An unmanned aerial vehicle computing offloading method based on conditional value at risk and whale optimization

Abstract

The application discloses a kind of based on conditional risk value and whale optimization's unmanned plane computing unloading method, comprising: constructing air-ground link channel state information estimation error uncertainty set, constructs opportunity constraint model;Joint optimization unmanned plane position deployment, unloading decision and resource allocation, establish air edge computing unloading model;Determine the association scheme of user and unmanned plane;Construct the distributed robust opportunity constraint of worst condition task delay, and based on the conservative estimation of conditional risk value theory to distributed robust opportunity constraint, it is converted into second order cone constraint problem;Second order cone constraint problem is decoupled into computing resource allocation problem and unloading decision problem;Solving obtains the resource allocation and unloading decision scheme that unmanned plane minimizes under satisfying multidimensional constraint in hierarchical air edge computing network.This application effectively solves the network performance optimization problem under the condition that air-ground communication link exists channel state information estimation error.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of UAV edge unloading, and particularly relates to a UAV computing unloading method based on conditional risk value and whale optimization. BACKGROUND

[0002] By deploying edge servers on the user terminal side, the mobile edge computing technology can significantly reduce the task response delay and guarantee the high requirements of 6G network computing-intensive tasks on service quality. At the same time, the UAV has the advantages of high mobility and on-demand deployment, and by adjusting the position and number of the UAV, the capacity and coverage of the communication network can be enhanced. Therefore, the UAV is regarded as an ideal carrier of the edge computing server. By combining the advantages of mobile edge computing technology and UAV, the UAV carrying the edge server can be used as an air base to provide temporary communication and computing services for remote areas lacking infrastructure and areas difficult to cover by communication networks, thereby helping to achieve global coverage of wireless communication services and build a network of ubiquitous interconnection between the sky and the earth.

[0003] However, due to the size, weight and battery capacity of the UAV, its load and task processing capacity are limited. In order to make up for the lack of the UAV in terms of endurance time and computing capacity, a high-altitude platform can be introduced to transfer a part of the computing tasks from the UAV to the high-altitude platform for processing, thereby reducing the burden of the UAV and improving the overall performance of the air mobile edge computing system. However, due to the high dynamics of the air-ground communication link, the channel state information is not perfect, and there is unpredictable estimation error between the channel gain and the ideal state, which affects the service quality of the user task and the timely updating and processing of the data. In addition, the position deployment, resource allocation and unloading decision of the UAV play a crucial role in the overall utility of the system and the service quality of the user. Therefore, in the air edge computing network, the distribution of the ground users and the communication demand should be comprehensively considered to optimize the deployment and joint unloading strategy of the UAV and the high-altitude platform, so as to meet the service quality requirements of the users and the multi-dimensional resource constraints of the system, and reduce the overall energy consumption of the system and prolong the service time. SUMMARY

[0004] In view of the network performance optimization problem under the condition that there is channel state information estimation error in the air-ground communication link, the present application provides a UAV computing unloading method based on conditional risk value and whale optimization.

[0005] To achieve the above technical purposes, the technical scheme adopted by the present application is as follows:

[0006] A UAV computing unloading method based on conditional risk value and whale optimization, the UAV computing unloading method comprising the following steps:

[0007] Step 1: Construct a hierarchical air-edge computing network framework to describe the computing resource allocation and offloading scenario;

[0008] Step 2: Based on the hierarchical air-edge computing network framework constructed in Step 1, combined with historical data statistics, construct an air-ground link channel state information estimation error uncertainty set, and further construct an opportunity constraint model for user task delay constraints;

[0009] Step 3: Based on the hierarchical air-edge computing network framework constructed in Step 1 and the opportunity constraint model obtained in Step 2, considering the multi-dimensional resource constraints of the UAV swarm and the high-altitude platform, jointly optimize the UAV position deployment, offloading decision and resource allocation, and establish an air-edge computing offloading model;

[0010] Step 4: Based on the air-edge computing offloading model proposed in Step 3, according to the user distribution location and the preset number of UAVs, the K-means algorithm is used to cluster the ground users, and the UAVs are deployed at the user cluster centers to obtain the UAV deployment location and determine the association scheme between users and UAVs;

[0011] Step 5: Based on the air-ground link channel state information estimation error uncertainty set obtained in Step 2, construct a distributed robust opportunity constraint for task delay under the worst condition, and based on the conditional value at risk theory, conservatively estimate the distributed robust opportunity constraint and convert it into a second-order cone constraint problem;

[0012] Step 6: Decouple the second-order cone constraint problem into a computing resource allocation problem and an offloading decision problem;

[0013] Step 7: Use a standard solver to solve the computing resource allocation problem to obtain the central processing unit frequency allocation scheme of the UAV and high-altitude platform server;

[0014] Step 8: Based on the allocation scheme obtained in Step 7, use the penalty term method to convert the offloading decision problem into an unconstrained model, and use the binary whale optimization search problem to find a feasible solution;

[0015] Step 9: Repeat Steps 7 and 8 to obtain the resource allocation and offloading decision scheme that minimizes the energy consumption of the UAV under multi-dimensional constraints in the hierarchical air-edge computing network.

