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

Abstract

The invention discloses an electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm, and the method comprises the steps: determining a plurality of sub-objective optimization functions, the sub-target optimization comprises an optimization target with the highest network area coverage rate, an optimization target with the minimum displacement of the electromagnetic spectrum monitoring equipment and an optimization target with the minimum redundant coverage area; carrying out weighted summation on the plurality of sub-objective functions and converting the sub-objective functions into a comprehensive objective function; the electromagnetic spectrum monitoring network deployment optimization problem is solved based on the multi-target differential evolution algorithm. According to the invention, the electromagnetic spectrum monitoring movement distance can be minimized as much as possible, so that the electromagnetic spectrum monitoring network deployment efficiency is improved; and a plurality of network performance indexes such as the coverage performance, the connectivity performance and the resource utilization efficiency of the electromagnetic spectrum monitoring network are enhanced.

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 in the mission area directly affects many network performance indicators such as the coverage performance, connectivity performance and resource utilization efficiency of the electromagnetic spectrum monitoring network. A scientific and effective method is needed to support the planning and adjustment deployment of the electromagnetic spectrum monitoring network in the mission area. Therefore, the deployment of the electromagnetic spectrum monitoring network in the mission area is an urgent problem to be solved. The deployment of the electromagnetic spectrum monitoring network is flexible and changeable. According to different mission requirements, the number of participating units, terrain restrictions, the number of equipment and other conditions, the network structure will also change. In addition, when the network performance index requirements are not met after the initial deployment, or the deployment needs to be adjusted quickly after the mission area changes, the electromagnetic spectrum monitoring network needs to be deployed again to improve the service performance of the electromagnetic spectrum monitoring network. It can be seen that it is unscientific to rely entirely on the experience of relevant personnel to deploy the electromagnetic spectrum monitoring network on the spot. There is an urgent need for a deployment method that can dynamically adjust the electromagnetic spectrum monitoring network according to user needs and situation changes.

[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. However, these methods have not fully considered the special application scenarios of electromagnetic spectrum monitoring networks, and are not very targeted and effective.

[0004] The deployment algorithm based on virtual force has high requirements on the initial distribution state of electromagnetic spectrum monitoring equipment during application. When the initial distribution of electromagnetic spectrum monitoring equipment is partially clustered, it may cause some uncovered areas in the mission area, and even cause some electromagnetic spectrum monitoring equipment to be moved out of the monitoring area, directly affecting the final network deployment effect. When the algorithm is applied to the deployment of electromagnetic spectrum monitoring networks with high connectivity requirements, some electromagnetic spectrum monitoring equipment may also be clustered.

[0005] The deployment algorithm based on computational geometry can achieve monitoring coverage of the mission area under the premise of sufficient number of electromagnetic spectrum monitoring equipment. However, the algorithm has high computational complexity. When the deployment of the electromagnetic spectrum monitoring network requires a large number of devices, the generation of the Voronoi diagram will result in large amount of calculation and long time consumption. If the boundary information of the monitoring area is missing, it is easy to cause the boundary area to not be covered.

[0006] The deployment method based on the particle swarm optimization algorithm shows high solution accuracy and fast computing speed in solving the problem of regional coverage of the electromagnetic spectrum monitoring network. However, when the particle swarm optimization algorithm is used to solve the problem of maximizing the regional coverage of the electromagnetic spectrum monitoring network, the optimization particles usually tend to gather towards their own optimal solution and the group optimal solution, which makes the particle population form a rapid convergence phenomenon, resulting in the optimization process of the regional coverage of the electromagnetic spectrum monitoring network converging prematurely or falling into the 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 angles, but few of them address the planning and adjustment and deployment of electromagnetic spectrum monitoring networks in response to changes in 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 moving distance of electromagnetic spectrum monitoring, thereby improving the deployment efficiency of the electromagnetic spectrum monitoring network 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 object, 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 goal of the highest network area coverage, the optimization goal of the minimum displacement of electromagnetic spectrum monitoring equipment, and the optimization goal of the minimum 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, 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, select the target vector and the mutation vector to cross-recombine to form an experimental vector;

