Unmanned aerial vehicle deployment method for mobile edge computing system

Abstract

The invention belongs to the technical field of unmanned aerial vehicle deployment, and provides a mobile edge computing system-oriented unmanned aerial vehicle deployment method, which comprises the following steps of: establishing a system model, and evaluating a coverage area of an LAP-UAV (Local Area Point-Unmanned Aerial Vehicle); the system model comprises U LAP-UAVs and a centralized unmanned aerial vehicle controller, the LAP-UAVs hover above a target area, and the centralized unmanned aerial vehicle controller acquires all information of the system so as to make a deployment decision for the LAP-UAVs during operation of the system; aiming at whether the centralized unmanned aerial vehicle controller is available or not, constructing an optimization problem of centralized deployment or distributed deployment, and forming a target function; and solving the objective function to obtain the optimal coordinate of each LAP-UAV. According to the method, the deployment strategy of the LAP-UAV can be effectively optimized, and meanwhile, the cost required for completing the MD calculation task in the heterogeneous network can be reduced in a limited manner through the distributed deployment mode.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle deployment, and particularly to a method for deploying unmanned aerial vehicles for a mobile edge computing system. Background Art

[0002] In recent years, research on deploying unmanned aerial vehicles (UAVs) as aerial base stations has received extensive attention. Due to frequent problems such as network outages, network congestion, and network scarcity, determining the optimal location for deploying UAVs has become one of the problems that must be solved in UAV-assisted mobile edge computing (MEC). This deployment problem is formulated by various objective functions, such as maximizing the wireless coverage area, minimizing the number of UAVs, minimizing power consumption, and maximizing network throughput. Solutions to the problem include meta-heuristic algorithms, deep reinforcement learning, successive convex approximation, etc.

[0003] Deployment algorithms for UAVs can be divided into two categories: centralized algorithms and distributed algorithms. In previous research, most researchers only considered using centralized algorithms to optimize UAV deployment. This approach relies on a central controller that is responsible for collecting all information and making global decisions. The central controller has global information and can achieve optimal deployment; however, the central controller needs to process a large amount of data, resulting in a heavy computational burden. Once the centralized controller fails, global information cannot be obtained for optimization, which may cause the entire system to collapse. Summary of the Invention

[0004] Aiming at the defects in the prior art, the present invention provides a method for deploying unmanned aerial vehicles for a mobile edge computing system to solve the problem that current UAV deployment algorithms only consider using centralized algorithms to optimize UAV deployment and ignore the inability to obtain global information for optimization when the centralized controller fails.

[0005] A method for deploying unmanned aerial vehicles for a mobile edge computing system provided by the present invention includes:

[0006] Establishing a system model and evaluating the coverage area of LAP-UAVs; the system model includes U LAP-UAVs and a centralized UAV controller. The LAP-UAVs hover above the target area, and the centralized UAV controller obtains all information of the system to make deployment decisions for the LAP-UAVs during system operation;

[0007] Constructing an optimization problem for centralized deployment or distributed deployment according to whether the centralized UAV controller is available, and forming an objective function;

[0008] Solving the objective function to obtain the optimal coordinates of each LAP-UAV.

[0009] As can be seen from the above technical solution, for the method for deploying unmanned aerial vehicles provided by the present invention, in view of whether the centralized unmanned aerial vehicle controller is working properly, the unmanned aerial vehicles are deployed by two methods, namely centralized deployment and distributed deployment respectively; it can effectively optimize the deployment strategy of LAP-UAV, and at the same time, the distributed deployment method can limitedly reduce the cost required to complete the MD calculation task in the heterogeneous network.

[0010] Optionally, the evaluating the coverage area of LAP-UAV includes:

[0011] Dividing the target area into several Voronoi polygons according to Voronoi partitioning; each Voronoi polygon contains only one LAP-UAV, and the distance from any vertex of the Voronoi polygon to this LAP-UAV is shorter than the distance from any other LAP-UAV to this LAP-UAV;

[0012] LAP-UAV N i The coverage area of is the Voronoi polygon area within the coverage range of LAP-UAV N i

[0013] Optionally, if the centralized unmanned aerial vehicle controller is available, an optimization problem for centralized deployment is constructed, and an objective function P1 is formed, including:

[0014] Defining the evaluation indexes for centralized deployment, including the MD non-coverage rate coverage non-uniformity task tendency and average distance

[0015] Calculating the index weights of each evaluation index;

[0016] Constructing the objective function The index weights satisfy w1 + w2 + w3 + w4 = 1.

[0017] Optionally, the evaluation indexes for centralized deployment specifically include:

[0018] The MD non-coverage rate

[0019] where represents the number of MDs not covered by LAP-UAV N i where the number of duplicate coverages is excluded, U represents the total number of LAP-UAVs, K represents the total number of MDs, and Num Cover (N i ) represents the number of MDs covered by LAP-UAV N i , and the subscript cen represents centralized deployment;​

[0020] The coverage non-uniformity

[0021] where is the standard deviation of the distances between each LAP-UAV and each vertex in its Voronoi polygon, is for LAP-UAV N i and the standard deviation of the distances between it and the vertices of its Voronoi polygon, is for LAP-UAV N i and the distance between it and the j-th vertex of its Voronoi polygon, k i V is the number of vertices of its Voronoi polygon, is for LAP-UAV N i and the average value of the distances between it and the vertices of its Voronoi polygon;

[0022] The task tendency

[0023] where, MAX[·] represents obtaining the maximum value within the brackets, D i represents the task size of the i-th MD, D max represents the maximum task size among all MDs, represents the distance between the i-th MD and its affiliated BS, represents the coverage radius of the BS to which the i-th MD belongs; D i / D max represents the importance degree that the i-th MD needs to be covered by the UAV. The larger the task size, the larger the ratio, and the more the MD needs to be covered; / is a mitigation of the coverage importance degree. When the i-th MD is closer to its affiliated BS, the ratio is smaller, and the degree to which the MD needs to be covered slows down;

[0024] The average distance

[0025] where, Mean m2l represents the average value of the distances between all MDs within the coverage range of the LAP-UAV and their corresponding LAP-UAVs, represents the minimum average distance Mean in the previous generations of UAV deployment strategies m2l , represents the maximum distance value between the LAP-UAV and its corresponding MD.

[0026] Optionally, the metric weights for centralized deployment are calculated according to the following method, including:

[0027] Calculate the index weights based on the analytic hierarchy process and use the entropy method for correction to obtain the corrected comprehensive weight \(W=(w_1, w_2, w_3, w_4)\).

[0028] Optionally, the solution method for the objective function \(P1\) includes:

[0029] S201. Initialize the population position;

[0030] S202. Use the objective function \(P1\) as the fitness function;

[0031] S203. Calculate the fitness value of each individual and select a best individual \(x\) best (t);

[0032] S204. Calculate the current iteration overall deviation \(e\) k (t), the previous iteration overall deviation \(e\) k-1 (t) and the deviation of the previous two iterations overall \(e\) k-2 (t);

[0033] S205. Calculate the dynamic proportional control coefficient Dynamic integral control coefficient And the dynamic differential control coefficient ;

[0034] S206. Calculate the system control amount \(\Delta u(t)\) at the iteration number \(t\);

[0035] S207. Update the population \(x(t + 1)\);

[0036] S208. After \(T\) PSA / 2 iterations, calculate the coefficient of variation \(\Omega\) PSA , if the coefficient of variation \(\Omega\) PSA < Variation threshold Perform mutation on \(x\) best (t) to obtain

[0037] S209. If the LAP-UAV coordinates in the individual cross the boundary or there are LAP-UAVs with pairwise distances less than the safety threshold , reset the LAP-UAV coordinates using the grid correction method;

[0038] S210. When the iteration number reaches the total iteration number \(T\) PSA , output the best LAP-UAV coordinates determined by the optimal individual and the optimal fitness value; otherwise, return to S203 and enter the next iteration round.

[0039] Optionally, the resetting of the LAP-UAV coordinates using the grid correction method includes:

[0040] S301. Divide the target area into several grid cells with a fixed size;

[0041] S302 Calculate the number of LAP-UAVs and MDs contained in each grid cell;

[0042] S303. Determine whether the coordinates of the LAP-UAVs in each individual are out of bounds, or whether there are LAP-UAVs with pairwise distances less than the safety threshold of the LAP-UAVs; if so, jump to S304, otherwise end;

[0043] S304. Put the LAP-UAVs with out-of-bounds coordinates or the LAP-UAVs with distances less than the safety threshold back into the grid cell with the fewest number of LAP-UAVs and the most number of MDs, and jump to S302 for data update.

