2, .., y N ]∈C A is the attack strategy, where C A is the attack strategy set; let W = [w1, w2, .., w N ]∈C D is a defensive strategy, where C D is a set of defensive strategies. i If attacked, y i =1, otherwise y i =0; Similarly, if edge e i If defended, then w i =1, otherwise w i = 0. At this time, |Y| = n a , |W|=n d .for If y i =1 and w i = 0, then edge e i The edge is invalidated by the attack, otherwise it continues to work. The invalid edge set is After one round of game, the network is recorded as

[0042] The profit function represents the profit of each player under various strategy combinations. A :|C A |×|C D | is the attacker's profit function, then R A (Y, W) represents the attacker's profit when the attack strategy is Y and the defense strategy is W. Calculate the attacker's and defender's profits under different attack and defense strategy combinations. The attacker's profit R A (Y, W) satisfies the relationship: The attacker's profit R D (Y, W) satisfies the relationship: Wherein, P(G) is the capability value of the kill net model, is the capability value of the kill net model under attack strategy Y and defense strategy W, The killnet model after one round of game with attack strategy Y and defense strategy W. It can be seen that the attacker's payoff function value is proportional to the number of edges in the killnet, and the payoff function shows that this game is a zero-sum game.

[0043] The embodiment of the present invention combines the benefits of the attacker and defender under different combinations of attack strategies and defense strategies to construct a benefit matrix for both attackers and defenders.

[0044] Step S13: Based on the profit matrix, a solution method corresponding to the scale of the profit matrix is ​​applied to solve the Nash equilibrium solution of the attack-defense game model.

[0045] In an embodiment of the present invention, for the attack and defense game model established above, the Nash equilibrium solution is used as the solution of the model. According to the different scales of the payoff matrix, at least one of the line drawing method, equal expectation method, linear programming method and reduction strategy method can be applied to solve the Nash equilibrium solution of the attack and defense game model. The reduction strategy method refers to reducing the original strategy set and then combining it with the linear programming method to solve the Nash equilibrium solution. Optionally, when the scale of the payoff matrix is ​​2×2, the line drawing method or the equal expectation method is used to solve the Nash equilibrium. The following Table 1 is the payoff matrix of the two-strategy two-person attack and defense game, that is, the payoff matrix with a scale of 2×2.

[0046] Table 1: 2×2 profit matrix

[0047]

[0048] According to the payoff matrix in Table 1, the underlining method can be applied to solve the Nash equilibrium solution. That is, underline the value with the largest payoff in each row of the attacker and underline the value with the largest payoff in each column of the defender. If there is a payoff pair (a ij , d ij ) are all underlined, then the corresponding attack strategy i and defense strategy i constitute a pair of Nash equilibrium strategies.

[0049] If there are no pairs of payoffs that are all crossed out, the method of equal expectation can be used to solve the mixed strategy Nash equilibrium solution: Let the probability of attacking strategy i be The probability of defensive strategy i is According to the definition of mixed Nash equilibrium, the following relationship is satisfied: That is, the sum of the defender's payoff in the same column of the payoff matrix is ​​equal to the product of the defender's payoff and the attack probability.

[0050] In an embodiment of the present invention, when the size of the payoff matrix is ​​greater than 2×2 and smaller than a preset size, a linear programming method is applied to solve the Nash equilibrium solution. The linear programming method satisfies the following conditions:

[0051] min Z i ,satisfy:

[0052]

[0053]

[0054]

[0055] min z j ,satisfy:

[0056]

[0057]

[0058]

[0059] Among them, q j is the probability of defensive strategy j, q i is the probability of attack strategy i, S a is the attack strategy set, is the defense strategy set, a ij is the payoff of the attacker with attack strategy i and defense strategy j, d ij is the payoff of the defender with attack strategy i and defense strategy j, Z i is the maximum value of the sum of the product of the attacker's payoff and the corresponding defensive strategy probability in each row of the payoff matrix, Z j It is the maximum value of the sum of the products of the defender’s payoff and the corresponding attack strategy probability in each column of the payoff matrix.

