A two-stage hybrid optimization-based method for optimal defense resource allocation.

Abstract

This invention discloses a two-stage hybrid optimization method for AC-ODRA (Optimal Defense Resource Allocation) problem. The key technical points of this invention include: First, a global coarse search is performed, using a slime mold algorithm to globally explore the AC-ODRA problem, quickly determining the deployment locations (discrete variables) of defense resources and obtaining a high-quality candidate solution; Second, resource input fine-tuning is performed, fixing the deployment locations of the candidate solution from the first stage, and employing an adaptive moment estimation optimization method with multi-starting-point random perturbations guided by instrument importance to perform high-precision local optimization of specific resource input amounts (continuous variables) within an augmented Lagrangian framework. This invention, by combining global search with local fine-tuning, significantly improves the solution accuracy and robustness of the AC-ODRA problem, enabling the acquisition of a lower-cost defense resource allocation scheme while ensuring power grid security, and possesses significant theoretical value and application prospects.

Description

Technical Field

[0001] This invention belongs to the field of smart grid security technology, specifically relating to a method for optimal defense resource allocation in a power network physical system to resist spurious data injection attacks targeting state estimation, and particularly to an optimization solution technique for large-scale power grids under an AC power model. Background Technology

[0002] With the deep integration of information and communication technologies and power systems, smart grids, while improving operational efficiency, are increasingly facing cyberattack threats, such as False Data Injection (FDIA) attacks. FDIAs maliciously tamper with measurement data, misleading grid operators into making incorrect estimates of system status, potentially leading to economic losses or even widespread safety incidents.

[0003] As a proactive defense strategy, Optimal Defense Resource Allocation (ODRA) aims to determine an optimal allocation strategy for defense resources (such as encryption modules, video surveillance, and security personnel) to ensure that no set of state variables can be tampered with by an attacker while minimizing the overall investment in defense resources (i.e., the minimum cost required to launch a successful attack on any subset of state variables should exceed the resources available to the attacker), thereby safeguarding power grid security.

[0004] Existing technologies have explored the ODRA problem in depth. For example, considering that the relationship between defense measures and attack costs often exhibits nonlinear characteristics in reality, a mixed integer nonlinear programming (MINLP) problem has been constructed. Since this problem is difficult to solve using traditional commercial solvers, Xu et al. proposed a Slime Mould Algorithm with Initialization Pool (SMA-IP) in their 2025 paper, "Optimal Defense Resource Allocation Considering Nonlinear Attack Cost in Power Systems," to solve it. However, this research was mainly conducted under a DC model. However, the essence of evolutionary algorithms like SMA is to perform a global random search. After determining the deployment location of defense resources (i.e., discrete variables), its ability to perform local fine-tuning optimization for continuous resource inputs (i.e., continuous variables) is relatively limited. This may lead to the final calculated defense cost not being the theoretical minimum, meaning there is still some optimization space.

[0005] Furthermore, to extend the ODRA problem to more challenging large-scale power grid scenarios, some literature has proposed a network partitioning-based strategy. While this research primarily validates its partitioning strategy under the DC model, it also proactively provides the fundamental mathematical framework for the ODRA problem under the AC model, such as defining a binary structure matrix that reflects the measurement-state dependencies under the AC model. However, this literature only uses the general SMA-IP algorithm to solve the partitioned subproblems and does not design specialized, high-precision solution methods for the inherent, more complex nonlinear and highly coupled characteristics of the AC model, especially for optimization of continuous variables.

[0006] In summary, existing technologies have the following shortcomings: when dealing with the increasingly important AC-ODRA problem, there is a lack of a hybrid solution framework that can balance global optimal configuration and local exact optimization; relying solely on single-stage evolutionary algorithms may lead to insufficient optimality of the solution. Therefore, how to design a novel optimization method to solve complex AC-ODRA problems to achieve better optimality is an urgent technical problem to be solved. Summary of the Invention

[0007] The purpose of this invention is to address the technical problems of insufficient optimality and inefficient resource allocation schemes in defense resource allocation schemes when existing ODRA solution methods rely solely on single-stage evolutionary algorithms when applied to complex communication models. This invention proposes a two-stage hybrid optimization method for optimal defense resource allocation in communication.