[0016] Step 1 further comprises:

[0017] Construct a hierarchical air-edge computing network scenario, which includes M users, N UAVs and 1 high-altitude platform. The UAV collects the computing tasks generated by the ground users, and according to the task requirements and the resource constraints of the UAV, it weighs whether to offload or forward to the high-altitude platform for further processing;

[0018] The position w of the m-th user is obtained based on the Cartesian three-dimensional coordinate system. m =(x m y m The horizontal position v of the nth drone. n =(x n y n All drones are set to a constant flight altitude z. n The location of the high-altitude platform is recorded as Record the user task as Where L m c represents the amount of data in the task. m This indicates the number of CPU cycles required per bit of data. Indicates the maximum tolerable latency for the task; Indicate whether there is a relationship between user m and drone n. This indicates that user m is associated with drone n, meaning the user offloads computing tasks to the drone; otherwise, they are not associated. Indicate whether user m's task was forwarded to the high-altitude platform via drone n; if so, then... on the contrary set f = {f m {m = 1, 2, ..., M} represents the CPU frequency allocated to the user task; v = {v n , n = 1, 2, ..., N} represents the horizontal position coordinates of the UAV.

[0019] Step 2 further includes:

[0020] Step 2-1: Let Δ be the estimation error between the actual channel state information and the ideal channel state information under environmental disturbances. m estimation error Δ m Follow the mean variance unknown distribution Its uncertain set is as follows:

[0021]

[0022] Step 2-2: Use Orthogonal Frequency Division Multiple Access (OFDMA) technology to transmit user tasks from the ground to the associated UAV. The transmission delay is:

[0023]

[0024] in For user uplink transmission channel gain, For the channel gain under ideal conditions, d represents the channel gain at a distance of 1m. m，n B represents the distance between the user and the drone. up is the channel transmission bandwidth. u The user equipment transmission power is n0, where n0 is the channel additive white Gaussian noise power spectral density. When the user task is unloaded locally by the UAV, the calculated delay is expressed as:

[0025]

[0026] The transmission latency of the user task being forwarded from the drone to the high-altitude platform is:

[0027]

[0028] Where p h For the drone's transmission power, For the UAV antenna transmit gain, B h For the transmission bandwidth of UAV channels, For free space path loss, L l For the total route loss, d n，h v represents the distance between the drone and the high-altitude platform. c For the speed of light, f c k is the center frequency. B Let T0 be the Boltzmann constant and T0 be the system noise temperature; the computational unloading delay of the task on the high-altitude platform is:

[0029]

[0030] The latency constraints for building the task are satisfied as follows:

[0031]

[0032] in α represents the total task latency. m Let be the confidence factor, representing the confidence factor in an uncertain set. Minimize the total latency of the user task with probability α m Not greater than the maximum tolerable latency of the task

[0033] Step 3 further includes:

[0034] Step 3-1: The energy consumption of the user task is calculated when the drone is processing it:

[0035]

[0036] Where, ε n The effective switching capacitance constant of the MEC server mounted on the UAV; the computational energy consumption of user tasks processed on the high-altitude platform is:

[0037]

[0038] Where, εh is the energy consumption coefficient of the edge computing server on the HAP; the transmission energy consumption of the task forwarded by the UAV to the HAP is:

[0039]

[0040] The total energy consumption of the single UAV is:

[0041]

[0042] The total energy consumption of the HAP is:

[0043]

[0044] Step 3-2: The UAV location deployment, offloading decision and resource allocation problem in the hierarchical aerial edge computing network is converted into a minimization objective function problem, which is modeled as a minimization system energy consumption problem P0 as follows:

[0045]

[0046] wherein and are the maximum energy of the UAV and the HAP, respectively, H is the maximum number of tasks handled by the HAP at the same time, and are the maximum central processor speed of the UAV and the HAP, respectively, [X min , X max ] and [Y min , Y max ] are the horizontal and vertical boundaries in the two-dimensional plane of the region.

[0047] Step 4 further comprises:

[0048] Step 4-1: randomly selecting N points in the region as the starting coordinates v of the UAV;

[0049] Step 4-2: calculating the distance between the UAV and the users according to the following formula:

[0050]

[0051] and re-allocating the users to the cluster closest to them;

[0052] Step 4-3: updating the position of the UAV according to the following formula:

[0053]

[0054] wherein denotes the number of users contained in the cluster

[0055] ​Step 4-4: Repeat steps 4-1 to 4-3 until the results converge and the deployment location v of the UAV is obtained;

[0056] Steps 4-5: Cluster Associate users with their corresponding drones and update the user-drone association indicator variable δ.

[0057] Steps 4-6: Transform the problem of minimizing system energy consumption P0 into problem P1:

[0058]

[0059] Step 5 further includes:

[0060] Step 5-1: For the latency-chance constraint model proposed in Step 2, construct its worst-case distributed robust chance constraint as follows:

[0061]

[0062] in, For random probability distribution The lower bound of the distribution, Total delay;

[0063] Step 5-2: For the chance constraint model proposed in Step 2, based on the first-order Taylor series expansion formula, construct its worst-case distributed robust chance constraint as follows:

[0064]

[0065] in

[0066]

[0067] In the formula, For random probability distribution The lower bound of the distribution;

[0068] Step 5-3: Based on conditional value at risk, transform the distributed robust chance constraint described in Step 5-2 into a mixed-integer second-order cone constraint:

[0069]

[0070] Where β m e m q m z m and s m As auxiliary variables; transform problem P1 into a mixed second-order cone-constrained problem P2:

[0071]

[0072] where β, e, q, z and s are vector sets of corresponding auxiliary variables.