[0060] In this embodiment of the present invention, when the size of the payoff matrix is ​​greater than or equal to the predetermined size, a representative set of reduced strategies is found based on the payoff matrix, and a Nash equilibrium solution for all strategies is calculated based on the reduced set of strategies. Optionally, the attack and defense strategy combinations are first initialized based on the payoff matrix. At the initial time t = 1, y1 is the strategy in the payoff matrix that maximizes the attacker's payoff. w1 is the defender's optimal pure response strategy to the attack strategy y1.

[0061] Then, based on the initialized attack and defense strategy combinations, an optimal reaction strategy set is obtained, and a sub-equilibrium or reduced strategy set is obtained based on the optimal reaction strategy set. The optimal reaction strategy set is the set of optimal pure reaction strategies at each moment. These optimal pure reaction strategies include the attack strategy with the highest attacker payoff in the payoff matrix and the defense strategy with the highest defender payoff corresponding to the attack strategy. In this embodiment of the present invention, the attack strategy with the highest attacker payoff corresponding to the defense strategy at the previous moment is taken as the optimal pure reaction strategy for the attacker at the current moment, and the defense strategy with the highest defender payoff corresponding to the optimal pure reaction strategy for the defender at the current moment is taken as the optimal pure reaction strategy for the defender at the current moment. If the optimal pure reaction strategy for the defender at the current moment is the same as the optimal pure reaction strategy for the defender at the previous moment, the combination of the optimal pure reaction strategy for the defender and the optimal pure reaction strategy for the defender at the current moment forms a Nash equilibrium solution, and the algorithm terminates. If the optimal pure reaction strategy for the defender at any moment before the previous moment is the same as the optimal pure reaction strategy for the defender at the current moment, the reduced strategy set is formed by combining all attack strategies and all defense strategies from that moment to the current moment. Otherwise, the optimal pure reaction strategy of the attacker and the optimal pure reaction strategy of the defender at the next moment are calculated cyclically. The specific process is as follows: Let t = t + 1, let the attack strategy y t For defensive strategy w t-1 The best response pure strategy; let the defensive strategy w t For the defender's attack strategy y t The best response pure strategy; if w t =w t-1 , then (y t , w t ) is a Nash equilibrium. The algorithm ends. If 0<u<t-1 exists such that w t =w u , then let the set S1={y v :u<v≤t}, S2={wv:u<v≤t}. Set S1 and set S2 are combined to form a reduction strategy set. If neither of the above two conditions is met, return to the step t=t+1.

[0062] Then calculate the first Nash equilibrium solution of the reduced strategy set, and determine whether it is the Nash equilibrium solution of the full strategy. The embodiment of the present invention applies the linear programming method to solve the first Nash equilibrium solution of the reduced strategy set; calculate the first optimal reaction pure strategy of the attacker to the mixed defense strategy in the first Nash equilibrium solution and the second optimal reaction pure strategy of the mixed attack strategy; if the payoff of the mixed defense strategy and the first optimal reaction pure strategy combination is equal to the payoff of the first Nash equilibrium solution, and the payoff of the mixed attack strategy and the second optimal reaction pure strategy combination is equal to the payoff of the first Nash equilibrium solution, then determine that the first Nash equilibrium solution is the Nash equilibrium solution of the full strategy. The specific description is as follows: Use the aforementioned linear programming method to calculate the first Nash equilibrium solution of set S1 and set S2, denoted as (σ1, σ2); calculate the first optimal reaction pure strategy y of the attacker to the mixed defense strategy σ2 * , calculate the second best response pure strategy w of the defender to the mixed attack strategy σ1 * ; If the attacker's income π1(σ1,σ2)=π1(y * ,σ2), and the defender's payoffπ2(σ1,σ2)=π2(σ1,w * ). Then the first Nash equilibrium solution of the reduced strategy set is the Nash equilibrium solution of the full strategy. The algorithm ends.