[0008] The objective of this invention is achieved through the following technical solution: a two-stage hybrid optimization-based method for allocating optimal defense resources, comprising the following steps:

[0009] Step 1, Global Configuration Coarse Search Phase: Using the SMA-IP algorithm, a global exploratory search is performed on the entire solution space of the AC-ODRA problem. The main task of this phase is to solve for the discrete binary variables in the problem, i.e., to determine which measurement instruments the defense resources should be deployed on. The output of this step is a high-quality candidate solution, which includes a definite defense deployment location (the value of the binary decision variable vector φ) and a corresponding initial defense resource allocation (the initial value b of the continuous decision variable vector b). initial ).

[0010] Step Two, Resource Investment Fine-tuning Stage: Fixing the defense deployment position φ obtained in Step One, the original problem is transformed into a non-convex optimization subproblem concerning only the continuous decision variable vector b. To solve this subproblem with high accuracy, this invention employs an adaptive moment estimation (Multi-Start Adam) optimization method based on multi-starting-point random perturbation. Within the augmented Lagrange double-loop optimization framework, the inner loop undergoes local fine-tuning, specifically including the following sub-steps:

[0011] 2.1 First deterministic optimization: For the k-th outer loop, in the first (i.e. j=1) of the N-th inner loop optimization, Adam optimization is performed directly using the original starting point of the Adam optimizer to obtain a baseline fine adjustment.

[0012] 2.2 Multiple Random Perturbation Optimization: In the subsequent N-1 inner loop optimizations (i.e., j = 2, ..., N), non-uniform randomness guided by instrument importance is introduced to the starting point to generate N-1 new starting points; for each new starting point, Adam optimization based on the augmented Lagrangian framework is repeatedly performed.

[0013] 2.3 Optimal Solution Selection: From the baseline fine adjustment obtained in step 2.1 and the N-1 optimization results obtained in step 2.2, select the solution with the smallest objective function value in the inner loop as the result of this inner loop and return it to the outer loop to update the Lagrange multipliers.

[0014] The beneficial effects of this invention are as follows:

[0015] 1. Improved optimality of the solution: This invention combines the powerful global search capability of evolutionary algorithms with the superior local optimization capability of the Adam optimizer. This two-stage hybrid optimization approach can find a more accurate solution than a single evolutionary algorithm, thereby significantly reducing the total cost required to deploy defense resources while ensuring the same level of security.

[0016] 2. Enhanced robustness of the solution: The second stage adopts a "multi-starting point + random perturbation" strategy guided by the importance of the instrument, which effectively overcomes the defect of traditional gradient optimization methods that are prone to getting trapped in bad local minima, and greatly improves the stability and success rate of the algorithm in finding global or high-quality local optimal solutions.

[0017] 3. Filling a technological gap in the field: This invention is the first to apply this advanced two-stage hybrid optimization framework, especially the Adam optimizer with multi-starting point random perturbation, to solve the complex AC-ODRA problem, providing a new and high-performance solution approach for this field and effectively solving the accuracy bottleneck of existing technologies. Attached Figure Description

[0018] Figure 1A flowchart of the optimal defense resource allocation method based on two-stage hybrid optimization provided in this embodiment of the invention;

[0019] Figure 2 The block diagram for the second-stage augmented Lagrange-multi-starting-point Adam optimization provided in this embodiment of the invention. Detailed Implementation

[0020] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0021] I. AC-ODRA Problem Statement

[0022] First, we establish the mathematical model for the AC-ODRA problem. In an AC power system with n state variables and m measuring instruments, the problem can be constructed as a mixed integer nonlinear programming (MINLP) problem as follows:

[0023] Minimize:

[0024] 1 T b

[0025] Subject to:

[0026] RH * ·[φ1f1(b1),φ2f2(b2),v,φ m f m (b m )] T ≤0

[0027] 1 T φ-M≤0

[0028] b≥0, φ∈{0,1} m

[0029] in:

[0030] 1 is an m-dimensional column vector whose elements are all 1s. T This represents the transpose of 1, changing it from a column vector to a row vector. Similarly, 0 is an n-dimensional column vector with all elements equal to 0.