[0073] Step 6 further comprises:

[0074] The mixed second-order cone constrained problem P2 is originally decomposed into a continuous variable problem P3 and a binary variable problem P4:

[0075]

[0076] Step 8 further comprises:

[0077] Step 8-1: according to the constraint conditions in the binary variable problem P4, the following functions are defined respectively:

[0078]

[0079] Step 8-2: according to the objective function in the binary variable problem P4, a penalty term is introduced The fitness function Γ(λ) is constructed as follows:

[0080]

[0081] where H(·) is an indicator function, defined as follows:

[0082]

[0083] The binary variable problem P4 is converted into the following problem P5:

[0084]

[0085] Step 8-3: for problem P5, the binary whale optimization algorithm is used to iteratively optimize the calculation offloading decision variable λ, to obtain the optimized binary offloading decision variable λ and the fitness function Γ(λ).

[0086] Step 8-3 further comprises:

[0087] Initialize the relevant parameters, calculate the fitness of each whale individual according to the fitness function Γ, and obtain the optimal individual corresponding to the current minimum fitness value Iterate, for each individual in the whale population, update the parameters A, C and a, execute the spiral enclosure mechanism, the enclosure contraction mechanism or the exploration mechanism according to the probability and the value of the parameter |A|, calculate the distance vector, update the whale position and the fitness function value of each whale individual, and obtain the optimal individual in the population, until the maximum number of iterations is reached, to obtain the optimized binary offloading decision variable λ and the fitness function Γ(λ).

[0088] Compared with the prior art, the beneficial effects of the present application are as follows:

[0089] Firstly, the UAV computing offloading method based on conditional value at risk and whale optimization of the present application proposes a hierarchical aerial edge computing network framework, which provides communication and computing services for ground users in combination with UAVs and high-altitude platforms; constructs an opportunity constraint model in view of the delay requirement of user tasks, pre-deploys the positions of UAVs by using a clustering algorithm, conservatively estimates the opportunity model based on a distributed robust optimization algorithm and conditional value at risk theory, optimizes the computing resource allocation decision, and designs a binary whale optimization algorithm to optimize the UAV offloading decision, so as to realize the energy-saving deployment and decision optimization of the double-layer aerial edge computing system, and effectively solve the network performance optimization problem in the case that there is an estimation error of channel state information in the air-ground communication link.

[0090] Secondly, the UAV computing offloading method based on conditional value at risk and whale optimization of the present application optimizes the deployment and joint offloading strategy of UAVs and high-altitude platforms in combination with the distribution of ground users and communication requirements, meets the quality of service requirement of users and the multi-dimensional resource constraint of the system, and reduces the overall energy consumption of the system and prolongs the service time. BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1 It is a scenario diagram of the aerial edge computing network model based on multiple UAVs and high-altitude platforms in the present application;

[0092] Figure 2 It is a flowchart of the binary whale optimization algorithm proposed in the present application;

[0093] Figure 3 It is a flowchart of the UAV computing offloading method based on conditional value at risk and whale optimization proposed in the present application;

[0094] Figure 4 It is a comparison of the optimization results of the algorithm proposed in the present application and the traditional algorithm;

[0095] Figure 5 It is a comparison of the system energy consumption of the algorithm proposed in the present application and the ideal state;

[0096] Figure 6 It is a relationship diagram of the maximum tolerable delay of tasks and the total energy consumption of the system in the present application;

[0097] Figure 7 It is a relationship diagram of the transmission power of users and the total energy consumption of the system in the present application. DETAILED DESCRIPTION

[0098] The technical solutions of the present application will be further described in detail below in combination with the drawings of the specification and the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0099] Figure 1 is the aerial edge computing network model based on multiple unmanned aerial vehicles and high altitude platform provided by the application, specifically, which includes M users, N unmanned aerial vehicles and 1 high altitude platform, After the unmanned aerial vehicle is deployed, it hovers at a fixed height, collects the computing tasks generated by the ground users, and according to the requirements of the tasks and the resource constraints of the unmanned aerial vehicle, the unloading in the unmanned aerial vehicle or the forwarding to the high altitude platform for further processing is balanced.

[0100] Figure 2 is the flow chart of the binary whale optimization algorithm provided by the application, specifically, first, the relevant parameters are initialized, and the position of each individual in the whale population is randomly set, and the objective function value of each whale individual in the current iteration is calculated; for each whale individual, update parameters A, C and a, according to the probability and the value of parameter |A|, execute the spiral surrounding mechanism, surrounding contraction mechanism or exploration mechanism, update the whale position, and recalculate the fitness function value of each whale individual, update the optimal individual in the population; repeat the above process until the maximum iteration number is reached, and the algorithm terminates.