[0063] If the first Nash equilibrium solution is not the Nash equilibrium solution of the full strategy, then the reduced strategy set is cyclically updated according to the first Nash equilibrium solution, and the first Nash equilibrium solution is updated based on the updated reduced strategy set until the Nash equilibrium solution of the full strategy is obtained. The best reaction pure strategy is added to the reduced strategy set. That is, if the attacker's profit of the combination of the defense strategy in the first Nash equilibrium solution and the first best reaction pure strategy is greater than the attacker's profit corresponding to the first Nash equilibrium solution, then the first best reaction pure strategy is added to the attack strategy set in the reduced strategy set to obtain an updated reduced strategy set, that is, if π1(Y * ,σ2)>π1(σ1,σ2), then S1←S1∪{y * If the defensive payoff of the combination of the attack strategy in the first Nash equilibrium solution and the second best response pure strategy is greater than the defensive payoff corresponding to the first Nash equilibrium solution, then the second best response pure strategy is added to the defensive strategy set in the reduced strategy set to obtain an updated reduced strategy set, that is, if π2(σ1, W * )>π2(σ1,σ2), then S2←S2∪{w * Then return to the previous step, update the first Nash equilibrium solution based on the updated reduction strategy set, and repeat this cycle until the Nash equilibrium solution of the full strategy is obtained.

[0064] Step S14: Optimizing the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution.

[0065] After obtaining the Nash equilibrium solution, the attack and defense strategies of the link-based combat network can be set as the attack strategy and defense strategy of the Nash equilibrium solution.

[0066] The embodiment of the present invention uses a randomly generated kill network as an example to carry out application research and verify the feasibility and effectiveness of the game optimization method of the link-based combat network attack and defense strategy. First, the strategy set of the attack and defense game model is generated, and the Nash equilibrium under the full strategy model is calculated, and the characteristics of the Nash equilibrium solution are analyzed; then, the Nash equilibrium under two typical strategies, random attack and defense and target attack and defense, is calculated. Figure 4 As shown in the figure, a combat network with 5 reconnaissance nodes, 3 command nodes, and 4 strike nodes is used as an example to calculate the payoff matrix and the Nash equilibrium solution of this attack-defense game. The capability values ​​of the reconnaissance, command, and strike nodes in the combat network range from (1-10), and the randomly generated values ​​are as follows: reconnaissance nodes: [s1, s2, s3, s4, s5] = [4, 9, 8, 10, 7]; command nodes: [d1, d2, d3] = [4, 7, 1]; strike nodes: [a1, a2, a3, a4] = [10, 5, 8, 1]. At this time, the kill net capability value P0 is:

[0067]

[0068] in, is the communication capability value between the reconnaissance node and the command node, It is the communication capability value between the command node and the attack node.

[0069] In order to make the game results significant and reduce interference variables, continue to refer to Figure 4 , let all layers of this combat network be fully connected, and let the communication capability value be 1. Therefore, the kill net capability value E0 at this time is:

[0070]

[0071] For a homogeneous network, the edge weight is defined as follows: IM(c ij )=x i ×y j , where x i 、y j For edge c ijThe weights of the connected nodes. However, the killnet is heterogeneous, and the impact of an edge on the killnet depends not only on the capabilities of the nodes at its ends but also on the capabilities of the other nodes in the kill chain. In general, the importance of an edge in a killnet depends on the capabilities of all the kill chains it is part of. Based on this, the formula for calculating edge weights in a killnet is:

[0072]

[0073] Among them, Z k For node y j The weight of the connected nodes, The importance of the edges in the above example (top 10) is ranked as shown in Table 2 and Figure 5 As shown, the weight of the edge can be represented by the thickness of the edge.