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

[0017] S5: If the maximum number of iterations is reached, execute S6; if the maximum number of iterations is not reached, 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 a multi-objective differential evolution algorithm, the optimization goal of achieving the highest 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 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 in the mission area, it is determined that the electromagnetic spectrum monitoring device set covers the grid point (x, y), and the coverage rate of the electromagnetic spectrum monitoring device set O is recorded as:

[0023]

[0024] The task area is divided by the single grid area Δx×Δy in the task area, so that 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 a 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 target 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 electromagnetic spectrum monitoring network deployment method based on the multi-objective differential evolution algorithm further includes:

[0038] The electromagnetic spectrum monitoring equipment deployment scheme is regarded as an individual in the population, and the individuals are 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 in the mission area.

[0041] Furthermore, in the above-mentioned electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm, the process of population initialization 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 a 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 mutation vector formed 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 to cross-recombine 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 a 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 implemented 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 adopts an improved multi-objective differential evolution algorithm to simultaneously optimize 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. While improving the regional coverage performance of the electromagnetic spectrum monitoring network, it can also minimize the electromagnetic spectrum monitoring moving 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 drawings required for use in the embodiments will be briefly introduced below. 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 paying 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 schematic diagram of network deployment coverage based on a single-objective differential evolution algorithm;

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

[0062] Figure 5 It 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 schematic diagram of network deployment coverage based on multi-objective differential evolution algorithm;

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

[0066] Fig. 9It is the evolution curve of network redundant coverage area based on multi-objective differential evolution algorithm;

[0067] Fig.10 Displacement and evolution curve of electromagnetic spectrum monitoring equipment based on multi-objective differential evolution algorithm;

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

[0069] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain 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 can be combined with each other as long as they do not conflict with each other.

[0070] The terms "first", "second", "third", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0071] The multi-objective optimization problem is described from a mathematical perspective and consists 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 domain 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, including 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) with the highest network area coverage is expressed as:

[0077] Construct an electromagnetic spectrum detection network coverage model and represent 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 by 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 Cover any grid point (x, y) and record this state as I i , put I i The probability of occurrence is P(I i ) indicates that if the electromagnetic spectrum monitoring equipment O i No grid point (x, y) is covered, and this state is recorded as P(I i ) is the electromagnetic spectrum monitoring equipment O i The probability of covering a grid point (x, y) is denoted as P(x, y, i ); if the grid point (x, y) is in contact with the electromagnetic spectrum monitoring device O i The distance between the electromagnetic spectrum monitoring equipment is less than or equal to O i The perception radius r i , that is, to identify the 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 device 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 in the mission area, assume that I j , and I i and I j Irrelevant, their 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 in the mission area, it is determined that the electromagnetic spectrum monitoring device set covers the grid point (x, y), then 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 by the area of ​​a single grid Δx×Δy in the task area, so that 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 the 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 optimization of electromagnetic spectrum monitoring network deployment, the sum of displacements of electromagnetic spectrum monitoring equipment is minimized as much as possible. By reducing displacement, the deployment time is shortened to improve 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:

[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 used as 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). The impact on the algorithm operation results and algorithm performance is particularly obvious. At the same time, due to the particularity of each problem when solving each problem, there are also different requirements for the setting of experimental parameters. Therefore, in order to achieve ideal experimental results and ensure the scientificity and accuracy of the solution to the optimization problem of the mobile electromagnetic spectrum monitoring network deployment of the Ministry of Defense, 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, the stronger the search ability is, and 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, so the calculation time is longer and it is not convenient to solve the problem. On the contrary, it is not conducive to the algorithm to obtain the optimal solution. Therefore, in general, the value of the group size is based on the dimension D of the problem space. If it is greater than 4D, the mutation operation can be ensured. 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 premature convergence is avoided due to too small a value. The crossover probability is used to control the degree of information exchange between the offspring and the previous generation and the intermediate mutant individuals, and to balance the local and global search capabilities. 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, thereby affecting 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 the 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 an 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 location coordinates of the electromagnetic spectrum monitoring equipment. Therefore, the location coordinates of the electromagnetic spectrum monitoring equipment are used as the encoding scheme of the chromosome. The deployment scheme of the electromagnetic spectrum monitoring equipment is described by individuals in the population, and the individuals are represented in the form of 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 device can indicate the adjustment of the position of the electromagnetic spectrum monitoring device, thus completing the mapping between the individual space and the problem decision space.