[0044] Optionally, if the centralized UAV controller is unavailable, construct an optimization problem for distributed deployment and form the objective function P2, including:

[0045] Define the evaluation metrics for distributed deployment, including the area non-coverage rate and the coverage non-uniformity

[0046] Construct the objective function P2: The metric weights and are constants, satisfying

[0047] Optionally, the area non-coverage rate is the ratio of the sum of the local coverage holes of all LAP-UAVs to the total area,

[0048]

[0049] where S i is the local coverage hole area of the i-th MD, and L 2 represents the area of the target area, and the subscript dis represents distributed deployment.

[0050] Optionally, the solution method of the objective function P2 includes:

[0051] S401. Use the objective function P2 as the fitness function;

[0052] S402. Initialize the population positions;

[0053] S403. Calculate the fitness value of each individual, and select a best individual x best (l);

[0054] S404. Calculate the overall deviation \(e^{(l)}\) of the current iteration, the overall deviation \(e^{(l - 1)}\) of the previous iteration, and the overall deviation \(e^{(l - 2)}\) of the previous two iterations when the number of iterations is \(l\); k (l), the overall deviation \(e\) of the previous iteration k-1 (l) and the overall deviation \(e\) of the previous two iterations k-2 (l);

[0055] S405. Calculate the dynamic proportional control coefficient the dynamic integral control coefficient and the dynamic derivative control coefficient

[0056] S406. Calculate the system control quantity \(\Delta u(l)\) at the iteration number \(l\);

[0057] S407. Update the population \(x(l + 1)\); \(\eta\) is expressed as an \(N\times1\) matrix, Rand6 is an \(N\times1\) matrix with values in the range \([0, 1]\), the element in PSA is the resultant force of all vertices in the set \(V\) of vertices of the Voronoi polygon that the LAP-UAV \(N\) is subjected to, PSA is the resultant force of all adjacent LAP-UAVs that the LAP-UAV \(N\) is subjected to, \(N\) is the size of the population, and \(o(l)\) is the adjustment factor; in is the LAP-UAV \(N\) i subjected to the resultant force of all vertices in the Voronoi polygon vertex set \(V\) i N in; is the LAP-UAV \(N\) i subjected to the resultant force of all its adjacent LAP-UAVs, \(N\) PSA is the size of the population, and \(o(l)\) is the adjustment factor;

[0058] S408. After \(T / 2\) iterations, calculate the coefficient of variation \(\Omega\). If the coefficient of variation \(\Omega\) PSA-D is less than the variation threshold, mutate \(x(l)\) to obtain PSA PSA < the variation threshold mutate \(x(l)\) to obtain best (l);

[0059]

[0059] S409. If there is a LAP-UAV coordinate out of bounds or there are LAP-UAVs with pairwise distances less than the safety threshold among the individuals, reset the LAP-UAV coordinates using the grid correction method;

[0060] S410. When the number of iterations reaches the total number of iterations \(T\) PSA , output the best LAP-UAV coordinates and the optimal fitness value determined by the optimal individual; otherwise, return to S403 and enter the next iteration round.

[0061] Adopting the above technical solutions, the present application has the following beneficial effects:

[0062] A method for deploying unmanned aerial vehicles (UAVs) for a mobile edge computing system provided by the present invention deploys UAVs through two methods, namely centralized deployment and distributed deployment, according to whether the centralized UAV controller is working properly. When the centralized UAV controller is working properly, an objective function including four metrics, namely MD non-coverage rate, coverage uniformity, task preference, and average distance, is defined, and the IPSA algorithm is used to minimize the objective function. When the centralized UAV controller is damaged, an objective function including area non-coverage rate and coverage uniformity as metrics is given, and each LAP-UAV uses the IPSA-D algorithm for optimization separately. By adopting the above method, the deployment strategy of LAP-UAVs can be effectively optimized, and the distributed deployment method can limitedly reduce the cost required to complete MD computing tasks in a heterogeneous network. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0064] Figure 1 Shows a flowchart of a method for deploying unmanned aerial vehicles (UAVs) for a mobile edge computing system provided by an embodiment of the present invention;

[0065] Figure 2 Shows a schematic diagram of a system model provided by an embodiment of the present invention; where (a) is centralized deployment and (b) is distributed deployment;

[0066] Figure 3 Shows a schematic diagram of the coverage range and sensing range of LAP-UAV provided by an embodiment of the present invention;

[0067] Figure 4 Shows a schematic diagram of the Voronoi partition principle provided by an embodiment of the present invention;

[0068] Figure 5 Shows a schematic diagram of the Voronoi partition of a heterogeneous network provided by an embodiment of the present invention;

[0069] Figure 6 Shows a flowchart of the analytic hierarchy process provided by an embodiment of the present invention;

[0070] Figure 7 Shows a schematic diagram of the LAP-UAV deployment hierarchy provided by an embodiment of the present invention;

[0071] Figure 8 Shows a flowchart of the entropy weight method provided by an embodiment of the present invention;

[0072] Figure 9 Shows the flowchart of the grid correction method provided by the embodiments of the present invention;

[0073] Figure 10 Shows the schematic diagram of the virtual force between LAP-UAV and Voronoi vertices provided by the embodiments of the present invention;

[0074] Figure 11 Shows the schematic diagram of the virtual force between LAP-UAVs provided by the embodiments of the present invention;

[0075] Figure 12 Shows the simulation schematic diagram of the centralized deployment of LAP-UAVs provided by the embodiments of the present invention;

[0076] Figure 13 Shows the schematic diagram of the performance comparison of the centralized deployment algorithm of LAP-UAVs provided by the embodiments of the present invention;

[0077] Figure 14 Shows the schematic diagram of the relationship between the performance of the centralized deployment IPSA algorithm of LAP-UAVs and the number of LAP-UAVs provided by the embodiments of the present invention;

[0078] Figure 15 Shows the schematic diagram of the weighted sum performance of the delay and energy consumption of each algorithm for the centralized deployment of LAP-UAVs provided by the embodiments of the present invention;

[0079] Figure 16 Shows the schematic diagram of the influence of the maximum transmission power of the centralized deployment of LAP-UAVs on the weighted sum of time and energy consumption provided by the embodiments of the present invention;

[0080] Figure 17 Shows the schematic diagram of the influence of the number of UAVs in the centralized deployment of LAP-UAVs on the weighted sum of time and energy consumption provided by the embodiments of the present invention;

[0081] Figure 18 Shows the schematic diagram of the convergence curve of a specific distributed deployment algorithm of LAP-UAVs provided by the embodiments of the present invention;

[0082] Figure 19 Shows the simulation schematic diagram of the distributed deployment of LAP-UAVs provided by the embodiments of the present invention;

[0083] Figure 20 Shows the schematic diagram of the convergence curves of each algorithm for the distributed deployment of LAP-UAVs provided by the embodiments of the present invention;

[0084] Figure 21 Shows the schematic diagram of the weighted sum performance of the delay and energy consumption of each algorithm in the distributed deployment of LAP-UAVs provided by the embodiments of the present invention;

[0085] Figure 22 Schematic diagram showing the influence of the LAP-UAV distributed deployment task volume on the weighted sum of time and energy consumption provided by the embodiments of the present invention. Detailed implementation manners

[0086] Hereinafter, embodiments of the technical solutions of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solutions of the present invention more clearly, and thus are only examples and cannot be used to limit the protection scope of the present invention.

[0087] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in this application should be the ordinary meanings understood by those skilled in the art to which the present invention belongs.

[0088] For the convenience of understanding, the PSA algorithm involved in the embodiments of the present invention is explained below:

[0089] PSA (PID-based Search Algorithm) is a metaheuristic algorithm derived from a classical control algorithm, the PID algorithm. The components of PID include proportional control, integral control, and derivative control. By comparing the difference between the expected value and the actual value, and then adjusting the control parameters of the system according to this difference to achieve accurate and stable goals. Among them, the proportional controller considers the difference between the expected set value and the actual value to immediately reduce the error; the integral controller considers the error accumulated over time and corrects the long-term error by continuously integrating the error; the derivative controller considers the rate of change of the error and predicts and buffers the changing trend of the error.