[0074] Table 2 Edge weights

[0075] Serial number 1 2 3 4 5 6 7 8 9 10 side <![CDATA[da 21 ]]> <![CDATA[da 23 ]]> <![CDATA[sd 42 ]]> <![CDATA[da 11 ]]> <![CDATA[sd 22 ]]> <![CDATA[sd 32 ]]> <![CDATA[da 22 ]]> <![CDATA[da 13 ]]> <![CDATA[sd 52 ]]> <![CDATA[sd 41 ]]> Weight 2660 2128 1680 1520 1512 1344 1330 1216 1176 960

[0076] For the above combat network, only the target attack and defense strategies with maximum capability and random attack and defense strategies are considered. The payoff matrix is ​​shown in Table 3 below.

[0077] Table 3 Profit Matrix

[0078] Target Defense Random Defense Targeted Attack <![CDATA[R 11 ,-R 11 ]]> <![CDATA[R 12 ,-R 12 ]]> Random Attack <![CDATA[R 21 ,-R 21 ]]> <![CDATA[R 22 ,-R 22 ]]>

[0079] When the number of attacking nodes is the same as the number of defending nodes, R 11 = 0. When R 12 ≤R 22 When R 21 ≤R 22 , then the Nash equilibrium is (random attack, target defense), if R 21 >R 22 , then the Nash equilibrium is (random attack, random defense); when R 12 >R 22 When R 21 ≤R 22 , then the Nash equilibrium is (random attack, target defense), if R 21 >R 22 , then the Nash equilibrium is a mixed strategy Nash equilibrium, and the probability of target attack is: The probability of the target defending is:

[0080] The embodiment of the present invention also studies the situation of Nash equilibrium under attack and defense strategies with different node number ratios, such as Figure 6As shown, the white block in the lower left corner represents the Nash equilibrium solution of (target attack, target defense); the striped block represents the Nash equilibrium solution of (random attack, target defense). Figure 7 is the attacker's profit without defense, where r is the profit and θ1 is the attack cost. Figure 8 is the benefit r under different cost indicators, θ2 is the defense cost, r 11 This is the profit R in Table 3 11 , r 12 This is the profit R in Table 3 12 , r 21 This is the profit R in Table 3 21 , r 22 This is the profit R in Table 3 22 . Through the payoff matrix and Nash equilibrium solution, it can be seen that the target defense strategy is the dominant strategy, and when the strategy is targeted attack and random defense, the attacker's payoff is very large, which shows that the understanding of the key communication nodes in this combat network is relatively accurate. At the same time, since the attack and defense game model assumes that both the attacker and the defender have complete information about the entire game, the attack strategy is naturally a random attack. In addition, from the numerical value point of view, when the attack strategy adopts random attack, the difference between target defense and random defense is small, which shows that the value distribution of communication nodes in the combat network instance is uneven and has great heterogeneity. By comparing the ability values ​​of reconnaissance, accusation, and attack nodes, the correctness of the attack and defense game model is verified.

[0081] For the above attack-defense game model example, the embodiment of the present invention also studies the Nash equilibrium solutions of all strategies under a certain number of attacks and defenses. For 27 communication edges, the number of attack-defense edges is set to 4, that is, n a =n d =4, then the number of attack and defense strategy sets is: This full strategy model was solved using the link-based combat network attack and defense strategy game optimization method of the embodiment of the present invention. The results are shown in Table 4 below:

[0082] Table 4 Probability distribution of Nash equilibrium strategies

[0083]

[0084] And convert the specific strategy probability into the edge probability as shown in Table 5 below:

[0085] Table 5 Probability distribution of equilibrium strategies on the edge

[0086]

[0087]

[0088] The above results show that under the equilibrium strategy, the defender primarily defends high-value edges. Meanwhile, the attacker primarily attacks high-value edges. This strategy allows the defender to maximize the effectiveness of the kill net. However, the attacker gains greater benefits by attacking less important edges, as attacking edges defended by the defender will render the attack ineffective.