[0101] Figure 3 is the algorithm architecture diagram provided by the application, specifically, the application is divided into two stages of unmanned aerial vehicle deployment and computing offloading, first, the algorithm based on K-means is used to solve the unmanned aerial vehicle position and unmanned aerial vehicle-user association decision in problem P0; then, based on distributed robust optimization and conditional value at risk, the opportunity constraint in problem P1 is conservatively estimated, and further the mixed integer second order cone optimization problem P2 is decomposed into P3 and P4; finally, the problem P4 is converted into the unconstrained problem P5 by the penalty term method, and the integer offloading strategy of P5 is obtained based on the binary whale optimization algorithm.

[0102] Figure 4 is the relationship diagram of system energy consumption and scene scale based on different offloading algorithms provided by the application, which records the system energy consumption optimization results of different algorithms under different network scales. Specifically, the binary whale optimization algorithm is used to solve the task binary offloading decision, and compared and analyzed with other three algorithms, including the brute force search algorithm, the greedy algorithm and the simulated annealing algorithm. It can be seen that the result of the binary whale optimization algorithm is close to the optimal solution obtained by the brute force search algorithm, and is better than the results obtained by the greedy algorithm and the simulated annealing algorithm.

[0103] Figure 5The system energy consumption obtained based on the distributed robust optimization and the conditional value at risk and the system energy consumption in an ideal state are compared. It can be seen that, when the channel state estimation error exists, the total energy consumption of the system is higher than that in the ideal case, and this phenomenon is due to the fact that the edge computing server needs to allocate more computing resources when processing tasks in order to cope with the interference of the environment and the random error of the channel, so as to meet the delay requirement of the task. The figure verifies the robustness of the algorithm based on the distributed robust optimization and the conditional value at risk.

[0104] Figure 6 The relationship between the maximum tolerable delay of the task and the total energy consumption of the system is shown in the figure, the user task quantity is sequentially increased from 50Mbit, 55Mbit, 60Mbit, 65Mbit, 70Mbit, and the total energy consumption of the system under different maximum tolerable delays of the task is recorded. The results show that, as the user task quantity increases, the energy consumption of the system increases. In addition, the system energy consumption decreases significantly as the maximum tolerable delay of the task increases. This is because when the maximum tolerable delay of the task increases, the computing and processing time of the edge server for the task is prolonged, thereby reducing the central processor frequency number required by the task, resulting in reduced computing energy consumption of the unmanned aerial vehicle and the high-altitude platform, and reduced total energy consumption.

[0105] Figure 7 The relationship between the user transmission power and the total energy consumption of the system is shown in the figure, the user task quantity is sequentially increased from 50Mbit, 55Mbit, 60Mbit, 65Mbit, 70Mbit, and the total energy consumption of the system under different user transmission powers is recorded. It can be seen that, as the user transmission power increases, the total energy consumption of the aerial edge computing system decreases. This is because the increase of the user transmission power reduces the transmission delay of the user-unmanned aerial vehicle, prolongs the processing time of the edge server for the task, reduces the central processor frequency number required by the task, reduces the computing energy consumption of the unmanned aerial vehicle and the high-altitude platform, and reduces the total energy consumption of the aerial edge computing system.

[0106] The method for deploying the position of the unmanned aerial vehicle, computing offloading and resource allocation of the hierarchical aerial network based on the conditional value at risk and the whale optimization comprises the following steps:

[0107] Step 1: constructing a hierarchical aerial edge computing network framework to describe the computing resource allocation and offloading scenario;

[0108] Step 2: based on the scenario constructed in step 1, based on historical data statistical information, constructing an air-ground link channel state information estimation error uncertainty set, and further constructing an opportunity constraint model for the user task delay constraint;

[0109] Step 3: Based on the scenario constructed in step 1 and the opportunity constraint model obtained in step 2, considering the multi-dimensional resource constraints of the UAV group and the high-altitude platform, jointly optimizing the UAV position deployment, unloading decision and resource allocation, an air edge computing unloading model is established;

[0110] Step 4: Based on the model proposed in step 3, according to the user distribution position and the preset number of UAVs, the K-means algorithm is used to cluster the ground users, and the UAV is deployed at the user cluster center to obtain the UAV deployment position and determine the association scheme of the user and the UAV;

[0111] Step 5: Based on the air-ground link channel state information estimation error uncertainty set obtained in step 2, a distributed robust opportunity constraint of task delay under the worst condition is constructed, and a conservative estimation of the distributed robust opportunity constraint is made based on the conditional value at risk theory, which is converted into a second-order cone constraint;

[0112] Step 6: The problem is decoupled into a computing resource allocation problem and an unloading decision problem;

[0113] Step 7: The standard solver is used to solve the central processing unit frequency allocation scheme of the UAV and the high-altitude platform server;

[0114] Step 8: Based on the computing resource allocation scheme obtained in step 7, for the unloading decision problem model, the problem is converted into an unconstrained model by using the penalty term method, and the binary whale optimization is used to search for the feasible solution of the problem;

[0115] Step 9: Repeat steps 7 and 8 to obtain the resource allocation and unloading decision scheme that minimizes the energy consumption of the UAV under the multi-dimensional constraint in the air hierarchical edge computing network.