[0090] Assume that the population size of PSA is N PSA , the dimension of the individual is D PSA , its upper and lower bounds are Up PSA and Low PSA respectively, and the total number of iterations is T PSA . The initialization of the population is shown in Equation (A1)

[0091]

[0092] where x ij represents the j-th dimension of the i-th individual, and are the upper and lower bounds of the j-th dimension respectively, and rand represents a random number within [0,1]. The population update formula of PSA is

[0093] x(t + 1) = x(t) + η·Δu(t) + (1 - η)·o(t) (A2) where η is represented as N PSA1×1 matrix

[0094] η PSA = Rand1·cos(t / T PSA )(A3)

[0095] where Rand1 is a 1×1 matrix with values in the range [0,1]. Δu(t) represents the system control variable at iteration t PSA e

[0096]

[0097] e k (t) = x best (t - 1) - x(t - 1) (A5)

[0098] e k-1 (t) = e k (t - 1) + x best (t) - x best (t - 1) (A6)

[0099] e k-2 (t) = e k-1 (t - 1) (A7)

[0100] where Rand2, Rand3, and Rand4 are all 1×1 matrices with values in the range [0,1], PSA and and are the proportional control coefficient, integral control coefficient, and derivative control coefficient respectively. At iteration t, ek(t), e k-1 (t), and e k-2 (t) are the overall deviations at the current iteration, the previous iteration, and the iteration two steps ago respectively, as shown in formulas (A5) - (A6). x best (t) represents the best individual at iteration t. The exploration function of the algorithm is mainly completed by e k (t) - e k-1 (t) and e k (t) - 2e k-1 (t) + e k-2 (t). The exploitation function is mainly completed by e k (t). Therefore, a relatively small value will be assigned to K i PSA . o(t) represents a regulation factor, which has the effect of preventing the algorithm from falling into local optima:

[0101] o(t) = (cos(1 - t / T PSA ) + λ PSA ·Rand5·L PSA )ek (t) (A8)

[0102] λ PSA = [ln(T PSA - t + 2) / ln(T PSA )] 2 (A9)

[0103]

[0104] where Rand5 is an N PSA × 1 matrix with values in the range [0, 1], and λ PSA represents the adjustment coefficient, as shown in formula (A9). In the early stage of the algorithm, the slow decrease of λ PSA helps the full exploration of the algorithm. In the later stage of the algorithm, the rapid decrease of λ PSA makes the algorithm transition into the exploitation stage. L PSA is the Lévy flight function, as shown in formula (A10), where u PSA and v PSA represent N PSA × D PSA matrices of random numbers that conform to the standard normal distribution, and β PSA is a constant.

[0105] In previous UAV deployment studies, most researchers only considered using centralized algorithms to optimize UAV deployment, while ignoring the situation where global information cannot be obtained for optimization when the centralized controller fails. To address this problem, this embodiment provides a UAV deployment method for a mobile edge computing system, as Figure 1 shown, including:

[0106] S101. Establish a system model and evaluate the coverage area of LAP-UAVs; the system model includes U LAP-UAVs and a centralized UAV controller. The LAP-UAVs hover above the target area, and the centralized UAV controller obtains all the information of the system to make deployment decisions for the LAP-UAVs during system operation.

[0107] Consider a two-tier UAV-assisted MEC heterogeneous network system model in an MD-congested environment, as Figure 2As shown in parts (a) and (b), U LAP-UAVs hover above the target area, and there is a centralized drone controller that can obtain all information of the system and is responsible for making deployment decisions for LAP-UAVs during system operation. However, in the case of controller failure resulting in communication interruption with LAP-UAVs, LAP-UAVs can make deployment decisions in a self-organizing manner, and information can be exchanged between each drone through LOS links, but it does not include information related to MD (Mobile Device). Assume that the target area is a square area of size L×L, and at the same time assume that the height of LAP-UAVs is consistent and fixed. The set of LAP-UAVs is represented as where is the 3D position of LAP-UAV N i . In addition, the Euclidean distance between LAP-UAV N i and N j is represented as

[0108]

[0109] The radius of the ground coverage area of LAP-UAV N i can be represented as The radius of the sensing range is represented as LAP-UAVs within the sensing range can exchange information. Generally speaking, the sensing range of drones is greater than the ground coverage range, that is Figure 3 Multiple horizontal cross-sectional views of the coverage range and sensing range of LAP-UAVs are given.

[0110] In step S101, the coverage area of LAP-UAVs is evaluated, specifically including:

[0111] The target area is divided into several Voronoi polygons according to Voronoi partitioning; each Voronoi polygon contains only one LAP-UAV, and the distance from any vertex of the Voronoi polygon to this LAP-UAV is shorter than the distance from any other LAP-UAV to this LAP-UAV;

[0112] Then the coverage area of LAP-UAV N i is the Voronoi polygon area within the coverage range of LAP-UAV N i .

[0113] In this embodiment, to evaluate the area covered by the LAP-UAV in the above heterogeneous network system model, the target area is divided into many sub-regions using Voronoi partitioning. This sub-region is also known as the Thiessen polygon and is formed by the Delaunay triangulation. The Delaunay triangulation consists of multiple triangles, and each vertex in the triangle belongs to the UAV coordinate set. By finding the circumcenter of the circumcircle of the Delaunay triangle, the vertices of the Voronoi polygon for each vertex of the triangle can be obtained, as Figure 4 shown.

[0114] After Voronoi partitioning, each Voronoi polygon contains only one LAP-UAV, and the distance from any vertex of this polygon to the LAP-UAV is shorter than the distance from any other LAP-UAV to this LAP-UAV. For LAP-UAV N i , the area of its corresponding Voronoi polygon is called the local polygon area, which is represented by . The local coverage area of LAP-UAV N i is the local polygon area within the coverage range of LAP-UAV N i , which is represented by . Its local coverage hole is the local polygon area outside the coverage range of LAP-UAV N i , which is represented by .

[0115] Figure 5 An example of the Voronoi partitioning of the LAP-UAV set and the Voronoi polygon of a single LAP-UAV is given. Let V i N = {V1, V2, …, V kiV} be the set of vertices of the Voronoi polygon of LAP-UAV N i , be the number of vertices of this Voronoi polygon. In Figure 5 (b), LAP-UAV N i has 6 Voronoi polygon vertices, that is its vertex set is V i N = {V1, V2, V3, V4, V5, V6}.

[0116] S102. Regarding whether the centralized UAV controller is available, an optimization problem for centralized deployment or distributed deployment is constructed, and an objective function is formed.

[0117] When the centralized UAV controller is operating normally, the performance of the MEC system can be optimized by covering more target areas with a given number of LAP-UAVs. Assuming that all LAP-UAVs have the same coverage range, sensing range, and optimal flight altitude, and there are no high-altitude obstacles, the two-dimensional deployment optimization problem of LAP-UAVs is discussed based on the above conditions.

[0118] If the centralized UAV controller is not damaged, an optimization problem for centralized deployment is constructed, and an objective function P1 is formed, including:

[0119] First, for this optimization problem, evaluation metrics for centralized deployment are defined, including the MD non-coverage rate coverage non-uniformity task tendency and average distance

[0120] 1. MD non-coverage rate

[0121] To effectively evaluate the coverage optimization performance of heterogeneous networks, the MD non-coverage rate is defined as the ratio of the number of MDs not covered by LAP-UAVs to the total number of MDs in the heterogeneous network. The expression is

[0122]

[0123] where represents the number of MDs not covered by LAP-UAV N i after removing the number of duplicate coverages. U represents the total number of LAP-UAVs, K represents the total number of MDs, and Num Cover (N i ) represents the number of MDs covered by LAP-UAV N i . The subscript cen represents centralized deployment.

[0124] 2. Coverage non-uniformity

[0125] Define as the standard deviation of the distances between each LAP-UAV and each vertex in its corresponding Voronoi polygon. This metric can effectively control that each LAP-UAV is in the central area of its Voronoi polygon, reducing the overlapping coverage area of LAP-UAVs.