[0089] The link-based game optimization method for combat network attack and defense strategies in this embodiment of the present invention considers attack and defense strategies within the combat network. From a network perspective, it establishes a killnet model based on communication relationships for the equipment system and considers the attack and defense game model within the killnet, providing a new approach for optimizing attack and defense strategies within the combat network. This embodiment of the present invention establishes a killnet model based on communication relationships and an attack and defense game model within the killnet. It then calculates Nash equilibria for both random attack and defense and targeted attack and defense strategies, and analyzes the impact of different numbers of attack and defense edges on the Nash equilibrium solution. It also calculates the Nash equilibrium under all strategies and analyzes the characteristics of the Nash equilibrium solution. This embodiment of the present invention fully considers the attack and defense game problem within the killnet and proposes a killnet attack and defense game model from the perspective of a two-player game, addressing the problem of optimizing attack and defense strategies in confrontation. The Nash equilibria for traditional deliberate attack and defense and random attack and defense strategies under different numbers of attacks are studied. It is found that when the attacker has sufficient destructive power over the entire killnet, deliberate attack is a relatively good attack strategy. Conversely, if the attacker lacks sufficient destructive power, random attack is less effective. For defenders, protecting the most valuable targets in the kill net is always a better strategy. In the full-strategy attack-defense game model, defenders still defend the most valuable targets, while attackers will attack targets with relatively higher value.

[0090] The game optimization method for the link-based combat network attack and defense strategy of the embodiment of the present invention constructs a kill net model according to the communication relationship between each node in the link-based combat network to obtain the capacity value of the kill net model; constructs an attack and defense game model of the attacking and defending parties, and obtains the profit matrix of the attacking and defending parties in combination with the capacity value of the kill net model; based on the profit matrix, a solution method corresponding to the scale of the profit matrix is ​​applied to solve the Nash equilibrium solution of the attack and defense game model; and according to the Nash equilibrium solution, the attack and defense strategy of the link-based combat network is optimized, which can realize accurate attack and defense strategy selection in the link-based combat network confrontation.

[0091] The foregoing description is of specific embodiments of the present invention. In some cases, the actions or steps described in the embodiments of the present invention may be performed in an order different from that shown in the embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0092] Based on the same concept, the embodiment of the present invention also provides a game optimization device for link-based combat network attack and defense strategy. Applied to the server. Figure 9 As shown, the game optimization device for link-based combat network attack and defense strategy includes: a kill net construction unit, a benefit matrix acquisition unit, a game solving unit and a strategy optimization unit.

[0093] a killnet construction unit, configured to construct a killnet model based on the communication relationships between nodes in the link-based combat network and obtain a capability value of the killnet model;

[0094] A benefit matrix acquisition unit, configured to construct an attack-defense game model for both the attacker and defender, and to acquire the benefit matrix of both the attacker and defender based on the capability value of the kill net model;

[0095] a game solving unit, configured to solve a Nash equilibrium solution of the attack-defense game model based on the payoff matrix by applying a solving method corresponding to the scale of the payoff matrix;

[0096] A strategy optimization unit is used to optimize the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution.

[0097] For the convenience of description, the above devices are described as being divided into various modules according to their functions. Of course, when implementing the embodiments of the present invention, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0098] The apparatus of the above embodiment is applied to the corresponding method of the above embodiment and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0099] Based on the same inventive concept, an embodiment of the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and runnable on the processor, wherein when the processor executes the program, the method described in any one of the above embodiments is implemented.

[0100] An embodiment of the present invention provides a non-volatile computer storage medium, wherein the computer storage medium stores at least one executable instruction, and the computer executable instruction can execute the method described in any one of the above embodiments.

[0101] Figure 10 1004, a more specific hardware structure diagram of an electronic device provided in this embodiment is shown. The device may include: a processor 1001, a memory 1002, an input / output interface 1003, a communication interface 1004, and a bus 1005. The processor 1001, the memory 1002, the input / output interface 1003, and the communication interface 1004 are communicatively connected to each other within the device via the bus 1005.