[0116] To optimize the above technical solutions, the specific measures taken also include:

[0117] The hierarchical air edge computing network scenario constructed in the above step 1 includes M users, N UAVs and 1 high-altitude platform. The UAV collects the computing tasks generated by the ground users, and according to the task demand and the resource constraint of the UAV, it weighs whether to unload or forward to the high-altitude platform for further processing. Based on the Cartesian three-dimensional coordinate system, the position of the user is w m =(x m ,y m ), the horizontal position of the UAV is v n =(x n ,y n ), and the flight height of all UAVs is a constant value z n . The position of the high-altitude platform is The user task is where L mData volume representing a task, c m Number of central processor cycles required per bit of data, Maximum latency that the task can tolerate. Indicates whether the user m is associated with the UAV n, if Indicates that the user m is associated with the UAV n, and the user offloads the task to the UAV, and vice versa. Indicates whether the task of the user m is forwarded to the HAP through the UAV n, if yes, then Otherwise The server carried by the UAV and the HAP can adopt dynamic voltage and frequency scaling technology to dynamically adjust the computing frequency allocated to the user task, and the set f = {f m , m = 1, 2,..., M} represents the central processor frequency allocated to the user task. v = {v n , n = 1, 2,..., N} represents the horizontal position coordinates of the UAV.

[0118] The above step 2 includes:

[0119] Step 2-1: Δ m is the estimation error between the actual channel state information and the ideal channel state information under environmental disturbance. Based on historical data statistical information, the observation of the channel is set to be a random channel state information estimation error Δ m obeys an unknown distribution with mean and variance Its possible distribution set is as follows:

[0120]

[0121] Where is the uncertain set of uncertain parameter Δ m .

[0122] Step 2-2: The communication link between the UAV and the ground user is modeled as a large-scale fading model, and the channel gain in the ideal state is represented as

[0123]

[0124] Where is the channel gain when the distance is 1m, d m，n is the distance between the user and the UAV. Considering the high dynamics and time-varying of the air-ground link, the actual channel gain is represented as:

[0125]

[0126] The user task is transmitted from the ground to the associated UAV using orthogonal frequency division multiple access technology, and the transmission delay is:​

[0127]

[0128] where B u is the channel transmission bandwidth, p u is the user equipment transmission power, b0is the channel additive white Gaussian noise power spectral density. The computation latency when the user task is offloaded at the local unmanned aerial vehicle is:

[0129]

[0130] The transmission latency when the user task is forwarded by the unmanned aerial vehicle to the high-altitude platform is:

[0131]

[0132] where p h is the unmanned aerial vehicle transmission power, is the unmanned aerial vehicle antenna transmission gain, B h is the unmanned aerial vehicle channel transmission bandwidth, is the free space path loss, L l is the total route loss, d n，h is the distance between the unmanned aerial vehicle and the high-altitude platform, v c is the speed of light, f c is the center frequency, k B is the Boltzmann constant, and T0is the system noise temperature. The computation offloading latency when the task is at the high-altitude platform is:

[0133]

[0134] The delay constraint of the task is satisfied:

[0135]

[0136] where is the total task latency, a m is a confidence factor, indicating that the total latency of the user task under the uncertain set is less than the maximum tolerable latency of the task with a probability a m not greater than

[0137] The above step 3 includes:

[0138] Step 3-1: The computation energy consumption when the user task is processed at the unmanned aerial vehicle is

[0139]

[0140] where, e nAn effective switching capacitance constant for the MEC server carried on the UAV. The calculation energy consumption of the user task when processed on the high-altitude platform is

[0141]

[0142] wherein ε h is the energy consumption coefficient of the edge computing server carried on the high-altitude platform, which is related to the server chip structure. The transmission energy consumption of the task forwarded by the UAV to the high-altitude platform is

[0143]

[0144] Based on the system model constructed in step 1, the total energy consumption of a single UAV is

[0145]

[0146] The total energy consumption of the high-altitude platform is

[0147]

[0148] Step 3-2: Based on the model of step 1, the UAV position deployment, unloading decision and resource allocation problem in the hierarchical aerial edge computing network is converted into a minimization objective function problem, which is modeled as the following minimization system energy consumption problem P0:

[0149]

[0150] wherein are the maximum energy of the UAV and the high-altitude platform, H is the maximum number of tasks that can be processed by the high-altitude platform at the same time, and are the maximum central processor speed of the UAV and the high-altitude platform, respectively. min , X max ] and [Y min , Y max ] are the horizontal and vertical boundaries in the two-dimensional plane of the region.

[0151] The above step 4 includes:

[0152] Step 4-1: Randomly select N points in the region as the starting coordinates v of the UAV.

[0153] Step 4-2: Calculate the distance between the UAV and the user according to the following formula:

[0154]

[0155] And re-allocate the user to the cluster closest to it.

[0156] Step 4-3: Update the position of the UAV according to the following formula:

[0157]

[0158] wherein denotes the cluster containing the number of users.

[0159] Step 4-4: Repeat the above process until the result converges, and the deployment location v of the UAV is obtained.

[0160] Step 4-5: Associate the users in the cluster and the corresponding UAV, and update the user-UAV association indicator variable δ.

[0161] Step 4-6: According to the above steps, the deployment location v of the UAV and the user-UAV association indicator variable δ are obtained. The problem P0 described in the above step 3 is transformed into the problem P1 as follows:

[0162]

[0163] The above step 5 includes:

[0164] Step 5-1: For the time delay opportunity constraint model proposed in step 2, construct its distributed robust opportunity constraint in the worst case as follows:

[0165]

[0166] wherein is the lower bound of the distribution of the random probability distribution .