[0126]

[0127]

[0128]

[0129] Among them, and are the standard deviation and average value of the distance between LAP-UAV N i and the vertices of its Voronoi polygon, respectively. is the distance between LAP-UAV N i and the j-th vertex of its Voronoi polygon. is the number of vertices of its Voronoi polygon. To unify the magnitude range of each index, the coverage non-uniformity is defined and normalized. The expression is

[0130]

[0131] 3. Task Tendency

[0132] In the MEC heterogeneous network constructed in step S101, the MD has limited computing resources and cannot process large tasks in a timely manner. Therefore, drones are added to accelerate the task processing time. However, in the LAP-UAV deployment optimization, there may be a situation where the MD with a small amount of tasks covered by the LAP-UAV consumes less resources for local computing by the MD than for offloading computing. Therefore, the LAP-UAV does not need to cover this MD, but should cover the MD with a large amount of tasks that is not covered.

[0133] Therefore, a utility function is defined to assist the LAP-UAV in covering the MD with large tasks is a negative attribute function, which means that the smaller the value, the better the optimization performance. ranges from (0, 1], and the expression is

[0134]

[0135] Among them, MAX[·] represents obtaining the maximum value within the brackets, D i represents the task size of the i-th MD, and D max represents the maximum task size among all MDs. represents the distance between the i-th MD and its affiliated BS (Base Station), represents the coverage radius of the BS to which the i-th MD belongs; D i / D max represents the importance degree that the i-th MD needs to be covered by the drone. The larger the task size, the larger the ratio, and the more the MD needs to be covered; / is a mitigation of the previous coverage importance degree. When the i-th MD is closer to its affiliated BS, the ratio is smaller, and the degree that the MD needs to be covered slows down; the utility function The MDs that are currently most in need of being covered by drones will be screened out, so as to optimize the LAP-UAV deployment and improve the heterogeneous network performance.

[0136] 4. Average distance

[0137] Next, in the constructed MEC heterogeneous network, the MDs can offload their computing tasks to the LAP-UAVs. Therefore, the transmission distance between the LAP-UAVs and the MDs is a key point affecting the energy consumption and time generated by the transmission tasks. We define a utility function to shorten the distance between the LAP-UAVs and the MDs and enhance the transmission performance. The value range of

[0138]

[0139] is (0, 1], and the expression is m2l where Mean represents the average value of the distances between all MDs within the coverage range of the LAP-UAVs and their corresponding LAP-UAVs, m2l , represents the minimum average distance Mean

[0140] Let the set of MDs belonging to the coverage range of LAP-UAV N i be and their three-dimensional coordinates be represented as Therefore Mean m2l and are calculated as

[0141]

[0142]

[0143]

[0144]

[0145] where MIN[·] represents obtaining the minimum value within the brackets, (Mean l2h )′ and (Mean l2h )″ respectively represent the average distances in the previous generation and the generation before the previous generation of drone deployment strategies, represents the average distance between the i-th LAP-UAV and the MDs it covers. It should be noted that when the i-th LAP-UAV does not cover any MDs, The value of is the distance from the LAP-UAV to its coverage boundary. f4 Cover Same as f3 Cover Likewise, it is a negative attribute function. When Mean l2h and are not equal, a negative attribute value (non-negative value) will be generated.

[0146] For the above four evaluation indicators, different weights are further assigned according to their attributes and importance levels to calculate the index weights of each evaluation indicator.

[0147] Therefore, this embodiment designs a method combining the analytic hierarchy process (AHP) and the entropy weight method: calculating the index weights based on the AHP and using the entropy value method for correction to obtain the corrected comprehensive weight W = (w1, w2, w3, w4).

[0148] The AHP judges the evaluation indicators subjectively according to the experience of experts regarding the evaluation indicators, numerically quantifies the relationship between them through the importance levels between pairwise indicators, and calculates the values of relevant evaluation indicators from multiple criteria. However, its result is easily affected by the subjective factors of experts, leading to certain deviations in the index weights. The entropy weight method can determine more objective weights based on the degree of variation of the evaluation indicators. This method can avoid the deviations caused by subjective factors, but it also has disadvantages. The entropy weight method usually does not consider the correlation between evaluation indicators. If there may be correlations between evaluation indicators, this method may ignore the inherent importance and actual situation of the evaluation indicators, resulting in large deviations in the results. Therefore, combining the AHP and the entropy weight method can complement each other, and the calculation of the index weights for the decision-making objective will be more accurate. Specifically:

[0149] First, use the AHP to preliminarily calculate the index weights, and its process is as Figure 6 shown.

[0150] Step (1): Establish the hierarchical structure. In the scoring mechanism of the AHP, with the optimal LAP-UAV coordinate distribution as the goal, the non-coverage rate, coverage uniformity, task tendency, and average distance are used as evaluation indicators, and its hierarchical structure is as Figure 7 shown.

[0151] Step (2): Construct the judgment matrix. Starting from the goal layer, according to the mutual influence relationship between pairwise indicators, compare the influence degrees of these indicators on the goal layer. Using the expert scoring method, experts score according to their experience using the scale 1 - 9 and construct the judgment matrix A

[0152]

[0153] where, a ijIndicates the ratio of the importance of the i-th indicator to the j-th indicator, a ij =1 / a ji , n=4.

[0154] Step (3): Normalize the judgment matrix and calculate the matrix weight vector. First, calculate the element product B of each row in the judgment matrix i and B i The nth root of As shown in formulas (14) to (15). Then, After normalization, the weight C of the judgment matrix A is finally obtained, as shown in equations (16) to (17):

[0155]

[0156]

[0157]

[0158] C=(c1,c2,…,c n ) (17)

[0159] Step (4): Calculate the maximum eigenvalue λ of the judgment matrix max

[0160]

[0161] Step (5): Consistency test. The consistency test can ensure that the importance of the indicators does not conflict, that is, to test the rationality of the judgment matrix. First, calculate the consistency index CI and consistency ratio CR of the matrix

[0162]

[0163]

[0164] Among them, RI represents the consistency test index, and the value is shown in Table 1. If CR<0.1, it means that the construction of the judgment matrix A is reasonable and the weight W can be used; on the contrary, if CR≥0.1, the judgment matrix A needs to be reconstructed.

[0165] Table 1

[0166] n 1 2 3 4 5 6 7 8 9 RI 0 0 0.52 0.89 1.12 1.26 1.36 1.41 1.46

[0167] Next, the entropy weight method is used to correct the indicator weights. The process is as follows: Figure 8 shown.

[0168] Step (1): Normalize the judgment matrix A. According to formula (21), the normalized matrix is calculated as

[0169]

[0170]

[0171] Step (2): Calculate the proportion of the \(i\)-th sample under each index.

[0172]

[0173] Step (3): Calculate the information entropy \(e\) of each index. j and the information utility value

[0174]

[0175]

[0176] Step (4): Calculate the entropy weight value and the comprehensive weight of each index. First, normalize the information utility value to obtain the weight of each index

[0177]

[0178] Then, multiply the weights calculated by the analytic hierarchy process and the entropy weight method, and perform normalization to obtain the corrected comprehensive weight

[0179] W=(w1, w2, …, w n ) (27)

[0180]

[0181] To optimize the network coverage, two indicators are considered: the uncovered rate and the coverage uniformity. At the same time, to optimize the network performance, two other indicators need to be considered: the task tendency and the average distance. Therefore, the above four indicators are combined to construct an objective function to optimize the position of the LAP-UAV cluster N. Therefore, the above four indicators are combined to construct an objective function to optimize the position of the LAP-UAV cluster, and then the objective function is constructed

[0182]

[0183] s.t. 0 ≤ x i LU ≤ L i = 1, 2, …, U (30)

[0184]

[0185]

[0186] s.t. w1 + w2 + w3 + w4 = 1 (33)

[0187] Among them, formulas (30) and (31) represent the horizontal coordinates of the LAP-UAVs within the square area of L×L; formula (32) represents the distance between every two LAP-UAVs must not be less than the safety distance Formula (33) indicates that the sum of the weights of all indicators must be equal to 1, and the weight values are obtained from formula (27).

[0188] If the centralized UAV controller is damaged, an optimization problem for distributed deployment is constructed, and the objective function P2 is formed. In the case of the damage of the centralized UAV controller, a given number of LAP-UAVs can be used to cover more target areas. Since each LAP-UAV is distributed, it cannot actively obtain its own position information and task information relative to the MD. Therefore, for the two-dimensional deployment optimization problem of LAP-UAVs, the two evaluation indicators of task preference and average distance will no longer be considered, and two new evaluation indicators are defined to construct the optimization objective.