[0102] The processor 1001 can be implemented as a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided by the method embodiments of the present invention.

[0103] The memory 1002 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage devices, dynamic storage devices, etc. The memory 1002 can store an operating system and other application programs. When the technical solutions provided by the method embodiments of the present invention are implemented through software or firmware, the relevant program codes are stored in the memory 1002 and called and executed by the processor 1001.

[0104] The input / output interface 1003 is used to connect input / output modules to implement information input and output. The input / output modules can be configured as components in the device (not shown in the figure) or can be externally connected to the device to provide corresponding functions. Input devices may include a keyboard, mouse, touch screen, microphone, various sensors, etc., and output devices may include a display, speaker, vibrator, indicator light, etc.

[0105] The communication interface 1004 is used to connect to a communication module (not shown) to enable communication between the device and other devices. The communication module can communicate via a wired method (such as USB, network cable, etc.) or a wireless method (such as mobile network, WIFI, Bluetooth, etc.).

[0106] The bus 1005 comprises a path for transmitting information between the various components of the device (eg, the processor 1001 , the memory 1002 , the input / output interface 1003 , and the communication interface 1004 ).

[0107] It should be noted that although the above device only shows the processor 1001, the memory 1002, the input / output interface 1003, the communication interface 1004, and the bus 1005, in a specific implementation, the device may also include other components necessary for normal operation. In addition, those skilled in the art will understand that the above device may only include the components necessary to implement the embodiments of the present invention, and does not necessarily include all the components shown in the figure.

[0108] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present application is limited to these examples. Within the scope of the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the present application as described above, which are not provided in detail for the sake of simplicity.

[0109] This application is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the embodiments of the present invention. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present invention should be included in the scope of protection of this application.

Claims

1. A game optimization method for link-based combat network attack and defense strategy, characterized in that: The method comprises: Constructing a killnet model according to the communication relationship between nodes in the link-based combat network, and obtaining a capability value of the killnet model; Constructing an attack and defense game model for both sides, and obtaining the profit matrix of both sides in combination with the capability value of the kill net model; Solving the Nash equilibrium solution of the attack-defense game model based on the profit matrix using a solution method corresponding to the scale of the profit matrix; Optimizing the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution; The killnet model is constructed according to the communication relationship between nodes in the link-based combat network, including: According to the kill link of reconnaissance-communication-command and control-communication-strike in the link-based combat network, the kill network model is constructed by taking reconnaissance, command and control, and strike as nodes of the network and the communication relationship between reconnaissance, command and control, and strike as edges of the network; The kill net model is shown in a figure Represents that, where the node set V is composed of the reconnaissance equipment set , Command and Control Equipment Collection , Strike Equipment Collection The edge set E consists of the communication equipment set The IC is the communication equipment set behind the reconnaissance equipment and the command and control equipment, and the CA is the communication equipment set between the command and control equipment and the strike equipment. represents the reconnaissance capability value of the jth reconnaissance node, represents the capability value of the jth accusation node, represents the capability value of the j-th attack node; The obtaining the capability value of the kill net model includes: The capability value of the kill network model is calculated by applying the following relationship based on the reconnaissance equipment set, the command equipment set, the strike equipment set, and the communication equipment set. : ， in, is a row vector composed of the capability values ​​of each reconnaissance node, is the communication capability value between the reconnaissance node and the command node, is a diagonal matrix, and the elements on the diagonal are the capability values ​​of the accusation nodes. is the communication capability value between the accusation node and the attack node, is a column vector composed of the capability values ​​of each attack node; The construction of the attack and defense game model of the attack and defense parties, and the acquisition of the profit matrix of the attack and defense parties in combination with the capability value of the kill net model, include: Initializing an attack strategy set and a defense strategy set of the attack and defense game model; Calculate the benefits of the attacker and defender under different combinations of attack and defense strategies. Satisfies the relationship: , the attacker's profit Satisfies the relationship: ,in, is the capability value of the kill net model, is the capability value of the kill net model under attack strategy Y and defense strategy W, The killing net model after a round of game with attack strategy Y and defense strategy W; Combine the benefits of the attacker and defender under different combinations of attack and defense strategies to construct a benefit matrix for both parties.