[0103] S1: Initialize the population

[0104] Before the initialization operation, the individuals need to be encoded. The encoding method affects the convergence effect of the algorithm. When using the multi-objective differential evolution algorithm to solve the problem, the algorithm operation efficiency is improved by adopting the real number encoding method. 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 shown in the following formula:

[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 mutation vector formed 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] In the crossover operation, the target vector X is 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 through 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, which is achieved by 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 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 generated by the most recent selection operation is output as the optimal solution; otherwise, it goes to S2 to continue the evolution; the new individual generated 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 operation process of the differential evolution algorithm usually starts with the population initialization operation. An important part of this operation is to clarify the adjustable control parameters and individual fitness evaluation functions that affect the operation process of the differential evolution algorithm. The random generation of the initial population also means the beginning of the algorithm mutation operation. This operation selects the difference vector of two individuals in the initial population, and then forms a mutant individual by summing it with the third individual under weighted rules. In the crossover operation stage, the experimental individual is generated by multi-point crossover through the mutation vector and the selected target vector to provide candidate vectors. In the selection operation stage, the survival of the fittest operation is performed by comparing the fitness evaluation functions of the experimental individual and the target individual, and the vector with better fitness is selected to be retained and introduced into the next generation of evolution, so that the differential evolution process ends.

[0124] In order to evaluate the performance of the proposed electromagnetic spectrum monitoring network regional 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 s 8m, and the transmission radius r of the electromagnetic spectrum monitoring equipment is met 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 t in the optimization process was set to 40. max The parameter is set to 4000. The simulation results of single-objective optimization and multi-objective optimization are analyzed below.

[0126] Figure 2 This is a schematic diagram of the initial network deployment coverage. 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 location and coverage of each electromagnetic spectrum monitoring device in the network are shown in the figure. Figure 2 shown.

[0127] Figure 3 The following is a schematic diagram of network deployment coverage based on the single-objective differential evolution algorithm. In the simulation experiment, the coverage rate 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 area 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 to the coverage blind area. 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 shown in the figure. Figure 3 As shown, its network area coverage has been greatly improved. Figure 4 The schematic diagram of the network area coverage evolution curve based on the single-objective differential evolution algorithm shows the relationship between the electromagnetic spectrum monitoring network area coverage and the number of optimization iterations. Figure 4As shown in Figure 2, 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 network redundant coverage area evolution curve based on the single-objective differential evolution algorithm, Figure 6 is the displacement and evolution curve of the electromagnetic spectrum monitoring equipment based on the single-objective evolutionary algorithm. When only the coverage rate 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 as shown in Figure 2. Figure 5 , Figure 6 shown.

[0130] Figure 7 This is a schematic 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, such as Figure 7 As shown in the figure, under 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 regional coverage rate, redundant coverage area and equipment displacement of the electromagnetic spectrum monitoring network are optimized simultaneously.

[0131] Figure 8 The network area coverage evolution curve based on the multi-objective differential evolution algorithm is verified by verifying the weighted parameters ω1:ω2:ω3=5:3:2 in the above embodiment. When performing multi-objective optimization, the weighted factors of objective functions 1, 2, and 3 are 0.5, 0.3, and 0.2 respectively, and objective function 3 is divided by 1000 to reach the same order of magnitude. The coverage of the electromagnetic spectrum monitoring network deployment area after 4000 iterations of multi-objective optimization is shown in the figure. 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 8 shown.