[0189] 1. Area non-coverage rate

[0190] Since each LAP-UAV can only utilize the local information of itself and the surrounding UAVs and cannot obtain any information about the MD, in this embodiment, the "MD non-coverage rate" is changed to the "area non-coverage rate". And the area non-coverage rate is the ratio of the sum of the local coverage holes of all LAP-UAVs to the total area

[0191]

[0192] where S i is the local coverage hole area of the i-th MD. The subscript dis represents distributed deployment.

[0193] 2. Coverage non-uniformity

[0194] The coverage non-uniformity used here is consistent with formula (6). For the case of the failure of the centralized UAV deployment controller, in order to optimize the network coverage, the area non-coverage rate and the coverage non-uniformity are used as evaluation indicators to optimize the positions of the LAP-UAV cluster N. Then the objective function P2 is constructed as:

[0195]

[0196]

[0197] (30)~(32)(37)

[0198] Among them, formula (36) indicates that the sum of the weights of the two evaluation indicators is equal to 1, and the remaining constraint conditions remain unchanged, as shown in formulas (30) to (32). Since there are only two evaluation indicators in the objective function, in this embodiment, they are defined as two constants:

[0199] S103. Solve the objective function to obtain the optimal coordinates of each LAP-UAV.

[0200] In one embodiment, for the centralized UAV deployment method, this embodiment considers using the PSA algorithm to solve the objective function P1, and at the same time optimizes the PSA algorithm to enhance the algorithm performance. The solution method of the objective function P1 includes:

[0201] S201. Initialize the population position;

[0202] S202. Take the objective function P1 as the fitness function;

[0203] S203. Calculate the fitness value of each individual, and select a best individual x best (t);

[0204] S204. Calculate the current iteration total deviation e k at iteration t, the previous iteration total deviation e k-1 and the previous two iteration total deviation e k-2 (t);

[0205] S205. Calculate the dynamic proportional control coefficient the dynamic integral control coefficient and the dynamic differential control coefficient

[0206] S206. Calculate the system control amount Δu(t) at iteration t;

[0207] S207. Update the population x(t + 1);

[0208] S208. After T PSA / 2 iterations, calculate the mutation coefficient Ω PSA , if the mutation coefficient Ω PSA < the mutation threshold Mutate x best (t) to obtain

[0209] S209. If the coordinates of the LAP-UAV in the individual cross the boundary or there are LAP-UAVs with pairwise distances less than the safety threshold , use the grid correction method to reset the LAP-UAV coordinates;

[0210] S210. When the number of iterations reaches the total number of iterations T PSA , output the best LAP-UAV coordinates determined by the optimal individual and the optimal fitness value; otherwise, return to S203 to enter the next iteration round.

[0211] In this embodiment, the objective function P1 is used as the fitness function f. The smaller the fitness value, the better the deployment strategy.

[0212]

[0213] The PSA algorithm includes a proportional control coefficient an integral control coefficient and a differential control coefficient According to formula (26) and the basic principle of PID, it can be known that the exploration ability of the PSA algorithm is related to and is related, and the development ability is related to Therefore, it is considered to change the values of these three coefficients from constants to linear dynamic values, where and will linearly decrease with the increase of the number of cycles, will linearly increase with the increase of the number of cycles. The PSA algorithm will conduct a large-scale exploration in the early stage and improve the local development ability in the later stage. The formulas for the dynamic proportional control coefficient, integral control coefficient, and differential control coefficient are as follows:

[0214]

[0215]

[0216]

[0217] Among them, and respectively represent the maximum values of the proportional control coefficient, dynamic integral control coefficient, and dynamic differential control coefficient, and respectively represent the minimum values of the proportional control coefficient, integral control coefficient, and differential control coefficient, and t PSA represents the current iteration number of the algorithm.

[0218] To avoid the problem that the PSA algorithm falls into local optimum, an improved differential mutation strategy is proposed, and its structure adopts the structure of the discrete differential mutation strategy. Mutate x best (t) to generate a new position and increase the probability of jumping out of the local optimum. PSA has good exploration ability in the early stage. To avoid affecting the guiding effect of x best (t) in the early stage, it is decided that after the algorithm has carried out T PSAMutate it after the 2nd iteration. First, calculate the coefficient of variation Ω for x(t) in the adjacent five cycles best (t). PSA

[0219]

[0220] where represents the optimal fitness of the i-th cycle, represents the average value of the optimal fitness of the adjacent five cycles

[0221]

[0222] The coefficient of variation Ω PSA is compared with the mutation threshold . When , x best (t) mutates, otherwise it remains unchanged. The mutation formula of x best (t) is as follows

[0223]

[0224] where Q represents the scale coefficient, and represent the random individuals in the t-th cycle.

[0225] The LAP-UAVs are deployed in an L×L square space. During the process of the PSA algorithm searching for the best deployment position, there is a probability that the coordinates of the LAP-UAVs go out of bounds or the LAP-UAVs are closely dependent on each other. For the problem of out-of-bounds coordinates, the PSA algorithm originally replaces the out-of-bounds coordinates with a random coordinate in the space, but the disadvantage is that it cannot guarantee that the replaced coordinate can avoid being closely dependent on other LAP-UAVs, and using random coordinates cannot accelerate the convergence speed of the algorithm. To address the above problems, we use the grid correction method to correct the coordinates of the out-of-bounds LAP-UAVs according to the density of the UAV distribution and separate the closely connected LAP-UAVs.

[0226] In one embodiment, the method for solving the objective function P1 includes:

[0227] S201. Initialize the population position;

[0228] S202. Use the objective function P1 as the fitness function;

[0229] S203. Calculate the fitness value of each individual and select a best individual x best (t) from the population;

[0230] S204. Calculate the current iteration total deviation e at iteration t k(t), the overall deviation e of the previous iteration k-1 (t) and the overall deviation e of the previous two iterations k-2 (t);

[0231] S205. Calculate the dynamic proportional control coefficient The dynamic integral control coefficient and the dynamic derivative control coefficient

[0232] S206. Calculate the system control quantity Δu(t) at the iteration number t;

[0233] S207. Update the population x(t + 1);

[0234] S208. After T / 2 PSA iterations, calculate the mutation coefficient Ω PSA , if the mutation coefficient Ω PSA < the mutation threshold Perform mutation on x best (t) to obtain

[0235] S209. If the coordinates of the LAP-UAV in the individual cross the boundary or there are LAP-UAVs with pairwise distances less than the safety threshold , use the grid correction method to reset the coordinates of the LAP-UAV;

[0236] S210. When the iteration number reaches the total iteration number T PSA , output the best LAP-UAV coordinates and the optimal fitness value determined by the optimal individual; otherwise, return to S203 and enter the next iteration round.

[0237] In summary, the pseudocode of the solution method for the objective function P1 is shown in Algorithm 1.

[0238]

[0239] The process of the grid correction method is as Figure 9 shown and includes the following steps:

[0240] S301. Divide the target area into several grid cells of fixed size;

[0241] S302 Calculate the number of LAP-UAVs and MDs contained in each grid cell;

[0242] S303. Judge whether the coordinates of the LAP-UAV in each individual cross the boundary, or whether there are LAP-UAVs with pairwise distances less than the safety threshold ; if so, jump to S304, otherwise end;

[0243] S304. Re-put the LAP-UAV with out-of-bounds coordinates or the LAP-UAV with a distance less than the safety threshold into the grid cell with the fewest LAP-UAVs and the most MDs, and jump to S302 for data update.

[0244] When using the improved PSA algorithm (Improved PSA, IPSA) to solve the problem, the candidate solutions of the problem are abstracted as individuals, that is the optimal individual outputs the optimal solution of the objective function.

[0245] In one embodiment, for the case where the centralized satellite controller fails, a distributed UAV deployment algorithm based on IPSA-D is proposed, and the IPSA-D algorithm is used to solve the objective function P2. Similarly, in order to enhance the algorithm performance, the virtual force strategy is used for optimization in the distributed manner.

[0246] Virtual forces are used to simulate the forces and interactions between objects. Past research usually divides virtual forces into three types, namely the attractive and repulsive forces between nodes, and the repulsive force of the regional boundary on nodes. The optimization focus of the distributed UAV deployment algorithm is that each UAV can obtain the optimal fitness value more quickly by using the IPSA-D algorithm. Therefore, considering the attractive force i generated by the vertex of the Voronoi polygon and the LAP-UAV N inside the polygon i and the attractive force between the LAP-UAV N and its neighboring LAP-UAVs i Therefore, the virtual force received by the LAP-UAV N is the resultant force of and and moves effectively according to the magnitude and direction of the resultant force . By establishing the virtual force model of the LAP-UAV and deploying the LAP-UAV according to the force balance, the convergence speed of the IPSA-D algorithm can be effectively accelerated.

