Electromagnetic spectrum monitoring network deployment method based on multi-objective differential evolution algorithm

Abstract

The present application discloses a method for deploying an electromagnetic spectrum monitoring network based on a multi-objective differential evolution algorithm, the method comprising: determining multiple sub-objective optimization functions, the sub-objective optimization including the optimization objective of maximizing network area coverage, the optimization objective of minimizing electromagnetic spectrum monitoring equipment displacement, and the optimization objective of minimizing redundant coverage area; converting the weighted sum of multiple sub-objective functions into a comprehensive objective function; solving the electromagnetic spectrum monitoring network deployment optimization problem based on the multi-objective differential evolution algorithm. The present invention can minimize the electromagnetic spectrum monitoring moving distance as much as possible, thereby improving the deployment efficiency of the electromagnetic spectrum monitoring network, and enhancing many network performance indicators such as the coverage performance, connectivity performance, and resource utilization efficiency of the electromagnetic spectrum monitoring network.

Description

Technical Field

[0001] The present application relates to the field of communication network coverage technology, and more specifically, to an electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm. Background Art

[0002] The deployment of electromagnetic spectrum monitoring equipment within a mission area directly impacts numerous network performance indicators, including coverage, connectivity, and resource efficiency. Therefore, a scientific and effective method is needed to support the planning and deployment adjustments of the electromagnetic spectrum monitoring network within the mission area. Therefore, the deployment of the electromagnetic spectrum monitoring network within the mission area is an urgent issue that needs to be addressed. The deployment of electromagnetic spectrum monitoring networks is flexible and adaptable, and the network structure can change depending on various factors, such as mission requirements, the number of participating units, terrain constraints, and the number of devices. Furthermore, if network performance requirements are not met after the initial deployment, or if rapid deployment adjustments are required due to changes in the mission area, a secondary deployment of the electromagnetic spectrum monitoring network is necessary to improve service performance. Therefore, relying solely on the experience of relevant personnel to deploy the electromagnetic spectrum monitoring network on an ad hoc basis is unscientific. A method that can dynamically adjust the deployment of the electromagnetic spectrum monitoring network based on user needs and changing circumstances is urgently needed.

[0003] At present, researchers have proposed a variety of deployment methods for traditional radio sensor networks based on virtual forces, computational geometry, particle swarm optimization algorithms, etc., which have not fully considered the special application scenarios of electromagnetic spectrum monitoring networks and are not very targeted and effective.

[0004] The virtual force-based deployment algorithm places high demands on the initial distribution of electromagnetic spectrum monitoring equipment. If these equipment are initially clustered, this can lead to uncovered areas within the mission area and even cause some equipment to be removed from the monitoring area, directly impacting the final network deployment. When this algorithm is applied to an electromagnetic spectrum monitoring network with high connectivity requirements, some equipment may become clustered.

[0005] Deployment algorithms based on computational geometry can achieve complete coverage of the mission area, assuming a sufficient number of electromagnetic spectrum monitoring devices. However, this algorithm has a high computational complexity. When deploying an electromagnetic spectrum monitoring network that requires a large number of devices, generating the Voronoi diagram can be computationally intensive and time-consuming. Lack of monitoring area boundary information can easily result in coverage issues at the edges.

[0006] Deployment methods based on the particle swarm optimization algorithm demonstrate high solution accuracy and fast computational speed when solving the regional coverage problem of electromagnetic spectrum monitoring networks. However, when using the particle swarm optimization algorithm to solve the problem of maximizing regional coverage of electromagnetic spectrum monitoring networks, the optimizing particles often tend to aggregate toward their own optimal solutions and the group's optimal solution, causing the particle population to quickly converge, resulting in premature convergence of the optimization process for regional coverage of the electromagnetic spectrum monitoring network or trapping it in a local optimal solution.

[0007] At present, there is no unified model for the deployment of electromagnetic spectrum monitoring networks. The above methods consider the problem from different perspectives, but few of them address the planning and adjustment deployment of electromagnetic spectrum monitoring networks under changing user needs and situations. Summary of the Invention

[0008] In response to at least one defect or improvement need in the prior art, the present invention provides an electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm, which can minimize the electromagnetic spectrum monitoring moving distance as much as possible, thereby improving the electromagnetic spectrum monitoring network deployment efficiency and enhancing many network performance indicators of the electromagnetic spectrum monitoring network, such as coverage performance, connectivity performance and resource utilization efficiency.

[0009] To achieve the above objectives, according to a first aspect of the present invention, a method for deploying an electromagnetic spectrum monitoring network based on a multi-objective differential evolution algorithm is provided, the method comprising:

[0010] Determine multiple sub-objective optimization functions, including the optimization goals of maximizing network area coverage, minimizing electromagnetic spectrum monitoring equipment displacement, and minimizing redundant coverage area.