[0031] b = [b1, b2, ..., b m ] T It is an m-dimensional continuous decision variable vector, representing the amount of defense resources invested in each instrument. The optimization objective of this invention is to minimize the total investment, i.e.

[0032] φ=[φ1,φ2,...,φ m ] T It is an m-dimensional binary decision variable vector. When φ i When φ = 1, it indicates that defensive resources are deployed on the i-th instrument; when φ = 1, it indicates that defensive resources are deployed on the i-th instrument. i If the value is 0, it will not be deployed.

[0033] f i (b i ) is the attack cost function on the i-th instrument, which represents the cost of attack when the defense resource investment is b. i The cost an attacker would incur to compromise the instrument. This function can be linear or non-linear.

[0034] M is an integer representing the maximum number of instruments that the defender can deploy defensive measures, i.e., the defense budget.

[0035] R is an n-dimensional vector whose elements are all R, where R represents the upper limit of the total resources that the attacker can use to launch an attack.

[0036] H * It is an n×m binary matrix that reflects the topological dependencies between the state variables and measuring instruments of the power grid under the AC model. If, in the AC model of the power system, the j-th state variable x... j The change will affect the i-th measuring instrument z. i Then the corresponding element in the matrix Otherwise, it is 0.

[0037] The core meaning of the first constraint is: for any state variable, the total attack cost (i.e., the sum of the attack costs of all its related instruments) required for an attacker to successfully tamper with it must be greater than the attacker's resource limit R. Note that this constraint is expressed in vector form and actually contains n sub-constraints.

[0038] The core meaning of the second constraint is: the maximum number of instruments that the defender can deploy for defensive measures is M.

[0039] The third constraint represents the fundamental properties of the decision variables.

[0040] II. Explanation of the Two-Stage Hybrid Optimization Algorithm

[0041] This invention proposes a novel two-stage hybrid optimization method for solving the AC-ODRA (Optimal Defense Resource Allocation) problem in AC power grids. The overall process of this method is as follows: Figure 1 As shown, its core is to decompose the complex mixed-integer nonlinear programming problem into two related sub-stages in order to balance the globality and accuracy of the solution.

[0042] The first stage is the global configuration coarse search stage. Figure 1 Step one (in the process) aims to utilize the global search capability of evolutionary algorithms to quickly pinpoint the optimal combination of defensive resource deployment locations. The second stage is the resource allocation fine-tuning stage (…). Figure 1 Step two in the process involves using advanced local optimization algorithms to perform detailed calculations on the specific amount of resources that should be invested in each location, based on the deployment locations determined in the previous stage, in order to achieve the lowest possible cost.

[0043] The specific implementation methods for each step are explained in detail below.

[0044] Step 1: Global Configuration Coarse Search Phase

[0045] Because the AC-ODRA problem is a highly nonlinear and nonconvex MINLP problem, traditional solvers struggle to solve it efficiently. Therefore, this step employs an advanced evolutionary algorithm, the Slime Mold Algorithm with Initialization Pool (SMA-IP), for solving the problem. This algorithm has been proven in the prior art to have good performance in solving such problems. The SMA-IP algorithm explores the solution space by simulating the foraging behavior of slime molds. Its individual encoding simultaneously contains binary variables φ and continuous variables b. Through its unique initialization strategy and evolutionary mechanism, the algorithm can efficiently search within a complex feasible region that satisfies the constraints.

[0046] The purpose of this stage is not to directly obtain the final optimal solution, but to prepare for the fine-tuning in the next stage. After sufficient iterative search, the SMA-IP algorithm will output the best individual it has found, i.e., a high-quality candidate solution.

[0047] The candidate solution includes:

[0048] A defined, fixed defensive deployment location – a binary decision variable vector: φ * ;

[0049] A corresponding initial value for the initial defense resource input – the continuous decision variable vector b: b initial .

[0050] This candidate solution (φ) * ,b initial This will be used as input for step two for further precise optimization.