[0247] Assume that the planar coordinates of the LAP-UAV N i are and the set of vertices of the Voronoi polygon to which it belongs is V i N , and each vertex generates an attractive force on the LAP-UAV N i . Therefore, the LAP-UAV N i generates an attractive force with k i V vertices. Assume that the vertex V j of the Voronoi polygon ∈ V iN The planar coordinates of Then its distance from LAP-UAV N i can be expressed as

[0248]

[0249] LAP-UAV N i The attraction to vertex V j is The resultant force it receives from all vertices in the vertex set V i N is

[0250]

[0251]

[0252] Among them, 0 < ξ v2n < 1 represents the attraction weight between the LAP-UAV and the vertex, represents the vector direction of the attraction force, and the vector direction is from LAP-UAV N i to vertex V j .

[0253] For example Figure 10 as shown, LAP-UAV N i has 5 Voronoi polygon vertices V1, V2, V3, V4, V5. Therefore, the resultant force received by LAP-UAVN i from all vertices is

[0254] Given that the sensing range of LAP-UAV N i is R i p , the set of neighboring LAP-UAVs within its sensing range is where k Ni is the number of neighboring UAVs. Assume that the distance threshold d th

[0255]

[0256] where 0 ≤ η ≤ 2 is the distance threshold coefficient.

[0257] When , the neighboring LAP-UAV N j ′ and LAP-UAV N i generate an attraction force, causing the two UAVs to move away from each other to obtain a larger coverage area; otherwise, when When there is no virtual force generated between LAP-UAVs. LAP-UAV N i is subjected to N j ′s attraction force as and the resultant force from all its neighboring LAP-UAVs is

[0258]

[0259]

[0260] where 0 < θ n2n <1 represents the attraction weight between LAP-UAVs, represents the vector direction of the attraction force, which is from LAP-UAV N i pointing to LAP-UAV N j ′.

[0261] For example Figure 11 as shown, neighboring LAP-UAVs N1′, N2′, N3′ are all within the sensing range R i of LAP-UAV N i p . N1′ and N2′ are outside the distance threshold d i of N th , so they can both generate attraction forces on LAP-UAV N i , which are respectively represented as and while N3′ is within the distance threshold d th , so it does not generate an attraction force with LAP-UAV N i . Therefore, the resultant attraction force received by LAP-UAV N i is

[0262] LAP-UAV N i will simultaneously be subjected to a virtual force of and resultant force

[0263]

[0264] Update the individual positions in the IPSA-D algorithm through the virtual forces received by each LAP-UAV to enhance the effect of optimizing the LAP-UAV deployment

[0265]

[0266] where Rand6 is an N with a value range of [0, 1] PSARow 1 column matrix.

[0267] In the process of the IPSA-D algorithm, each LAP-UAV first broadcasts its local information and receives the information of surrounding LAP-UAVs to update its local information; then, each LAP-UAV updates its position according to the IPSA algorithm, with an iteration period of 50, and calculates the local coverage area and local coverage holes waiting to be solved through Voronoi partition information. Finally, an optimal deployment strategy in one operation cycle is obtained, and the next cycle continues to run. After running T PSA-D cycles, the optimal deployment strategy is obtained.

[0268] In one embodiment, the solution method of the objective function P2 includes:

[0269] S401. Take the objective function P2 as the fitness function;

[0270] S402. Initialize the population position;

[0271] S403. Calculate the fitness value of each individual, and select a best individual x best (l);

[0272] S404. Calculate the overall deviation e k (l) of the current iteration, the overall deviation e k-1 (l) of the previous iteration, and the overall deviation e k-2 (l) of the previous two iterations;

[0273] S405. Calculate the dynamic proportional control coefficient dynamic integral control coefficient and dynamic differential control coefficient

[0274] S406. Calculate the system control quantity Δu(l) at the iteration number l;

[0275] S407. Update the population x(l + 1); η is expressed as an N PSA row 1 column matrix, Rand6 is an N with a value range of [0, 1] PSA row 1 column matrix, The element in is the resultant force of all vertices of the LAP-UAV N i affected by the set of vertices V of the Voronoi polygon i N in all vertices, is the resultant force of the LAP-UAV N i affected by all its neighboring LAP-UAVs, N PSAis the size of the population, and o(l) is the adjustment factor;

[0276] S408. At T PSA-D / 2 iterations, calculate the coefficient of variation Ω PSA , if the coefficient of variation Ω PSA <mutation threshold Perform mutation on x best (l) to obtain

[0277] S409. If there is an out-of-bounds LAP-UAV coordinate in the individual or there are LAP-UAVs with pairwise distances less than the safety threshold reset the LAP-UAV coordinates using the grid correction method;

[0278] S410. When the number of iterations reaches the total number of iterations T PSA-D , output the best LAP-UAV coordinates determined by the optimal individual and the optimal fitness value; otherwise, return to S403 to enter the next iteration round.

[0279] In summary, the pseudocode of the solution method for the objective function P2 is shown in Algorithm 2.

[0280]

[0281]

[0282] The method provided in this embodiment is simulated as follows. The simulation is carried out on a computer equipped with an AMD Ryzen 9 7945HX processor and 16.00G RAM. The algorithm research on the deployment of LAP-UAVs in heterogeneous networks is carried out on the MATLAB 2021b platform, and at the same time, the optimal deployment scheme of LAP-UAVs is adopted to simulate the performance optimization of heterogeneous networks. In the simulation, the initial positions of LAP-UAVs of the same type are determined by random deployment, and the deployment area is a square area with a side length L = 360m.

[0283] For the case where the centralized UAV deployment controller is not damaged, the weights of its various indicators are first calculated by the analytic hierarchy process and then corrected by the entropy weight method to obtain the final values, as shown in Table 2.

[0284] Table 2 Weights of evaluation indicators

[0285] Evaluation Index Information Entropy Information Utility Value Entropy Weight Index Weight Corrected Weight MD Uncoverage Rate 0.096 0.904 0.325 0.714 0.779 Coverage Uniformity 0.277 0.723 0.260 0.117 0.102 Task Tendency 0.414 0.586 0.210 0.099 0.070 Average Distance 0.429 0.571 0.205 0.070 0.049

[0286] The system simulation parameters are shown in Table 3.

[0287] Table 3 Simulation parameters

[0288]

[0289] For the proposed LAP-UAV deployment algorithm, performance metrics including the objective function value, area coverage rate, MD coverage rate, and coverage uniformity are used for evaluation. At the same time, the ABC algorithm, HHO (Harris Hawk Optimization) algorithm, SHO (Seahorse Optimization Algorithm) algorithm, SOA (Seagull Optimization Algorithm) algorithm are compared with the IPSA algorithm and the IPSA-D algorithm. To reduce the impact of the randomness of simulation experiments on the algorithm performance, the proposed algorithm and the comparative algorithms are independently run 20 times in the same experimental environment, and the average value is taken as the evaluation index.

[0290] The following is the simulation analysis of centralized deployment. The initial random deployment of LAP-UAVs is as Figure 12 shown in part (a). The number of LAP-UAVs is 20. Figure 12 In it, the blue circles represent the coverage range of the UAVs, and the red centers in the circles represent the deployment positions of the LAP-UAVs. It can be seen that there are many coverage holes and overlapping areas in the target area, and the distribution is very uneven, interfering with the entire ground coverage area. After executing IPSA, the final deployment is as Figure 12 shown in part (b). It can be seen that the coverage of the LAP-UAVs for the target area is quite uniform, and the coverage area has been greatly improved.

[0291] Figure 13 Part (a) shows the convergence curves of the IPSA algorithm and the comparative algorithms with respect to the objective function f. The number of LAP-UAVs is 20. It can be observed that the IPSA algorithm reaches convergence first, the SOA algorithm converges after about 420 iterations, the HHO algorithm converges after about 500 iterations, and the SHO algorithm converges last. In addition, the objective function values obtained by the IPSA algorithm after convergence are better than those of the SOA, HHO, and SHO algorithms. Figure 13 Parts (b) and (c) show the bar charts of coverage uniformity and MD coverage rate respectively. The IPSA algorithm obtains the minimum coverage uniformity and the maximum MD coverage rate, and their values are 0.97 and 9.67 respectively. It should be noted that during the algorithm optimization process, since the objective function of centralized control deployment does not include the area coverage rate index, the change of the area coverage rate is irregular.