[0011] Transform the weighted sum of multiple sub-objective functions into a comprehensive objective function;

[0012] The electromagnetic spectrum monitoring network deployment optimization problem is solved based on the multi-objective differential evolution algorithm, specifically including:

[0013] S1: Encode the individuals in the initial population, complete population initialization, and obtain the target vector;

[0014] S2: Randomly select several individuals in the population to participate in the mutation operation to form a mutation vector;

[0015] S3: under the action of crossover probability, the target vector and the mutation vector are selected for crossover recombination to form an experimental vector;

[0016] S4: comparing the fitness evaluation function values ​​of the target vector and the experimental vector, and saving the vector with a better fitness evaluation function value;

[0017] S5: If the maximum number of iterations is reached, execute S6; if not, jump to S2.

[0018] S6: The best individual generated in the last iteration is taken as the optimal solution and output.

[0019] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the optimization goal of maximizing the network area coverage is specifically expressed as:

[0020] When electromagnetic spectrum monitoring equipment O i Cover any grid point (x, y) in the task area and record this state as I i , put I i The probability of occurrence is expressed as P(I i )express:

[0021]

[0022] When the grid point (x, y) is covered by any electromagnetic spectrum monitoring device in the electromagnetic spectrum monitoring device set O within the mission area, it is considered that the electromagnetic spectrum monitoring device set covers the grid point (x, y). The coverage rate of the electromagnetic spectrum monitoring device set O is recorded as:

[0023]

[0024] The task area is divided into a grid area Δx×Δy in the task area, and the task area is discretized to form a×b grids. The network area coverage function is:

[0025]

[0026] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the optimization goal of minimizing the displacement of the electromagnetic spectrum monitoring equipment is specifically expressed as:

[0027] Define the electromagnetic spectrum monitoring equipment during the optimization process i The displacement is D i , electromagnetic spectrum monitoring equipment O i The initial position and optimized position are represented by (x i ,y i ) and (x′ i ,y′ i )express;

[0028]

[0029] The displacement function of the electromagnetic spectrum monitoring equipment is:

[0030]

[0031] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the optimization objective of the minimum redundant coverage area is specifically expressed as:

[0032] The redundant coverage area function is defined as:

[0033]

[0034] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the weighted sum of multiple sub-objective functions is converted into a comprehensive objective function, which is specifically implemented by the following formula:

[0035] f gof (x)=ω1f1(x)+ω2f2(x)+ω3f3(x)

[0036] Among them, ω1 is the weighting factor of the network area coverage function, ω2 is the weighting factor of the displacement function of the electromagnetic spectrum monitoring equipment, and ω3 is the weighting factor of the minimum redundant coverage area function.

[0037] Furthermore, the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm further includes:

[0038] The electromagnetic spectrum monitoring equipment deployment plan is regarded as an individual in the group, and the individual is represented as a collection of genomes:

[0039] G={o1,o2,...,o i}, i∈m

[0040] Among them, i represents chromosomes, m represents the number of individuals in the population; o i =(x i ,y i ) represents the initial position coordinates of the electromagnetic spectrum monitoring device i within the mission area.

[0041] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the population initialization process specifically includes:

[0042] Construct an initial population with a population size of m and a vector dimension of n for each individual. Randomly generate m individuals in the n-dimensional space. The j-th dimension value of the individual numbered i is as follows:

[0043] X i,j (0) = L j-min +rand(0,1)(L j_max -Lj_min )i=1,2,...m,j=1,2,...n

[0044] Among them, rand j (0,1) is a random number between 0 and 1.

[0045] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the step of randomly selecting a number of individuals in the population to participate in the mutation operation to form a mutation vector specifically includes:

[0046] When iterating to the tth time, randomly select individual X from the population p1 (t), X p2 (t) and X p3 (t) Participate in the mutation operation and satisfy the condition p1≠p2≠p3. The resulting mutation vector is:

[0047] H i (t+1)=X p1 (t)+F.(X p2 (t)-X p3 (t))

[0048] Among them, (X p2 (t)-X p3 (t)) is the control deviation vector, and F is the scaling factor of the control deviation vector amplification coefficient.

[0049] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the step of selecting the target vector and the mutation vector for crossover recombination to form an experimental vector under the action of the crossover probability is implemented by the following formula:

[0050]

[0051] Among them, U i,j (t+1) is the experimental vector, X i,j (t) is the target vector H i,j (t+1) is the mutation vector.