[0051] Step Two: Resource Input Fine-tuning Phase

[0052] The objective of this phase is to establish defensive deployment locations φ as determined in the previous phase. * Based on this, the continuous defensive resource investment amount 'b' is optimized with high precision to find the feasible solution with the lowest cost. Detailed procedures for this stage can be found in [reference needed]. Figure 2 .

[0053] 2.1 Subproblem Transformation. When the binary decision variable vector φ * Once fixed, the original AC-ODRA problem is transformed into a nonlinear, nonconvex optimization subproblem with respect only to the continuous decision variable vector b. Its objective and constraints are the same as the model in step one, but φ is now treated as a constant. * .

[0054] 2.2 Optimization Framework: Augmented Lagrangian Method with Two-Layer Loop. To effectively handle the complex nonlinear inequality constraints in this subproblem, this invention employs the Augmented Lagrangian Method as the core optimization framework. This method works collaboratively through an outer loop and an inner loop. The outer loop is responsible for dynamically adjusting the Lagrange multipliers and penalty coefficients to guide the solution to approximate the feasible region; the inner loop, given the Lagrange multipliers and penalty coefficients, is responsible for solving for the optimal resource input under the current conditions.

[0055] 2.2.1 Outer Loop (Dual Update): The outer loop is the main process of the entire fine-tuning phase, responsible for iteratively updating the Lagrange multiplier vectors. And the penalty coefficient ρ.

[0056] 2.2.1.1 Initialization: At the beginning, initialize the defense resource investment amount b1 = b initial Lagrange multiplier vector And set an initial penalty coefficient ρ1 (for example, ρ1 = 10).

[0057] 2.2.1.2 Outer loop iteration (kth iteration):

[0058] ① Execute the inner loop:

[0059] Let the Lagrange multiplier vector be λ in the k-th outer loop. k =[λ 1,k ,λ 2,k ,...,λ n,k ] T With the current Lagrange multiplier vector λ k and penalty coefficient ρ k As input, the Adam optimizer in the inner loop is invoked to solve the problem of minimizing the augmented Lagrangian function P(b), resulting in an updated defense resource investment amount b. k+1 :

[0060]

[0061] Among them, g j(b) represents the relaxation level of the j-th sub-constraint in the first constraint, which aims to protect the j-th state variable from being tampered with. Its specific mathematical expression is:

[0062]

[0063] in It is a binary structure matrix H * The element in the j-th row and i-th column. When g j (b) > 0 indicates that the protection of state variable j is insufficient and the constraint is violated.

[0064] ② Update the Lagrange multiplier vector λ:

[0065] In obtaining b k+1 Then, calculate the corresponding actual constraint relaxation value g. j (b k+1 Then, for each sub-constraint (j = 1, ..., n), its corresponding Lagrange multiplier component λ is independently updated according to the following formula. j,k :

[0066] λ j,k+1 =max(0,λ) j,k +ρ k ·g j (b k+1 ))

[0067] The significance of this update lies in: for those constraints that are still being violated (i.e., g) j (b k+1 ()>0), its corresponding multiplier λ j,k+1 This will increase, which is equivalent to increasing the "penalty" for violating the constraint in the next inner loop, forcing the optimizer to find a solution that better satisfies the constraint.

[0068] ③ Update the penalty coefficient ρ:

[0069] To accelerate convergence, the penalty coefficient can be gradually increased:

[0070] ρ k+1 =γ·ρ k

[0071] Where γ > 1 is the growth rate.

[0072] The outer loop continues until the change in the Lagrange multipliers is less than a set threshold or the maximum number of iterations is reached, and all constraints are satisfied. After the outer loop iterations are complete, its final output b k+1 With φ in step one * Combined, they constitute the final optimal defense scheme (φ) for the aforementioned AC-ODRA problem sought in this invention. *,b k+1 ).

[0073] 2.2.2 Inner Loop (Primal Update): Solving subproblems based on multi-starting-point Adam.

[0074] The goal of the inner loop is to... k and ρ k Next, find the b that minimizes the augmented Lagrange function. k+1 :

[0075]

[0076] This invention does not employ the standard gradient descent method, but instead uses a more advanced Adam optimizer based on multi-starting-point random perturbation to accomplish this task.