[0292] Figure 14Show the influence of different numbers of LAP-UAVs on the IPSA algorithm, including the curve changes of the objective function value, area coverage rate, MD coverage rate, and coverage uniformity. It can be observed that as the number of LAP-UAVs increases, the objective function value decreases, the area coverage rate and MD coverage rate increase, and the coverage uniformity first decreases and then increases. In addition, the downward trend of the objective function value slows down after 25 LAP-UAVs, while the MD coverage rate is the opposite. When the number of LAP-UAVs is 30, the coverage uniformity is the smallest.

[0293] We study that optimizing the LAP-UAV deployment scheme can optimize the performance of heterogeneous networks and reduce the cost required to complete the computing tasks of all MDs. Therefore, considering 70 MDs, 20 LAP-UAVs, 1 HAP-UAV in the target area, and the remaining parameters are shown in Table 3.

[0294] Figure 15 Show the performance comparison of the LAP-UAV deployment scheme obtained for the IPSA algorithm with the COIBPSO-IAOS algorithm and the benchmark algorithm, with the task size D k ∈[10,50] Mbit, the maximum transmit power p max = 26 dBm, and the number of cycles required per bit is C k = C s = C u = C h = 1000 cycles / bit. It can be observed that the weighted sum of delay and energy consumption obtained by the COIBPSO-IAOS algorithm is the smallest, and the value obtained by the Random-AOS algorithm is the largest because of its excessive randomness.

[0295] Compared with the weighted sum of delay and energy consumption after convergence in the existing ones, it can be found that the difference between the benchmark algorithm and the COIBPSO-IAOS algorithm has become larger. This is because the increase in the number of MDs leads to an increase in the cost of completing MD computing tasks, and at the same time, it is also because the search performance of the benchmark algorithm is far inferior to that of the COIBPSO-IAOS algorithm. In addition, the performance of the COVPSO-AOS algorithm is not as good as that shown in the existing technology. Therefore, when facing variables with a large number of computing dimensions, the use of the VPSO algorithm should be reduced.

[0296] For the LAP-UAV deployment schemes obtained by the IPSA algorithm, SOA algorithm, HHO algorithm, SHO algorithm, and random initialization, use the existing COIBPSO-IAOS algorithm to compare and analyze the weighted sum of time and energy consumption under different maximum transmit powers of MDs. The maximum transmit power p max ∈[21,26] dBm, and the remaining parameters remain unchanged, as Figure 16As shown in the figure. It can be observed that the weighted sum of time and energy consumption obtained by all deployment schemes decreases with the increase of the maximum transmission power of the MD. The LAP-UAV deployment scheme obtained by the IPSA algorithm shows the optimal performance in optimizing the weighted sum of time and energy consumption, and the weighted sum of time and energy consumption obtained at each maximum transmission power is the smallest. In addition, with the increase of the maximum transmission power, the difference between the weighted sum of time and energy consumption obtained by the LAP-UAV deployment scheme based on the IPSA algorithm and the LAP-UAV deployment scheme based on other algorithms becomes larger and larger.

[0297] Figure 17 shows a comparative analysis of the weighted sum of time and energy consumption under different numbers of LAP-UAV deployment schemes. The LAP-UAV deployment schemes are obtained by using the IPSA algorithm and random initialization respectively, and the weighted sum of time and energy consumption is obtained by the COIBPSO-IAOS algorithm. The maximum transmission power p max = 26 dBm, and the other parameters remain unchanged. It can be observed that the cost optimization effect of the heterogeneous network by the LAP-UAV deployment scheme based on the IPSA algorithm weakens with the increase of the number of UAVs. This is because the increase of LAP-UAVs can reduce the number of uncovered MDs, and more MDs can offload their computing tasks. When the number of LAP-UAVs is 30 and 35, all MDs have been covered by LAP-UAVs. At this time, because the maximum offloading quantity received by each LAP-UAV is limited, there are some MDs within the coverage range of certain LAP-UAVs that cannot offload tasks. And because the increased LAP-UAVs overlap with the coverage of some LAP-UAVs, the MDs with the above situation can offload tasks, thus continuing to optimize the cost of the computing tasks in the heterogeneous network.

[0298] The following is the simulation analysis of distributed deployment. Now, select the LAP-UAV with horizontal coordinates (38.54, 151.55) for optimal deployment. The 5 vertices of its Voronoi polygons are located at (69.41, 110.47), (78.03, 175.75), (57.84, 195.58), (0, 94.22) and (0, 193.89). Figure 18 shows the area non-coverage rate obtained by deploying a specific LAP-UAV using the IPSA-D algorithm and the comparison algorithms. The local area non-coverage rate of this LAP-UAV decreases with the increase of the cycle. The convergence speed of the IPSA-D algorithm is significantly faster than that of the SOA algorithm, HHO algorithm and SHO algorithm. When the number of cycles is 15, the IPSA-D algorithm reaches convergence.

[0299] The initial random deployment of LAP-UAVs is as Figure 19As shown in part (a), many coverage holes and overlapping areas can be seen in the target area, interfering with the entire ground coverage area. After executing the IPSA-D algorithm, the global area coverage rate increases as the local coverage holes of each LAP-UAV decrease, as shown in Figure 19 parts (b) and (c). After optimizing for 100 cycles, the final LAP-UAV deployment is as shown in Figure 19 part (d). The deployment of LAP-UAVs is quite uniform, and the total coverage area is greatly improved. This proves that the IPSA-D algorithm proposed in this embodiment also has excellent performance in the case of the failure of the centralized UAV deployment controller.

[0300] Figure 20 Shows the convergence curves of the IPSA-D algorithm and the comparison algorithms with respect to the objective function f. The number of LAP-UAVs is 20. It can be observed that the IPSA-D algorithm reaches convergence first, the SOA algorithm and the HHO algorithm converge after about 68 iterations, and the SHO algorithm converges after about 80 iterations. In addition, the objective function value of the IPSA-D algorithm is the best after convergence.

[0301] Now, bring the LAP-UAV optimized deployment scheme into the heterogeneous network constructed by the existing technology. Considering that there are 70 MDs, 20 LAP-UAVs, and 1 HAP-UAV in the target area, and the other parameters are shown in Table 3.

[0302] Figure 21 Shows the LAP-UAV deployment scheme obtained for the IPSA-D algorithm. The weighted sum of time and energy consumption is compared with that of the COIBPSO-IAOS algorithm and the benchmark algorithm. The task size D k ∈[10,50] Mbit, the maximum transmit power p max = 26 dBm, and the number of cycles required per bit is C k = C s = C u = C h = 1000 cycles / bit.

[0303] Compared with the results in Figure 15 , it can be found that the weighted sum of time and energy consumption calculated by the LAP-UAV deployment scheme obtained using the IPSA-D algorithm is larger than that calculated by the LAP-UAV deployment scheme obtained using the IPSA algorithm. This is because the objective function of the ISPA-D algorithm is the weighted sum of the area coverage rate and the coverage uniformity. The increase in the area coverage rate does not mean that the MDs are effectively covered, resulting in a small MD coverage rate, so there are more MDs that cannot offload computing tasks. In addition, the performance of the COVPSO-AOS algorithm is similar to that in Figure 15 , and its performance is not the best.

[0304] For the LAP-UAV deployment schemes obtained by the IPSA-D algorithm, the SOA algorithm, the HHO algorithm, the SHO algorithm, and random initialization, the weighted sum of time and energy consumption is compared and analyzed using the COIBPSO-IAOS algorithm in the prior art under different MD maximum task sizes. The maximum task size varies between 50 Mbit and 150 Mbit, and the other parameters remain unchanged, as Figure 22 shown. It can be observed that the weighted sum of time and energy consumption obtained by all deployment schemes increases with the increase of the MD task size. In the face of different task sizes, the LAP-UAV deployment scheme obtained by the IPSA-D algorithm can always calculate the optimal weighted sum of time and energy consumption. In addition, the difference between the weighted sum of time and energy consumption calculated by the LAP-UAV deployment scheme obtained by the IPSA-D algorithm and the weighted sum of time and energy consumption calculated by the LAP-UAV deployment scheme obtained by the comparative algorithm is not large. This is also because the objective function of distributed deployment mainly optimizes the area coverage rate rather than the MD coverage rate.