[0052] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm, the fitness evaluation function values ​​of the target vector and the experimental vector are compared, and the vector with a better fitness evaluation function value is saved, which is achieved by the following formula:

[0053]

[0054] Among them, f(X i (t)) represents the fitness evaluation function of the t-th iteration individual numbered i.

[0055] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0056] The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm provided by the present invention simultaneously optimizes the optimization goal of the highest network area coverage rate, the optimization goal of the minimum displacement of the electromagnetic spectrum monitoring equipment, and the optimization goal of the minimum redundant coverage area by adopting an improved multi-objective differential evolution algorithm. While improving the regional coverage performance of the electromagnetic spectrum monitoring network, it can also minimize the electromagnetic spectrum monitoring movement distance, thereby improving the deployment efficiency of the electromagnetic spectrum monitoring network and enhancing many network performance indicators such as the coverage performance, connectivity performance, and resource utilization efficiency of the electromagnetic spectrum monitoring network. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0058] Figure 1 A flowchart of a method for deploying an electromagnetic spectrum monitoring network based on a multi-objective differential evolution algorithm provided in an embodiment of the present application;

[0059] Figure 2 This is a schematic diagram of the initial network deployment coverage;

[0060] Figure 3 This is a diagram of network deployment coverage based on the single-objective differential evolution algorithm;

[0061] Figure 4 Schematic diagram of the network area coverage evolution curve based on the single-objective differential evolution algorithm;

[0062] Figure 5 is the network redundancy coverage evolution curve based on the single-objective differential evolution algorithm;

[0063] Figure 6 The displacement and evolution curve of electromagnetic spectrum monitoring equipment based on single-objective evolutionary algorithm;

[0064] Figure 7 This is a diagram of network deployment coverage based on the multi-objective differential evolution algorithm;

[0065] Figure 8 is the network area coverage evolution curve based on the multi-objective differential evolution algorithm;

[0066] Figure 9This is the evolution curve of network redundancy coverage area based on multi-objective differential evolution algorithm;

[0067] Figure 10 The displacement and evolution curve of electromagnetic spectrum monitoring equipment based on multi-objective differential evolution algorithm;

[0068] Figure 11 Weighted index change curve for multi-objective optimization. DETAILED DESCRIPTION

[0069] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0070] The terms "first," "second," "third," and the like in the specification and claims of this application and the accompanying drawings are used to distinguish between different objects, not to describe a particular order. Furthermore, the terms "including," "having," and any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or elements is not limited to the listed steps or elements, but may optionally include steps or elements not listed, or may optionally include other steps or elements inherent to the process, method, product, or apparatus.

[0071] Multi-objective optimization problems are described from a mathematical perspective and consist of multiple objective functions, related inequalities, and equality constraint functions, which can be expressed as follows:

[0072]

[0073] Among them, the function f i (x), i=1,2,...,n is the objective function, function v i (x), g i (x) are the inequality constraint function and the equality constraint function respectively; x={x1,x2,x3,...,x m}∈R m is a design variable, then the feasible region of the above formula is {x|x∈R m ,v i (x)≥0,g j (x)=0,i=1,2,...,k,j=1,2,...,q}; the objective function f(x) corresponds to the mapping from the m-dimensional design variable space to the n-dimensional objective function space, expressed as f:R m →R n .

[0074] This application discloses a method for deploying an electromagnetic spectrum monitoring network based on a differential evolution algorithm. Figure 1 For a flow chart of a method for deploying an electromagnetic spectrum monitoring network based on a multi-objective differential evolution algorithm provided in an embodiment of the present application, please refer to Figure 1 The method comprises the following steps:

[0075] (1) Determine multiple sub-objective optimization functions. The sub-objective optimization includes the optimization goal of maximizing network area coverage, the optimization goal of minimizing the displacement of electromagnetic spectrum monitoring equipment, and the optimization goal of minimizing redundant coverage area.

[0076] Specifically, the optimization objective function (objective function 1) for achieving the highest network area coverage is expressed as follows:

[0077] Construct an electromagnetic spectrum detection network coverage model, and express the electromagnetic spectrum monitoring network coverage model in the mission area as {disk, (x i ,y i ),r i}, where disk describes the perception model of battlefield electromagnetic spectrum monitoring equipment using a two-dimensional Boolean perception model, (x i ,y i ) Describe electromagnetic spectrum monitoring equipment i The position coordinates, r i Describe electromagnetic spectrum monitoring equipment i Perception radius.

[0078] Assume that the mission area is a rectangular two-dimensional plane area, and the set of electromagnetic spectrum monitoring equipment in the mission area is O. i The coverage model is represented as O i ={x i ,y i ,r i}, where (x i ,y i ) Describe electromagnetic spectrum monitoring equipment i The position coordinates are expressed as r i Describe electromagnetic spectrum monitoring equipment i Perception radius.