[0077] 2.2.2.1 Adam Optimizer: Adam can optimize for each decision variable (i.e., each b) i ) Calculate an adaptive learning rate to achieve faster and more stable convergence in complex optimization surfaces.

[0078] Initialization: If the inner loop is the first iteration of the outer loop, then the initial point b of the inner loop is set. k,0 (i.e., b at t=1) k,t-1 Initialize to the initial value b1 of the defense resource investment in the first outer loop; otherwise, initialize to the result b of the previous outer loop. k .

[0079] Inner loop iteration: At time step t, the update equation is as follows:

[0080] ① Update the first moment (momentum term):

[0081]

[0082] in It is the gradient of the objective function P(b) with respect to b.

[0083] ② Update the second moment (adaptive learning rate term):

[0084]

[0085] ③ Deviation correction:

[0086]

[0087] ④ Update parameter b:

[0088]

[0089] Where α is the base learning rate, β1 and β2 are decay rates (usually 0.9 and 0.999), and ∈ is a minimum value (e.g., 10) set to prevent division by zero. -8 The inner loop continues until parameter b is reached. k,t The change in the value is less than a set threshold, or the maximum number of iterations is reached. After the inner loop iterations are completed, its final output b k,t This is the result of the inner loop portion within the outer loop. k+1 .

[0090] 2.2.2.2 Multi-starting point random perturbation strategy based on instrument importance

[0091] To further improve the solution quality of the inner loop and avoid getting trapped in undesirable local optima, this invention adopts a multi-start strategy for the above Adam optimization process. Each start point undergoes independent N Adam optimizations, while other start points besides the original start point are obtained by perturbing the original start point. Unlike the blind, uniform random perturbations in existing technologies, this invention proposes an adaptive perturbation method based on instrument importance. The core idea of ​​this method is that not all defense locations are equally important, and their perturbation exploration granularity should differ. Instruments located in critical topological positions of the power grid have a more sensitive impact on the overall system security due to resource investment and should be subject to more refined searches; while instruments located in less important positions can be explored over a wider range. The specific implementation is as follows... Figure 2 As shown, it includes the following sub-steps:

[0092] ① Initial deterministic inner loop optimization: For the k-th outer loop iteration, in the first iteration of the N-th inner loop optimization (i.e., j=1), the original starting point b of the Adam optimizer is directly used. start,1 =b k,0 (regardless of b) k,0 Is it initialized to b1 or b? k This ensures that the most direct optimization path is explored in its entirety, resulting in a baseline fine-tuning.

[0093] ② Inner loop optimization after multiple random perturbations: In the subsequent N-1 inner loop optimizations (i.e., j = 2, ..., N), a non-uniform randomness guided by instrument importance is introduced to the starting point. This process includes:

[0094] (1) Importance of the computing instrument: First, based on the binary structure matrix H of the AC model * To quantify the importance of each instrument. Specifically, by analyzing H... * The matrix is ​​summed along its columns to obtain an m-dimensional instrument importance weight vector w:

[0095] w = sum(H* ,1) T

[0096] Here, sum(·,1) represents the summation by column, and the result is a 1×m row vector, which is then transposed. T This results in an m×1 column vector w. The i-th element of the vector w... i This represents the number of state variables that the i-th instrument can influence, i.e., the "defense coverage" of that instrument. i The larger the value, the greater the "defense coverage" of the instrument.

[0097] (2) Generating the disturbance strength guided by instrument importance: Based on the instrument importance, for each effective decision variable b i (i.e. φ) i * A variable with a value of 1 generates a differentiated perturbation strength. The basic principle is: the more important the instrument, the more refined the perturbation (smaller strength); the less important the instrument, the bolder the perturbation (larger strength). This can be achieved as follows:

[0098] First, the instrument importance weight vector w is normalized to obtain the normalized weight vector w. norm This ensures that the range of its elements is [0,1].