[0305] A LAP-UAV deployment algorithm based on the PSA algorithm is proposed under the heterogeneous network model, including the IPSA algorithm and the IPSA-D algorithm, aiming to calculate the optimal deployment of LAP-UAV in the target area. When the centralized UAV controller works normally, an objective function including four indicators of MD non-coverage rate, coverage uniformity, task preference, and average distance is defined, and the IPSA algorithm is used to minimize the objective function.

[0306] When the centralized UAV controller is damaged, an objective function P2 including the area non-coverage rate and coverage uniformity as indicators is given, and each LAP-UAV uses the IPSA-D algorithm alone for optimization. The simulation results show that both the IPSA algorithm and the ISPA-D algorithm have excellent performance, can effectively optimize the deployment strategy of LAP-UAV, and at the same time, the distributed deployment method can limitedly reduce the cost required to complete the MD calculation task in the heterogeneous network.

[0307] The above-described embodiments only represent several implementation manners of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A method for deploying unmanned aerial vehicles in a mobile edge computing system, characterized in that Including: Establish a system model to evaluate the coverage area of LAP-UAVs; The system model includes U LAP-UAVs and a centralized UAV controller. The LAP-UAVs hover above the target area, and the centralized UAV controller obtains all information of the system to make deployment decisions for the LAP-UAVs during system operation; Regarding whether the centralized UAV controller is available, construct an optimization problem for centralized deployment or distributed deployment and form an objective function; Solve the objective function to obtain the optimal coordinates of each LAP-UAV.

2. The method according to claim 1, characterized in that, The evaluation of the coverage area of LAP-UAVs includes: Divide the target area into several Voronoi polygons according to Voronoi partitioning; each Voronoi polygon contains only one LAP-UAV, and the distance from any vertex of the Voronoi polygon to this LAP-UAV is shorter than the distance from any other LAP-UAV to this LAP-UAV; Coverage area of LAP-UAV N i is the coverage area of LAP-UAV N i and the Voronoi polygon area within the coverage range.

3. The method according to claim 2, wherein If the centralized UAV controller is available, construct an optimization problem for centralized deployment and form an objective function P1, including: Define the evaluation metrics for centralized deployment, including the MD non-coverage rate Coverage non-uniformity Task tendency and average distance Calculate the index weights of each evaluation index; Construct the objective function The index weights satisfy w1 + w2 + w3 + w4 = 1.

4. The method according to claim 3, wherein The evaluation indexes for centralized deployment specifically include: The MD non-coverage rate Among them represents the number of MDs not covered by LAP-UAV N i where the number of duplicates is excluded. U represents the total number of LAP-UAVs, K represents the total number of MDs, and Num Cover (N i ) represents the number of MDs covered by LAP-UAV N i with the subscript cen indicating centralized deployment; The coverage non-uniformity where is the standard deviation of the distances between each LAP-UAV and each vertex in its Voronoi polygon, is the standard deviation of the distances between LAP-UAV N i and the vertices of its Voronoi polygon, is the distance between LAP-UAV N i and the j-th vertex of its Voronoi polygon, is the number of vertices of its Voronoi polygon, is the average value of the distances between LAP-UAV N i and the vertices of its Voronoi polygon; The task tendency Among them, MAX[·] represents obtaining the maximum value within the brackets, D i represents the task size of the i-th MD, D max represents the maximum task size among all MDs, represents the distance between the i-th MD and its affiliated BS, represents the coverage radius of the BS to which the i-th MD belongs; D i / D max represents the degree of importance that the i-th MD needs to be covered by the UAV. The larger the task size, the larger the ratio, and the more the MD needs to be covered; is a mitigation of the importance of coverage. When the i-th MD is closer to its affiliated BS, the ratio is smaller, and the degree to which the MD needs to be covered slows down; The average distance Among them, Mean m2l represents the average distance between all MDs within the coverage of LAP-UAV and their corresponding LAP-UAVs, represents the minimum average distance Mean among the drone deployment strategies of all previous generations m2l , represents the maximum distance value between the LAP-UAV and its corresponding MD.

5. The method according to claim 4, characterized in that, The index weights for centralized deployment are calculated according to the following method, including: Calculate the index weights based on the analytic hierarchy process and use the entropy method for correction to obtain the corrected comprehensive weight W = (w1, w2, w3, w4).

6. The method according to claim 4, wherein The solution method for the objective function P1 includes: S201. Initialize the population position; S202. Use the objective function P1 as the fitness function; S203. Calculate the fitness value of each individual and select a best individual x best (t); S204. Calculate the current iteration overall deviation e at iteration number t k (t), the previous iteration overall deviation e k-1 (t), and the overall deviation of the two previous iterations e k-2 (t); S205. Calculate the dynamic proportional control coefficient Dynamic integral control coefficient and dynamic derivative control coefficient S206. Calculate the system control quantity Δu(t) at the iteration number t; S207. Update the population x(t + 1); S208. At T PSA After the 2nd iteration, calculate the coefficient of variation Ω PSA , if the coefficient of variation For x best (t) is mutated to obtain S209. If there is a LAP-UAV in the individual whose coordinates exceed the boundary or there are LAP-UAVs with pairwise distances less than the safety threshold reset the LAP-UAV coordinates using the grid correction method; S210. When the number of iterations reaches the total number of iterations T PSA Output the best LAP-UAV coordinates and the optimal fitness value determined by the optimal individual; otherwise, return to S203 and enter the next iteration round.

7. The method according to claim 6, characterized in that The resetting of the LAP-UAV coordinates using the grid correction method includes: S301. Divide the target area into several grid cells of fixed size; S302. Calculate the number of LAP-UAVs and MDs contained in each grid cell; S303. Determine whether the LAP-UAV coordinates in each individual exceed the boundary, or whether there are LAP-UAVs with pairwise distances less than the safety threshold ; if so, jump to S304, otherwise end; S304. Re-put the LAP-UAV with out-of-bounds coordinates or the LAP-UAV with a distance less than the safety threshold into the grid cell with the fewest LAP-UAVs and the most MDs, and jump to S302 for data update.

8. The method according to claim 7, wherein If the centralized UAV controller is not available, construct an optimization problem for distributed deployment and form an objective function P2, including: Define the evaluation metrics for distributed deployment, including the area non-coverage rate and the coverage non-uniformity Construct the objective function Index weight and are constants and satisfy 9. The method according to claim 8, wherein The area non-coverage rate is the ratio of the sum of the local coverage holes of all LAP-UAVs to the total area. Among them, S i is the area of the local coverage hole of the i-th MD, and L 2 represents the area of the target region, and the subscript dis indicates distributed deployment.

10. The method according to claim 9, characterized in that The solution method for the objective function P2 includes: S401. Use the objective function P2 as the fitness function; S402. Initialize the population position; S403. Calculate the fitness value of each individual and select a best individual x from the population best (l); S404. Calculate the overall deviation e of the current iteration when the number of iterations is l k (l), the overall deviation e of the previous iteration k-1 (l) and the overall deviation e of the iteration two times before k-2 (l); S405. Calculate the dynamic proportional control coefficient Dynamic integral control coefficient and dynamic derivative control coefficient S406. Calculate the system control quantity Δu(l) at the iteration number l; S407. Update the population x(l+1); η is denoted as N PSA A matrix of 1 row and 1 column, Rand6 is an N with a value range of [0,1] PSA A matrix of 1 row and 1 column, The elements in For LAP-UAV N i Subject to the resultant force of all vertices in the Voronoi polygon vertex set V i N The resultant force of all vertices in For LAP-UAVN i Subject to the resultant force of all its neighboring LAP-UAVs, N PSA is the size of the population, and o(l) is the adjustment factor; S408. At T PSA-D After 2 iterations, calculate the coefficient of variation Ω PSA , if the coefficient of variation For x best (l) perform mutation to obtain S409. If there is an LAP-UAV with out-of-bounds coordinates or there are LAP-UAVs with pairwise distances less than the safety threshold in the individual, reset the LAP-UAV coordinates using the grid correction method; for the LAP-UAVs; S410. When the number of iterations reaches the total number of iterations T PSA-D Output the best LAP-UAV coordinates and the optimal fitness value determined by the optimal individual; otherwise, return to S403 and enter the next iteration round.

Images