[0079] When electromagnetic spectrum monitoring equipment O i To cover any grid point (x, y), this state is recorded as I i , put I i The probability of occurrence is expressed as P(I i ) indicates that if the electromagnetic spectrum monitoring equipment O i No coverage is achieved for any grid point (x, y), and this state is recorded as P(I i ) is the electromagnetic spectrum monitoring equipment O i The probability of covering the grid point (x, y) is recorded as P(x, y, O i ); If the grid point (x, y) is in the same position as the electromagnetic spectrum monitoring device O i The distance between the electromagnetic spectrum monitoring equipment is less than or equal to O i Perception radius r i , that is, to identify electromagnetic spectrum monitoring equipment O i The grid point (x, y) has been covered, and the probability is 1; other cases indicate that the electromagnetic spectrum monitoring equipment O i The grid point (x, y) is not covered, and the probability is 0. i ) is a binary function:

[0080]

[0081] For the electromagnetic spectrum monitoring equipment set within the mission area, assuming that I j , and I i and I j It is irrelevant, and its existence relationship can be expressed as P(I i ∪I j ) represents; when the grid point (x, y) is covered by any electromagnetic spectrum monitoring device in the electromagnetic spectrum monitoring device set O within the mission area, it is determined that the electromagnetic spectrum monitoring device set covers the grid point (x, y), and the probability that the grid point (x, y) is covered by the battlefield electromagnetic spectrum monitoring device set O is I i The coverage of the electromagnetic spectrum monitoring equipment set O is:

[0082]

[0083] The task area is divided into a grid area Δx×Δy in the task area, and the task area is discretized to form a×b grids. The network area coverage function is:

[0084]

[0085] Furthermore, the optimization objective function (objective function 2) for minimizing the displacement of electromagnetic spectrum monitoring equipment is expressed as follows:

[0086] Define the electromagnetic spectrum monitoring equipment during the optimization process i The displacement is D i , electromagnetic spectrum monitoring equipment O i The initial position and optimized position are represented by (x i ,y i ) and (x′ i ,y′ i)express;

[0087]

[0088] In the deployment optimization of the electromagnetic spectrum monitoring network, the sum of the displacements of the electromagnetic spectrum monitoring equipment is minimized as much as possible. By reducing the displacement, the deployment time is shortened to improve the deployment efficiency. The displacement function of the electromagnetic spectrum monitoring equipment is:

[0089]

[0090] Furthermore, the optimization objective function (objective function 3) for minimizing the redundant coverage area is expressed as follows:

[0091] The redundant coverage area function is defined as:

[0092]

[0093] (2) In the process of dealing with the electromagnetic spectrum monitoring network deployment optimization problem based on multi-objective optimization, the weighted sum of the sub-objective functions is transformed into a comprehensive objective function, and the comprehensive objective function f gof (x) is the fitness function for solving the optimization problem based on the multi-objective differential evolution algorithm, and its calculation is shown in the following formula:

[0094] f gof (x)=ω1f1(x)+ω2f2(x)+ω3f3(x)

[0095] Among them, ω1 is the weighting factor of the network area coverage function, ω2 is the weighting factor of the displacement function of the electromagnetic spectrum monitoring equipment, and ω3 is the weighting factor of the minimum redundant coverage area function.

[0096] Comprehensive objective function f gof (x) The fitness function can also be used to measure the pros and cons of the multi-objective optimization algorithm to evaluate whether it reaches or is as close to the optimal solution as possible. After normalization, the differential evolution algorithm calculates the comprehensive objective function based on the set weighting factors. The value of the comprehensive objective function is a positive number less than 1. The smaller the value of the comprehensive objective function, the better the mobile electromagnetic spectrum monitoring network deployment optimization plan.

[0097] During the operation of the mobile electromagnetic spectrum monitoring network deployment optimization algorithm based on the multi-objective differential evolution algorithm, some controllable parameters involving mutation and cross-core operations have a great influence on the algorithm operation results and algorithm performance, especially the population size (NP), scaling factor (F) and crossover probability (CR). At the same time, due to the particularity of each problem itself, there are also different requirements for the setting of experimental parameters when solving each problem. Therefore, in order to achieve ideal experimental results and ensure the scientificity and accuracy of the solution to the XX mobile electromagnetic spectrum monitoring network deployment optimization problem, appropriate strategies should be adopted to reasonably set the controllable parameters in the algorithm operation.