[0099] Then, calculate the disturbance level vector p guided by the importance of the instrument. noise Its component p noise,i The calculation formula is:

[0100] p noise,i =r base ×(1-w norm,i )

[0101] Where, r base It is a base disturbance level (e.g., 0.1), w norm,i It is w norm The value of the i-th element. Thus, the higher the importance of the i-th instrument, the higher its corresponding disturbance level p. noise,i The smaller it is.

[0102] (3) Apply perturbation to generate a new starting point: At the start of the j-th (j>1) optimization, generate a new starting point b. start :

[0103] b start,j =max(0,b) k,0 ⊙(1+p noise ⊙p rand )⊙φ * )

[0104] Where ⊙ denotes element-wise multiplication of a vector, prand It is an element that is uniformly distributed in the interval [-1, 1] and is related to b. k,0 A random vector of the same dimension. (This is achieved through interaction with φ.) * Multiplication ensures that disturbances are applied only to instruments that have been identified as requiring defense deployment.

[0105] ③ Optimal solution selection: From the baseline fine-tuning obtained from the initial deterministic inner loop optimization and the N-1 optimization results obtained from the inner loop optimization after multiple random perturbations, select the solution with the smallest inner loop objective function value P(b) as the result b of this inner loop. k+1 And return it to the outer loop to update the Lagrange multipliers.

[0106] The above description is merely a preferred embodiment of the present invention. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention using the methods and techniques disclosed above, or modify them into equivalent embodiments with equivalent changes, without departing from the scope of the technical solutions of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall still fall within the protection scope of the technical solutions of the present invention.

Claims

1. A two-stage hybrid optimization-based method for allocating optimal defense resources, characterized in that, include: Global configuration coarse search stage: The slime mold algorithm with initialization pool is used to perform a global exploratory search on the entire solution space of the optimal defense resource allocation problem under the communication model, and output candidate solutions. The candidate solutions include a definite defense deployment location represented by a binary decision variable vector and a corresponding initial defense resource input represented by a continuous decision variable vector. Resource allocation fine-tuning phase: The defense deployment positions obtained in the global configuration coarse search phase are fixed, and the original problem is transformed into a nonlinear, non-convex optimization subproblem concerning only continuous decision variable vectors. An adaptive moment estimation optimization method based on multi-starting-point random perturbation is adopted. Within an augmented Lagrange framework with a double-layer loop, the inner loop performs local optimization of the defense resource allocation. The local optimal solution is returned to the outer loop to update the Lagrange multipliers. After the outer loop iteration is complete, the optimal defense resource allocation scheme is obtained. The inner loop of the augmented Lagrange framework specifically consists of: First deterministic inner loop optimization: during the process In the first iteration of the inner loop optimization, Adam optimization is performed directly using the original starting point of the Adam optimizer to obtain a baseline fine adjustment. Inner loop optimization with multiple random perturbations: in the subsequent In the inner loop optimization, a non-uniform randomness guided by instrument importance is introduced to the starting point to generate... A new starting point; For each new starting point, repeat the Adam optimization based on the augmented Lagrange framework to obtain... One solution; Optimal solution selection: Based on the baseline fine adjustment obtained from the initial deterministic optimization and the optimization obtained from multiple random perturbations. Among the solutions, the solution with the smallest objective function value in the inner loop is selected as the result of the current inner loop and returned to the outer loop.

2. The communication-optimal defense resource allocation method based on two-stage hybrid optimization according to claim 1, characterized in that, The augmented Lagrange framework works in concert through an outer loop and an inner loop. The outer loop is responsible for dynamically adjusting the Lagrange multipliers and penalty coefficients to guide the solution to approximate the feasible region. The inner loop, given the Lagrange multipliers and penalty coefficients, is responsible for solving the optimal amount of defense resources to be invested under the current conditions.

3. The optimal defense resource allocation method based on two-stage hybrid optimization according to claim 1, characterized in that, If the current inner loop is within the first outer loop, then the starting point of the inner loop is initialized to the initial value of the defense resource investment of the first outer loop; otherwise, it is initialized to the result of the previous outer loop.