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

[0133] Fig.11is the weighted index change curve of multi-objective optimization. In the multi-objective optimization process, the weighted comprehensive objective function value changes with the number of iterations as shown in Fig.11 As shown. The simulation results show that in the process of optimizing the deployment of the electromagnetic spectrum monitoring network, the multi-objective differential algorithm can simultaneously take into account the three optimization objectives of the electromagnetic spectrum monitoring network area coverage, equipment displacement and redundant coverage area; in terms of the electromagnetic spectrum monitoring equipment displacement, the equipment displacement based on the single-objective differential evolution algorithm converges to 640, while the equipment displacement based on the multi-objective differential evolution algorithm converges to 753, which is a decrease of 15%; in terms of the redundant coverage area of ​​the electromagnetic spectrum monitoring network, 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; from the above comparison, it can be seen that the multi-objective differential evolution algorithm can improve the regional coverage performance of the electromagnetic spectrum monitoring network while minimizing the moving distance of the electromagnetic spectrum monitoring equipment in the optimization of the regional deployment of the electromagnetic spectrum monitoring network, thereby speeding up the deployment of the electromagnetic spectrum monitoring network and winning precious time to achieve high efficiency in the deployment of the electromagnetic spectrum monitoring network.

[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 the present application is not limited by the described order of actions, because according to the present 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 the present application.

[0135] In the above embodiments, the description of each embodiment has its own emphasis. 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 the scope of the present disclosure cannot be limited thereto. 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 here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, 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 technical field not recorded in the present disclosure. The description and examples are 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 may be arbitrarily combined. 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 protection scope 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 goal of the highest network area coverage, the optimization goal of the minimum displacement of electromagnetic spectrum monitoring equipment, and the optimization goal of the minimum redundant coverage area; Transform the weighted sum of multiple sub-objective functions into a comprehensive objective function; The electromagnetic spectrum monitoring network deployment optimization problem is solved based on the multi-objective differential evolution algorithm, 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, select the target vector and the mutation vector to cross-recombine to form an experimental vector; S4: Compare the fitness evaluation function values ​​of the target vector and the experimental vector, and save the vector with a better fitness evaluation function value; S5: If the maximum number of iterations is reached, execute S6; if the maximum number of iterations is not reached, 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 as claimed in claim 1, wherein: The optimization goal of the highest network area coverage is specifically expressed as: 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 P(I i )express: When the grid point (x, y) is covered by any electromagnetic spectrum monitoring device in the electromagnetic spectrum monitoring device set O in the mission area, it is determined that the electromagnetic spectrum monitoring device set covers the grid point (x, y), and the coverage rate of the electromagnetic spectrum monitoring device set O is recorded as: The task area is divided by the single grid area Δx×Δy in the task area, so that the task area is discretized to form a×b grids. The network area coverage function is:

3. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm as claimed in claim 2, wherein: The optimization goal of minimizing the displacement of the electromagnetic spectrum monitoring equipment is specifically expressed as: 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; 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 as claimed in claim 3, wherein: The optimization target of the minimum redundant coverage area is specifically expressed as: The redundant coverage area function is defined as:

5. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm as claimed in claim 4, wherein: The weighted sum of multiple sub-objective functions is converted into a comprehensive objective function, which is specifically achieved by the following formula: f gof (x)=ω1f1(x)+ω2f2(x)+ω3f3(x) 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.

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 scheme is regarded as an individual in the population, and the individuals are represented as a collection of genomes: G={o1,o2,...,o i },i∈m 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 in the mission area.

7. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm as claimed in claim 1, wherein: The process of population initialization specifically includes: 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: X i,j (0)=L j _ min +rand(0,1)(L j _ max -L j _ min )i=1,2,...m,j=1,2,...n Among them, rand j (0,1) is a random number between 0 and 1.

8. The electromagnetic spectrum monitoring network deployment method based on a multi-objective differential evolution algorithm as claimed in claim 1, wherein: The randomly selected population includes several individuals participating in the mutation operation to form a mutation vector, which specifically includes: 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 mutation vector formed is: H i (t+1)=X p1 (t)+F.(X p2 (t)-X p3 (t)) 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.

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

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

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