[0098] Among them, the population size represents the amount of information of the individuals in the population. The larger the size, the more diverse it is, and the stronger the search ability is, the more conducive it is to finding the global optimal solution. However, if the population size is too large, while increasing the search cost, the amount of calculation becomes larger, which requires longer calculation time and is not convenient for solving the problem. On the contrary, it is not conducive to the algorithm obtaining the optimal solution. Therefore, in general, the value of the group size is based on the dimension D of the problem space. A size greater than 4D can ensure the realization of the mutation operation, and after considering the operation time factor, the population size value is usually set between 5D and 10D; the scaling factor determines the amplification coefficient of the bias vector. The size of the coefficient not only affects the diversity of the population, but also has a significant impact on the global search and optimization ability of the algorithm. The larger the coefficient, the greater the probability of jumping out of the local minimum, but it will prolong the convergence time. The smaller the coefficient, the better the local search ability, but it will cause the algorithm to converge prematurely. Therefore, under normal circumstances, the scaling factor is between 0.1 and 1, which can avoid the situation where the population convergence speed is reduced due to too large a value and the situation where the population converges prematurely due to too small a value. The crossover probability is used to control the degree of information exchange between offspring and previous generations and intermediate mutant individuals, and to balance the search ability between local and global. The larger the crossover probability in the algorithm, the faster the convergence. However, if the value is too large, the sensitivity of convergence to the scaling factor will gradually increase, resulting in slower convergence. The smaller the crossover probability, the less diversity of the algorithm population will be, which will affect the algorithm's search for the global optimal solution. Therefore, the crossover probability is usually between 0.1 and 0.9, which can avoid the situation where convergence slows down due to the population difference being less than the disturbance.

[0099] In addition to the above three parameters that can affect the efficiency and results of the algorithm solution, the number of iterations as a conditional parameter for terminating the evolutionary process will also affect the length of the calculation time and the accuracy of the optimal solution. Through verification on different problems, some better initial parameter setting combinations have been obtained. While providing experience-based reference and reference for the parameter setting of this section, the particular characteristics of the XX mobile electromagnetic spectrum monitoring network deployment optimization problem must also be considered. According to the experimental scenario, the controllable parameter settings should be appropriately adjusted to obtain the scientificity and accuracy of the simulation experimental results.

[0100] In one embodiment, when the weighted parameters ω1:ω2:ω3=5:3:2, the target differential evolution algorithm solves the optimal value. At this time, while improving the regional coverage performance of the electromagnetic spectrum monitoring network, the electromagnetic spectrum monitoring moving distance can be minimized as much as possible, thereby maximizing the deployment efficiency of the electromagnetic spectrum monitoring network.

[0101] (3) Solve the electromagnetic spectrum monitoring network deployment optimization problem based on the improved multi-objective differential evolution algorithm.

[0102] The decision space of the electromagnetic spectrum monitoring network deployment optimization problem corresponds to the adjustment of the position coordinates of the electromagnetic spectrum monitoring equipment. Therefore, the position coordinates of the electromagnetic spectrum monitoring equipment are used as the encoding scheme of the chromosome. The deployment plan of the electromagnetic spectrum monitoring equipment is described by individuals in the population, and the individuals are represented as a genome set, that is, G = {o1,o2,...,o i}, i∈m, where o i represents chromosomes, m represents the number of individuals in the population; o i =(x i ,y i ) represents the initial position coordinates of the electromagnetic spectrum monitoring device i in the mission area, so the real number encoding scheme adopted by the present invention is described as an encoding scheme based on the position coordinates of the electromagnetic spectrum monitoring device, that is, {<x1,y1><x2,y2> ... <x i ,y i >... <x m ,y m >}, the change of the position coordinates of the electromagnetic spectrum monitoring equipment can represent the adjustment of the position of the electromagnetic spectrum monitoring equipment, and complete the mapping between the individual space and the problem decision space.

[0103] S1: Initialize the population

[0104] Before the initialization operation, it is necessary to complete the encoding of the individuals. The encoding method affects the convergence effect of the algorithm. When using the multi-objective differential evolution algorithm to solve the problem, the real number encoding method is adopted to improve the algorithm operation efficiency. Construct an initial population with a population size of m and a vector dimension of n for each individual. In the n-dimensional space, m individuals can be randomly generated to meet the constraints. The j-th dimension value of the individual numbered i is as follows:

[0105] X i,j (0) = L j-min +rand(0,1)(L j_max -L j_min )i=1,2,...m,j=1,2,...n

[0106] Among them, rand j (0,1) is a random number between 0 and 1.

[0107] S2: mutation operation

[0108] The mutation operation is the key to the differential evolution algorithm. When it iterates to the tth time, the individual X in the population is randomly selected. p1 (t), X p2 (t) and X p3 (t) Participate in the mutation operation and satisfy the condition p1≠p2≠p3. The resulting mutation vector is:

[0109] H i (t+1)=X p1 (t)+F.(X p2 (t)-X p3 (t))

[0110] Among them, (X p2 (t)-X p3 (t)) is the control deviation vector, and F is the scaling factor of the control deviation vector amplification coefficient.