[0167] Step 5-2: Since the channel state estimation information error is much smaller than its theoretical value, based on the first-order Taylor expansion formula, the approximate expression of the total time delay is obtained as follows:

[0168]

[0169] The distributed robust opportunity constraint described in the above step 5-1 can be transformed into:

[0170]

[0171] wherein

[0172]

[0173]

[0174] Step 5-3: The conditional value at risk is defined as the conditional expected value of the loss exceeding a certain confidence level under a given probability distribution, which can be used to evaluate potential risk loss. The conditional value at risk constraint can constitute a conservative estimate of the distributed robust opportunity constraint in the worst case, as follows:

[0175]

[0176] where is the upper bound of the distribution of the random probability distribution φ(ξ) is the loss function of the random parameter ξ, denotes the conditional value-at-risk of φ(ξ) at the confidence level α. Based on the strong duality theorem, the worst-case conditional value-at-risk can be expressed as a second-order cone programming as follows: 0

[0177]

[0178] e-θ 0 +β+q-Θμ-z>0,

[0179] e≥0,z>0,

[0180]

[0181] where β, e, q, z and s are auxiliary variables, and μ and σ are the mean and standard deviation of the random parameter ξ, respectively. Based on the conditional value-at-risk, the distributed robust chance constraint described in step 5-2 above can be transformed into a mixed-integer second-order cone constraint as follows:

[0182]

[0183] where β m , e m , q m , z m and s m are auxiliary variables. According to the above steps, the problem P1 described in step 4 above can be transformed into a mixed second-order cone problem P2 as follows:

[0184]

[0185] where β, e, q, z and s are the vector sets of the corresponding auxiliary variables.

[0186] In step 6 above, for the problem P2 obtained in step 5 above, it is decomposed into a continuous variable problem P3 and a binary variable problem P4 as follows:

[0187]

[0188] and

[0189]

[0190] ​In step 7 above, for the continuous variable problem P3 obtained in step 6 above, a standard solver is used to obtain the computing resource allocation strategy f.

[0191] Step 8 above includes:

[0192] Step 8-1: According to the constraint conditions in the binary variable problem P4 obtained in step 6 above, the following functions are defined respectively:

[0193]

[0194] Step 8-2: According to the objective function in the binary variable problem P4 obtained in step 6 above, a penalty term is introduced. Solutions that violate constraints will be given a larger penalty, thereby avoiding obtaining invalid solutions. The fitness function Γ(λ) is constructed as follows:

[0195]

[0196] where is set to 10 5 , and H(·) is an indicator function defined as follows:

[0197]

[0198] Further, the problem P4 in step 6 above is converted into the following problem P5:

[0199]

[0200] Step 8-3: For the above problem P5, the binary whale optimization algorithm is used to iteratively optimize the computing offloading decision variable λ to obtain the optimal offloading strategy. As shown in the following equation: Figure 2 , the specific process is as follows:

[0201] Binary whale optimization is a population-based meta-heuristic algorithm, where each whale individual represents a potential binary candidate solution. In the iteration process, through the alternation of exploration and contraction behaviors, a number of whale individuals constantly update their positions until a satisfactory binary solution is found. In the binary whale optimization described in the present application, each potential solution X(i) is a binary offloading decision variable λ, where i is the current iteration number, and the optimization objective is to minimize the above fitness function Γ(λ).

[0202] First, the maximum number of iterations I max is set, and the initial positions of the binary whale population are randomly set. The fitness of each whale individual is calculated according to the above fitness function Γ, and the optimal individual corresponding to the current minimum fitness value is obtained.

[0203] The iteration is performed, and in each iteration, the binary whale optimization algorithm continuously adjusts the position of each candidate solution and updates the optimal solution found, so that the entire population gradually develops in a better direction until the number of iterations is reached, and the position of the optimal individual and the corresponding fitness function value are output. The iteration process includes the surrounding stage and the exploration stage. In the surrounding stage, the whale individual updates the current position based on the shrinkage surrounding mechanism or the spiral surrounding mechanism; in the exploration stage, the whale individual searches for a new solution space and updates the position using the foraging mechanism. For each individual in the whale population, repeat the following iteration process until the maximum number of iterations I max :

[0204] 1) Update parameters:

[0205] The parameter a is linearly reduced from 2 to 0 in the iteration:

[0206]

[0207] where i is the current number of iterations. Update parameters A and C as follows:

[0208]

[0209] and

[0210]

[0211] where and are random vectors in the range [0, 1].

[0212] 2) Generate a random number P rand ∈[0,1]。

[0213] 3) When P rand ≥0.5, execute the spiral surrounding mechanism. This mechanism simulates the behavior of a humpback whale forming a bubble net spiral around prey and gradually shrinking to catch prey, making the whale individual constantly approach the current optimal solution while maintaining a certain exploration to prevent falling into local optimum. The position update formula of the whale individual is as follows:

[0214]

[0215] where is the position of the whale individual in the next round of iteration, is the position of the whale individual in the current iteration, C(·) is the complement operation. P BWOA ∈[0,1] is a random value, τ su is the position update step size, which is used to control the probability of each bit flip, and is calculated as follows:

[0216]

[0217] where is the distance vector between the current whale individual and the current best solution.