2. The method according to claim 1, characterized in that: The method of solving the Nash equilibrium solution of the attack-defense game model based on the profit matrix and applying a solution method corresponding to the scale of the profit matrix includes: When the size of the profit matrix is ​​2×2, the Nash equilibrium angle is solved by the line drawing method or the equal expectation method; When the scale of the profit matrix is ​​greater than 2×2 and less than the preset scale, the linear programming method is used to solve the Nash equilibrium solution; When the scale of the profit matrix is ​​greater than or equal to the preset scale, a representative reduction strategy set is found according to the profit matrix, and a Nash equilibrium solution of the entire strategy is calculated according to the reduction strategy set.

3. The method according to claim 2, characterized in that: The step of finding a representative reduction strategy set according to the payoff matrix and calculating the Nash equilibrium solution of the entire strategy according to the reduction strategy set includes: Initialize the attack strategy and defense strategy combination according to the payoff matrix; Obtain an optimal response strategy set according to the initialized attack strategy and defense strategy combination, and obtain a sub-equilibrium or reduction strategy set according to the optimal response strategy set, wherein the optimal response strategy set is a set of optimal response pure strategies at each moment, and the optimal response pure strategy includes an attack strategy with the maximum benefit for the attacker in the benefit matrix and a defense strategy with the maximum benefit for the defender corresponding to the attack strategy; Calculate the first Nash equilibrium solution of the reduced strategy set, and determine whether it is the Nash equilibrium solution of the full strategy; If the first Nash equilibrium solution is not the Nash equilibrium solution of the full strategy, the reduction strategy set is cyclically updated according to the first Nash equilibrium solution, and the first Nash equilibrium solution is updated based on the updated reduction strategy set until the Nash equilibrium solution of the full strategy is obtained.

4. The method according to claim 3, characterized in that: The calculating the first Nash equilibrium solution of the reduced strategy set and determining whether it is the Nash equilibrium solution of the full strategy includes: Applying a linear programming method to solve the first Nash equilibrium solution of the reduction strategy set; Calculate the attacker's first best response pure strategy to the mixed defense strategy in the first Nash equilibrium solution and the second best response pure strategy to the mixed attack strategy; If the payoff of the mixed defense strategy and the first best response pure strategy combination is equal to the payoff of the first Nash equilibrium solution, and the payoff of the mixed attack strategy and the second best response pure strategy combination is equal to the payoff of the first Nash equilibrium solution, then it is determined that the first Nash equilibrium solution is the Nash equilibrium solution of the full strategy.

5. A game optimization device for link-based combat network attack and defense strategy, characterized in that: The device implements the method according to any one of claims 1 to 4, and the device comprises: A killnet construction unit, configured to construct a killnet model according to the communication relationship between nodes in the link-based combat network, and obtain a capability value of the killnet model; A profit matrix acquisition unit, used to construct an attack and defense game model of the attack and defense parties, and to obtain the profit matrix of the attack and defense parties in combination with the capability value of the kill net model; A game solving unit, used for solving the Nash equilibrium solution of the attack and defense game model based on the profit matrix by applying a solving method corresponding to the scale of the profit matrix; A strategy optimization unit is used to optimize the attack and defense strategy of the link-based combat network according to the Nash equilibrium solution.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 4 is implemented.

7. A computer storage medium, characterized in that: The storage medium stores at least one executable instruction, and the executable instruction enables the processor to execute the method as described in any one of claims 1-4.

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