[0111] Crossover Operation

[0112] During the crossover operation, the target vector X is obtained from the crossover probability. i (t) and the mutation vector H i (t) is selected to form a new experimental vector, and the number of interference vectors is increased by crossover operation to ensure the diversity of the population, which is achieved by the following formula:

[0113]

[0114] Among them, rand j Generate a random number for each dimension between [0,1].

[0115] This strategy can ensure that the experimental individual dimension has at least one i (t) Different.

[0116] S3: Select an action

[0117] During the selection operation, the target vector X is compared according to the selection strategy. i (t) and the experimental vector U i The fitness evaluation function value of (t+1) is compared with the fitness evaluation function values ​​of the two, and the one with better fitness evaluation function value is saved and introduced into the next round of evolution. This is achieved through the following formula:

[0118]

[0119] Among them, f(X i (t)) represents the fitness evaluation function of the t-th generation individual numbered i.

[0120] S4: Terminate the operation

[0121] If the entire evolutionary iteration generation has reached the set maximum generation t max Or the target requirement has been reached, that is, the evolution is terminated and the best individual produced by the most recent selection operation is output as the optimal solution; otherwise, the evolution is continued in S2; the new individual produced by the selection operation is expressed as follows, and the best individual in X(t+1) is recorded as X best (t+1).

[0122] X(t+1)=(X1(t+1),X2(t+1),X3(t+1),...,X m (t+1))

[0123] The basic operational flow of the differential evolution algorithm typically begins with population initialization. This operation also involves defining the adjustable control parameters and individual fitness evaluation functions that influence the algorithm's operation. The random generation of the initial population also marks the beginning of the algorithm's mutation operation. This operation involves selecting the difference vectors of two individuals from the initial population, applying weighted rules, and then summing them with a third individual to form a mutant individual. In the crossover phase, experimental individuals are generated by performing multi-point crossovers between the mutant vectors and the selected target vector, providing candidate vectors. In the selection phase, the fitness evaluation functions of the experimental individuals are compared with those of the target individual, performing a survival of the fittest selection process. The vectors with the best fitness are retained and introduced into the next generation of evolution, thus completing the differential evolution process.

[0124] In order to facilitate the performance evaluation of the proposed electromagnetic spectrum monitoring network area deployment optimization algorithm based on multi-objective differential evolution and simulation test, the simulation experiment takes the two-dimensional plane task area as the background and adopts a two-dimensional Boolean perception model. It is assumed that the perception radius r of the electromagnetic spectrum monitoring equipment in the task area is s is 8m, and has met the transmission radius r of the electromagnetic spectrum monitoring equipment c ≥2r s Conditions were set to study the deployment optimization of 25 electromagnetic spectrum monitoring devices after initial deployment in a 55m×55m two-dimensional plane mission area.

[0125] In order to obtain relatively ideal experimental results, some experimental parameters were adjusted several times during the simulation experiment. If the values ​​of the mutation factor (F) and the crossover probability (F) were too large, it would lead to convergence difficulties, while if the values ​​were too small, it would lead to slow convergence. According to the simulation results, it was finally determined that the population size (NP) parameter was set to 40, the mutation factor (F) parameter was set to 0.1, the crossover probability (CR) parameter was set to 0.1, and the number of iterations in the optimization process t max The parameter is set to 4000. The following analyzes the simulation results of single-objective optimization and multi-objective optimization respectively.

[0126] Figure 2 The initial network deployment coverage diagram is shown in Figure 2. At the beginning of the simulation experiment, the initial deployment of 25 electromagnetic spectrum monitoring devices in the electromagnetic spectrum monitoring network was randomly generated. The deployment position and coverage of each electromagnetic spectrum monitoring device in the network are shown in Figure 2. Figure 2 shown.

[0127] Figure 3 The diagram of network deployment coverage based on the single-objective differential evolution algorithm is shown in the figure. During the simulation experiment, the coverage of the electromagnetic spectrum monitoring network area is first used as the optimization objective function, and the single-objective differential evolution algorithm is selected for operation. The optimized electromagnetic spectrum monitoring deployment is shown in the figure. Figure 3 shown.