[0218] 4) When P rand < 0.5, and |A| ≥ 1, the exploration mechanism is executed. This mechanism imitates the behavior of whales in the sea to find prey. By randomly selecting a position in the solution space, the current solution is guided to move to a new area, thereby increasing the probability of finding the global optimal solution. The whale individual will move randomly to a certain position in the solution space, and the distance vector is calculated as follows:

[0219]

[0220] is the position of a random whale individual in the solution space. The position update formula is as follows:

[0221]

[0222] where

[0223]

[0224] 5) When P rand < 0.5, and |A| < 1, the shrinkage mechanism is executed. This mechanism simulates the behavior of humpback whales in gradually narrowing the encirclement when hunting prey. By constantly narrowing the distance between the whale individual and the current optimal solution, the whale population gradually approaches the optimal solution, thereby improving the local search ability of the algorithm. The distance vector is calculated as follows:

[0225]

[0226] The position update formula is as follows:

[0227]

[0228] where

[0229]

[0230] 6) Calculate the fitness function value Γ of each whale individual, update the current optimal individual

[0231] After the above iteration process, the optimized binary offloading decision variable λ and the fitness function Γ(λ) are obtained.

[0232] In step 9 above, given the computing resource allocation strategy f obtained in step 7, perform step 8 to optimize the binary offloading decision variable λ; given the binary offloading decision variable λ obtained in step 8, perform step 7 to optimize the computing resource allocation strategy f. Repeat the process until the result converges, obtaining the resource allocation and offloading decision scheme that minimizes the system energy consumption under the multi-dimensional constraints in the layered edge computing network over the air.

[0233] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the preferred embodiments by those skilled in the art once they learn of the basic inventive concepts. Therefore, the appended claims are intended to encompass within their scope all such variations and modifications as are included within the spirit and scope of the application.

[0234] Obviously, numerous modifications and variations of the present application are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A method for computational unloading of unmanned aerial vehicles (UAVs) based on conditional value at risk and whale optimization, characterized in that, The drone calculation and unloading method includes the following steps: Step 1: Construct a hierarchical aerial edge computing network framework to describe computing resource allocation and offloading scenarios; Step 2: Based on the hierarchical air edge computing network framework constructed in Step 1, and combined with historical data statistics, construct an uncertainty set for the estimation error of air-to-ground link channel state information, and further construct an opportunity constraint model for user task latency constraints; Step 3: Based on the hierarchical aerial edge computing network framework constructed in Step 1 and the opportunity constraint model obtained in Step 2, considering the multi-dimensional resource constraints of UAV swarms and high-altitude platforms, jointly optimize UAV location deployment, offloading decisions and resource allocation, and establish an aerial edge computing offloading model. Step 4: Based on the aerial edge computing offloading model proposed in Step 3, the K-means algorithm is used to cluster ground users according to the user distribution location and the preset number of drones, and drones are deployed at the centroid of the user clusters to obtain the drone deployment location and determine the association scheme between users and drones. Step 5: Based on the uncertainty set of air-to-ground link channel state information estimation error obtained in Step 2, construct the distributed robust opportunity constraint of mission delay under worst-case conditions, and make a conservative estimate of the distributed robust opportunity constraint based on the conditional risk value theory, transforming it into a second-order cone constraint problem. Step 6: Decouple the second-order cone constraint problem into a computational resource allocation problem and an unloading decision problem; Step 7: Use the standard solver to solve the computational resource allocation problem and obtain the CPU frequency allocation scheme for the servers mounted on the UAV and the high-altitude platform; Step 8: Based on the allocation scheme obtained in Step 7, the unloading decision problem is transformed into an unconstrained model using the penalty term method, and the binary whale optimization is used to search for feasible solutions to the problem. Step 9: Repeat steps 7 and 8 to obtain the resource allocation and offloading decision scheme that minimizes UAV energy consumption under multidimensional constraints in the hierarchical aerial edge computing network.

2. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 1, characterized in that, Step 1 further includes: Construct a hierarchical aerial edge computing network scenario, which includes M users, N drones and 1 high-altitude platform. The drones collect computing tasks generated by the ground users and, based on the task requirements and the resource constraints of the drones, either offload the tasks to the drones or forward them to the high-altitude platform for further processing. The position w of the m-th user is obtained based on the Cartesian three-dimensional coordinate system. m =(x m y m The horizontal position v of the nth drone. n =(x n y n All drones are set to a constant flight altitude z. n The location of the high-altitude platform is recorded as Record the user task as Where L m c represents the amount of data in the task. m This indicates the number of CPU cycles required per bit of data. Indicates the maximum tolerable latency for the task; Indicate whether there is a relationship between user m and drone n. This indicates that user m is associated with drone n, meaning the user offloads computing tasks to the drone; otherwise, they are not associated. Indicate whether user m's task was forwarded to the high-altitude platform via drone n; if so, then... on the contrary set f = {f m {m = 1, 2, ..., M} represents the CPU frequency allocated to the user task; v = {v n , n = 1, 2, ..., N} represents the horizontal position coordinates of the UAV.

3. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 2, characterized in that, Step 2 further includes: Step 2-1: Let Δ be the estimation error between the actual channel state information and the ideal channel state information under environmental disturbances. m Estimation error Δ m Follow the mean variance unknown distribution Its uncertain set is as follows: Step 2-2: Use Orthogonal Frequency Division Multiple Access (OFDMA) technology to transmit user tasks from the ground to the associated UAV. The transmission delay is: in For user uplink transmission channel gain, For the channel gain under ideal conditions, d represents the channel gain at a distance of 1m. m，n B represents the distance between the user and the drone. u p is the channel transmission bandwidth. u The user equipment transmission power is n0, where n0 is the channel additive white Gaussian noise power spectral density. When the user task is unloaded locally on the UAV, the calculated delay is expressed as: The transmission latency of the user task being forwarded from the drone to the high-altitude platform is: Where p h For the drone's transmission power, For the UAV antenna transmit gain, B h For the transmission bandwidth of UAV channels, For free space path loss, L l For the total route loss, d n，h v represents the distance between the drone and the high-altitude platform. c For the speed of light, f c k is the center frequency. B Let T0 be the Boltzmann constant and T0 be the system noise temperature; the computational unloading delay of the task on the high-altitude platform is: The latency constraints for building the task are satisfied as follows: in α represents the total task latency. m Let be the confidence factor, representing the confidence factor in an uncertain set. Minimize the total latency of the user task with probability α m Not greater than the maximum tolerable latency of the task 4. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 3, characterized in that, Step 3 further includes: Step 3-1: The energy consumption of the user task is calculated when the drone is processing it: Where, ε n The effective switching capacitance constant of the MEC server mounted on the UAV; the computational energy consumption of user tasks processed on the high-altitude platform is: Where, ε h The energy consumption coefficient of the edge computing server mounted on the high-altitude platform; the energy consumption for transmitting tasks from the drone to the high-altitude platform is: The total energy consumption of a single drone is: The total energy consumption of the aerial platform is: Step 3-2: Transform the UAV location deployment, offloading decision, and resource allocation problems in the hierarchical aerial edge computing network into a minimization objective function problem, which is modeled as the following minimization system energy consumption problem P0: in and Here, H represents the maximum energy of the drone and the high-altitude platform, respectively, and H represents the maximum number of tasks that the high-altitude platform can handle simultaneously. and These represent the maximum central processing unit rotation speeds for the drone and the high-altitude platform, respectively. min X max ] and [Y min Y max ] represents the horizontal and vertical boundaries within the two-dimensional plane of the region.

5. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 4, characterized in that, Step 4 further includes: Step 4-1: Randomly select N points within the area as the starting coordinates v of the UAV; Step 4-2: Calculate the distance between the drone and the user using the following formula: And reassign the user to the nearest cluster; Step 4-3: Update the drone's position according to the following formula: in Cluster The number of users included; Step 4-4: Repeat steps 4-1 to 4-3 until the results converge and the deployment location v of the UAV is obtained; Steps 4-5: Cluster Associating users with their corresponding drones, and updating the user-drone association indicator variable. Steps 4-6: Transform the problem of minimizing system energy consumption P0 into problem P1:

6. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 5, characterized in that, Step 5 further includes: Step 5-1: For the latency-chance constraint model proposed in Step 2, construct its worst-case distributed robust chance constraint as follows: in, For random probability distribution The lower bound of the distribution, Total delay; Step 5-2: For the chance constraint model proposed in Step 2, based on the first-order Taylor series expansion formula, construct its worst-case distributed robust chance constraint as follows: in In the formula, For random probability distribution The lower bound of the distribution; Step 5-3: Based on conditional value at risk, transform the distributed robust chance constraint described in Step 5-2 into a mixed-integer second-order cone constraint: Where β m e m q m z m and s m As auxiliary variables; transform problem P1 into a mixed second-order cone-constrained problem P2: Where β, e, q, z, and s are vector sets of corresponding auxiliary variables.

7. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 6, characterized in that, Step 6 further includes: The hybrid second-order cone constraint problem P2 is originally decomposed into a continuous variable problem P3 and a binary variable problem P4:

8. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 7, characterized in that, Step 8 further includes: Step 8-1: Based on the constraints in problem P4 (binary variable), define the following functions: Step 8-2: Based on the objective function in binary variable problem P4, introduce a penalty term. The fitness function Γ(λ) is constructed as follows: Where H(·) is the indicator function, defined as follows: The binary variable problem P4 is transformed into the following problem P5: Step 8-3: For problem P5, iteratively optimize the calculation of the unloading decision variable λ based on the binary whale optimization algorithm to obtain the optimized binary unloading decision variable λ and fitness function Γ(λ).

9. The UAV computational offloading method based on conditional value at risk and whale optimization according to claim 8, characterized in that, Step 8-3 further includes: Initialize the relevant parameters, calculate the fitness of each whale individual according to the fitness function Γ, and obtain the optimal individual corresponding to the current minimum fitness value. The process is iterated, updating the parameters for each individual in the whale population. Based on the probability and the value of parameter |A|, the spiral encirclement mechanism, the encirclement contraction mechanism, or the exploration mechanism are executed respectively to calculate the distance vector, update the whale position and the fitness function value of each individual whale, and obtain the optimal individual in the population until the maximum number of iterations is reached, and obtain the optimized binary unloading decision variable λ and fitness function Γ(λ).

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