4. The optimal defense resource allocation method based on two-stage hybrid optimization according to claim 1, characterized in that, The inner loop optimization involving multiple random perturbations specifically involves: First, based on the binary structure matrix of the communication model Quantify the importance of each instrument. It is The binary structure matrix, where The number of state variables. To measure the number of instruments, This reflects the topological dependency between the state variables of the power grid and the measuring instruments in the AC model. If in the AC model... State variables The changes will affect the first individual measuring instruments ,but Corresponding element Otherwise, it is 0; through the Perform column-wise summation to obtain a The importance weight vector of the instrument in dimension : in, This indicates summing by column, and the result is a single... The row vector, after being transposed, yields... column vectors ; Column vector The first in element Representing the The number of state variables that a single instrument can affect, i.e., the defense coverage of that instrument; Then, based on the importance of the instrument, a differentiated disturbance intensity is generated for each effective decision variable to obtain the disturbance level vector. The disturbance principle is that the more important the instrument, the smaller the disturbance intensity, and the less important the instrument, the larger the disturbance intensity. Finally, a new starting point is generated by combining the random vector, the perturbation horizontal vector, and the defense deployment position obtained in the global configuration coarse search phase.

5. The optimal defense resource allocation method based on two-stage hybrid optimization according to claim 4, characterized in that, The formula for calculating the horizontal component of the disturbance of the i-th instrument is: in, It is a basic disturbance level. It normalizes the range of elements to The first instrument importance weight vector Each element value.

6. The method for optimal defense resource allocation based on two-stage hybrid optimization according to claim 4, characterized in that, For the starting point Introducing a new starting point based on non-uniform randomness guided by instrument importance. The calculation formula is: in, This represents element-wise multiplication of vectors. It is an element in Uniformly distributed within the interval and with Random vectors of the same dimension It is the perturbation horizontal vector. It refers to the defense deployment location obtained during the global configuration coarse search phase.

7. The method for optimal defense resource allocation based on two-stage hybrid optimization according to claim 1, characterized in that, The outer loop of the augmented Lagrange framework is specifically as follows: The initial defense resource investment is the initial defense resource investment obtained in the global configuration coarse search phase; the Lagrange multipliers and penalty coefficients are initialized. In each iteration of the outer loop, the current Lagrange multipliers and penalty coefficients are first used as inputs to call the Adam optimizer in the inner loop to solve the problem of minimizing the augmented Lagrange function and obtain the updated defense resource investment. Then, based on the updated defense resource investment, the actual constraint relaxation value is calculated and the Lagrange multipliers are updated. Finally, the penalty coefficient is increased. The outer loop continues until the change in the Lagrange multiplier is less than the set threshold or the maximum number of iterations is reached, and all constraints are satisfied. After the outer loop iteration ends, the final output of the defense resource input is combined with the defense deployment position obtained by the global configuration coarse search order to form the optimal defense resource allocation scheme.

8. The method for optimal defense resource allocation based on two-stage hybrid optimization according to claim 1, characterized in that, In having One state variable and In an AC power system with multiple measuring instruments, the optimal defense resource allocation problem under the AC model is constructed as a mixed-integer nonlinear programming problem, i.e., minimizing... And it satisfies the following three constraints: in, yes A continuous decision variable vector, representing the amount of defense resources invested in each instrument; yes A two-dimensional binary decision variable vector, when Time indicates the time in the Deploy defense resources on each instrument, when At that time, no deployment is required; It is the first The attack cost function on each instrument represents the cost of attacking when defense resources are invested. The cost an attacker would incur to compromise the instrument; This represents the maximum number of instruments that the defending side can deploy for defensive measures; All elements are of dimensional vector, This represents the maximum total resources an attacker can use to launch an attack. yes The binary structure matrix reflects the topological dependency between the state variables of the power grid and the measuring instruments under the AC model; the first constraint includes Individual constraints.

9. The communication-optimal defense resource allocation method based on two-stage hybrid optimization according to claim 8, characterized in that, In the The outer loop is given a Lagrange multiplier vector. and penalty coefficient The goal of the inner loop is to minimize the augmenting Lagrange function. Defense resource investment : in, Indicates the first constraint The degree of relaxation of a sub-constraint, which is intended to protect the first... Each state variable is not tampered with.

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