[0128] In the initial situation, the positions of electromagnetic spectrum monitoring equipment are unevenly distributed, and a large coverage blind spot appears in the target area, resulting in a low coverage rate of the electromagnetic spectrum monitoring network. Through the optimization of the proposed algorithm, the position of the electromagnetic spectrum monitoring equipment is moved and adjusted to the coverage blind spot. When only the regional coverage rate of the electromagnetic spectrum monitoring network is optimized, the position movement of the electromagnetic spectrum monitoring equipment and the changes in regional coverage after the optimization iteration are completed are as follows: Figure 3 As shown in the figure, its network area coverage has been greatly improved. Figure 4 The evolution curve of network area coverage based on single-objective differential evolution algorithm is shown in Figure 2. The relationship between the coverage of electromagnetic spectrum monitoring network area and the number of optimization iterations is shown in Figure 2. Figure 4As shown in Figure 3, when the network area coverage increases from the initial 83% to 100%, it is determined that the algorithm converges to the optimal value.

[0129] Figure 5 is the evolution curve of network redundant coverage area based on single-objective differential evolution algorithm, Figure 6 The displacement and evolution curve of electromagnetic spectrum monitoring equipment based on the single-objective evolutionary algorithm are shown as follows. When only the coverage of the electromagnetic spectrum monitoring network area is optimized and the equipment displacement and redundant coverage are ignored, the redundant coverage area of ​​the electromagnetic spectrum monitoring network and the displacement of the electromagnetic spectrum monitoring equipment change with the number of iterations. Figure 5 、 Figure 6 shown.

[0130] Figure 7 This is a diagram of network deployment coverage based on the multi-objective differential evolution algorithm. The initial deployment of the electromagnetic spectrum monitoring network in the mission area remains unchanged, as shown in the following example. Figure 7 As shown in the figure, in the same simulation experiment scenario, the performance of the electromagnetic spectrum monitoring network regional deployment optimization algorithm based on multi-objective differential evolution is verified again, and the electromagnetic spectrum monitoring network regional coverage, redundant coverage area and equipment displacement are optimized simultaneously.

[0131] Figure 8 The network area coverage evolution curve based on the multi-objective differential evolution algorithm is verified for the weighted parameters ω1:ω2:ω3=5:3:2 in the above embodiment. When performing multi-objective optimization, the weighting factors for objective functions 1, 2, and 3 are 0.5, 0.3, and 0.2 respectively, and objective function 3 is divided by 1000 to achieve the same magnitude. The coverage of the electromagnetic spectrum monitoring network deployment area after 4000 iterations of multi-objective optimization is shown in the figure below. Figure 7 The coverage rate of the electromagnetic spectrum monitoring network area increased from the initial 83% to 97% and then stabilized. The relationship between the coverage rate of the electromagnetic spectrum monitoring network area and the number of iterations is shown in Figure 2. Figure 8 shown.

[0132] Figure 9 is the network redundancy coverage area evolution curve based on the multi-objective differential evolution algorithm, Figure 10 The displacement and evolution curve of electromagnetic spectrum monitoring equipment based on the multi-objective differential evolution algorithm are shown in Figure 2. Taking into account the three objectives of electromagnetic spectrum monitoring network area coverage, equipment displacement and redundant coverage area, the changes of electromagnetic spectrum monitoring network redundant coverage area and electromagnetic spectrum monitoring equipment displacement and with the number of iterations are shown in Figure 2. Figure 9 、 Figure 10 shown.

[0133] Figure 11This is the weighted index change curve for multi-objective optimization. In the multi-objective optimization process, the weighted comprehensive objective function value changes with the number of iterations as shown in the following figure: Figure 11 As shown. The simulation results show that in the process of electromagnetic spectrum monitoring network deployment optimization, the multi-objective differential algorithm can simultaneously take into account the three optimization objectives of electromagnetic spectrum monitoring network area coverage, equipment displacement and redundant coverage area; in terms of electromagnetic spectrum monitoring equipment displacement, the equipment displacement sum based on the single-objective differential evolution algorithm converges to 640, while the equipment displacement sum based on the multi-objective differential evolution algorithm converges to 753, which is a decrease of 15%; in terms of electromagnetic spectrum monitoring network redundant coverage area, the redundant coverage area based on the single-objective differential evolution algorithm converges to 390, while the redundant coverage area based on the multi-objective differential evolution algorithm converges to 1070, a decrease of about 63.6%; in terms of the regional coverage of the electromagnetic spectrum monitoring network, the regional coverage based on the multi-objective differential evolution algorithm converges to 97%, which is only 3 percentage points less than the regional coverage based on the single-objective differential evolution algorithm; through the above comparison, it can be seen that the multi-objective differential evolution algorithm can not only improve the regional coverage performance of the electromagnetic spectrum monitoring network during the regional deployment optimization of the electromagnetic spectrum monitoring network, but also minimize the moving distance of the electromagnetic spectrum monitoring equipment, thereby accelerating the deployment of the electromagnetic spectrum monitoring network, saving valuable time, and achieving high efficiency of the electromagnetic spectrum monitoring network deployment.

[0134] It should be noted that for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by this application.

[0135] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0136] The above is only an exemplary embodiment of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure herein, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any variation, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art that are not recorded in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0137] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0138] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for deploying an electromagnetic spectrum monitoring network based on a multi-objective differential evolution algorithm, characterized in that: include: Determine multiple sub-objective optimization functions, including the optimization goals of maximizing network area coverage, minimizing electromagnetic spectrum monitoring equipment displacement, and minimizing redundant coverage area. In the process of solving the electromagnetic spectrum monitoring network deployment optimization problem based on multi-objective optimization, the weighted sum of multiple sub-objective optimization functions is transformed into a comprehensive objective function, and the comprehensive objective function is used as the fitness evaluation function for solving the optimization problem based on the multi-objective differential evolution algorithm; The electromagnetic spectrum monitoring network deployment optimization problem is solved based on the multi-objective differential evolution algorithm, specifically including: S1: Encode the individuals in the initial population, complete population initialization, and obtain the target vector; S2: Randomly select several individuals in the population to participate in the mutation operation to form a mutation vector; S3: under the action of crossover probability, the target vector and the mutation vector are selected for crossover recombination to form an experimental vector; S4: comparing the fitness evaluation function values ​​of the target vector and the experimental vector, and saving the vector with a better fitness evaluation function value; S5: If the maximum number of iterations is reached, execute S6; if not, jump to S2. S6: The best individual generated in the last iteration is taken as the optimal solution and output.

2. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 1, wherein: The optimization goal of achieving the highest network area coverage is specifically expressed as: When electromagnetic spectrum monitoring equipment For any grid point in the task area Achieve coverage and record this state as ,Bundle The probability of occurrence is express: ； When the grid point A collection of electromagnetic spectrum monitoring equipment within the mission area If any of the electromagnetic spectrum monitoring equipment is covered, the electromagnetic spectrum monitoring equipment set is considered to be the grid point Achieve coverage and integrate electromagnetic spectrum monitoring equipment The coverage rate is recorded as: ； Take the area of ​​a single grid in the mission area Divide the task area into discrete grids, the network area coverage function is: ； Indicates electromagnetic spectrum monitoring equipment Perception radius; Indicates electromagnetic spectrum monitoring equipment The location coordinates of Indicates electromagnetic spectrum monitoring equipment No grid points Achieve a covered state.

3. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 2, wherein: The optimization goal of minimizing the displacement of the electromagnetic spectrum monitoring equipment is specifically expressed as: Definition of electromagnetic spectrum monitoring equipment during optimization process The displacement is , electromagnetic spectrum monitoring equipment The initial position and optimized position are respectively and express; ； The displacement function of the electromagnetic spectrum monitoring equipment is: 。 4. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 3, wherein: The optimization goal of the minimum redundant coverage area is specifically expressed as: The minimum redundant coverage area function is defined as: 。 5. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 4, wherein: The weighted summation of multiple sub-objective functions is converted into a comprehensive objective function, which is specifically achieved by the following formula: ； in, is the weighting factor of the network area coverage function, is the weighting factor of the displacement function of the electromagnetic spectrum monitoring device, is the weighting factor of the minimum redundant coverage area function.

6. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to any one of claims 1 to 5, wherein: Also includes: The electromagnetic spectrum monitoring equipment deployment plan is regarded as an individual in the population, and the individual is represented as a collection of genomes: ； in, Represents chromosomes, Represents the number of individuals in the population; Indicates electromagnetic spectrum monitoring equipment within the mission area The initial position coordinates of .

7. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 1, wherein: The process of population initialization specifically includes: The population size is constructed as , each individual vector dimension is The initial population, Randomly generated in dimensional space Individuals, numbered The individual's The dimension value is as follows: ； in, A random number between 0 and 1.

8. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 1, wherein: The random selection of several individuals in the population to participate in the mutation operation to form a mutation vector specifically includes: Iterate to the At this time, randomly select individuals from the population 、 and Participate in mutation operations and meet the conditions , the mutation vector formed is: ； in, is the control deviation vector, is the scaling factor that controls the amplification factor of the deviation vector.

9. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 1, wherein: The target vector is selected under the crossover probability to cross-recombine with the mutation vector to form an experimental vector, which is achieved by the following formula: ； in, is the experimental vector, is the target vector, is the mutation vector.

10. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm according to claim 1, wherein: The comparison of the fitness evaluation function values ​​of the target vector and the experimental vector and the preservation of the vector with a better fitness evaluation function value is achieved by the following formula: ； in, Indicates the number No. The fitness evaluation function value of the target vector of the iteration individual.

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