Joint optimization method for UAV deployment and computation offloading based on convex optimization

Abstract

The present invention relates to a joint optimization method for drone deployment and computation offloading based on convex optimization. The method designs an algorithm based on convex optimization to minimize the average task response time in a drone-assisted mobile edge computing system by jointly optimizing drone deployment and computation offloading. First, the original problem is decomposed into three sub-problems of drone deployment optimization, ground equipment access optimization, and computation task offloading optimization by the block coordinate descent method; then, the approximate optimal solution of the original problem is obtained by alternately solving the above sub-problems; finally, the performance of the algorithm is evaluated. Simulation results show that the algorithm designed by the present invention can generate a joint optimization solution within a few seconds, and has a superior performance of 4.37% to 43.04% over other classical methods.

Description

Technical Field

[0001] The present invention relates to a joint optimization method for unmanned aerial vehicle deployment and computation offloading based on convex optimization. Background Art

[0002] With the popularity of mobile devices (such as smartphones, tablets, and wearable devices), more and more new mobile applications have emerged. Among them, more and more applications are resource-intensive and delay-sensitive, such as face recognition and augmented reality applications. However, due to physical limitations such as CPU and battery life, the growing capacity of mobile devices still lags behind people's needs. Therefore, executing resource-intensive and delay-sensitive tasks on mobile devices is a very challenging task.

[0003] Mobile edge computing is an effective computing paradigm to solve the above challenges. It sinks the computing power of the cloud center to the edge of the network by deploying edge servers at the edge of the network, and uses the relatively rich computing resources of edge servers to make up for the shortcomings of mobile devices. The high mobility of drones allows them to not only enter dangerous scenes that rescuers cannot enter to perform search and rescue missions, but also act as temporary communication base stations in areas without basic communication facilities or damaged basic communication facilities, providing communication and computing services for rescue equipment. Combining the characteristics and advantages of mobile edge computing and drones, applying drones as edge servers to the mobile edge computing paradigm to form a drone-enabled mobile edge computing system can solve the problem of insufficient computing resources of mobile devices in special scenarios to a certain extent. In this type of system, multiple drones are deployed collaboratively, and each mobile device selects a suitable drone and performs computing offload on demand. In order to improve the service quality for mobile devices, it is necessary to jointly optimize drone deployment and computing offload. Considering that the location and computing requirements of mobile devices often change, the above joint deployment and offloading schemes also need to be adjusted accordingly. Selecting a suitable joint optimization scheme faces a combinatorial explosion problem. Therefore, it is necessary to find an efficient joint optimization scheme generation method to meet the real-time requirements of computing offload.

[0004] In existing research works, authors usually use heuristic algorithms or search algorithms to solve edge deployment problems, which takes tens or even hundreds of seconds to find a suitable edge deployment solution, which is difficult to meet the needs of rapid deployment of drones in drone-enabled mobile edge computing systems. In recent years, some research works have used deep reinforcement learning methods to solve the optimization problems of drone deployment and computational offloading in drone-enabled mobile edge computing systems, but such methods require a large amount of data for model training before solving the problem, and the optimization effect is limited in the absence of data. In addition, some research works have used convex optimization related methods to solve the optimization problems of drone deployment and computational offloading in drone-enabled mobile edge computing systems, but in the scenarios considered in these research works, computing tasks can only be completely offloaded, and cannot be offloaded on demand to fully utilize the computing resources of edge and mobile devices, resulting in low resource utilization. Summary of the invention

[0005] The purpose of the present invention is to formally define the joint optimization problem of drone deployment, ground user access and computing task offloading for a drone-enabled mobile edge computing system, aiming to minimize the average task response time, and provide a joint optimization method for drone deployment and computing offloading based on convex optimization.

[0006] To achieve the above-mentioned purpose, the technical solution of the present invention is: a joint optimization method for UAV deployment and computational offloading based on convex optimization, which decomposes the joint optimization problem into three sub-problems: UAV deployment optimization, ground equipment access optimization, and computational task offloading optimization; and obtains an approximate optimal solution to the joint optimization problem by alternately solving the three sub-problems to minimize the average task response time.

[0007] Compared with the prior art, the present invention has the following beneficial effects:

[0008] The present invention has advantages in algorithm convergence, algorithm execution efficiency and system performance. It can generate a joint optimization solution within a few seconds and can be used in a drone-assisted mobile edge computing system composed of multiple drones and multiple ground devices. It can make quick decisions on the deployment location of the drone and the task offloading plan of ground users to reduce the average response time of computing tasks of various ground devices in the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 Mobile edge computing system enabling multiple drones.

[0010] Figure 2 It is the convergence curve of the system average response time in different scenarios.

[0011] Figure 3 Comparison of the average task response time obtained by AO-BS and advanced algorithms in different system scenarios.

[0012] Figure 4 Comparison of execution time between AO-BS and advanced algorithms in different system scenarios.

[0013] Figure 5 Comparison of the average task response time obtained by AO-BS and its variant algorithms in different system scenarios. DETAILED DESCRIPTION

[0014] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0015] The present invention discloses a joint optimization method for UAV deployment and computation offloading based on convex optimization, which decomposes the joint optimization problem into three sub-problems: UAV deployment optimization, ground equipment access optimization and computation offloading optimization. The approximate optimal solution of the joint optimization problem is obtained by alternately solving the three sub-problems to minimize the average response time of the task.

[0016] The following is the specific implementation process of the present invention.

[0017] The present invention considers a Figure 1 The multi-UAV-enabled mobile edge computing system shown in FIG. 1 is composed of two layers, namely, the ground layer consisting of M ground devices and the air layer consisting of N UAVs. All ground devices and UAVs in the system are respectively and Without loss of generality, we use a three-dimensional Euclidean coordinate system to represent the positions of ground equipment and drones in the system. The coordinates of can be expressed as in and It is used to represent the position of the ground equipment m on the horizontal plane. The deployment positions of all drones in the system are Indicates that is the deployment location of UAV n, and It is used to represent the deployment position of the drone n on the horizontal plane, and H represents the flight altitude of the drone. We assume that the drone flies at a fixed altitude H>0 during the execution of the computing task. The drone working at this altitude can avoid all obstacles in the working area without frequent ascent and descent. Ground equipment With drones The wireless channel between them can be simulated using the free space path loss model, which has been verified by recent field trials by Qualcomm. Therefore, the wireless channel gain between them is

[0018]

[0019] in represents the spatial distance between the ground device m and the UAV n, and φ0 represents the wireless channel gain per unit spatial distance. The transmission rate of the wireless channel between the ground device m and the UAV n is

[0020]

[0021] Where B represents the wireless channel bandwidth, P m represents the transmission power of ground equipment m, σ 2 is the Gaussian white noise power in the wireless channel.

[0022] Define a binary variable To represent the access relationship between ground equipment and UAV, where ξ m,n ∈{0,1} represents the access relationship between ground device m and UAV n. When ground device m decides to offload the computing task to UAV n for execution, ξ m,n =1, otherwise ξ m,n = 0. We assume that each ground device only offloads the computing task to one UAV for execution, that is,

[0023]

[0024] In addition, due to the limited parallel computing capability of drones, we limit the number of tasks received by each drone during the execution of computing tasks to not exceed its maximum parallel number N. max , that is, there are the following constraints

[0025]

[0026] Ground equipment The computational task A m You can use a positive tuple m ,C m ,O m ,D m > indicates that I m Indicates A m The size of the input data (such as program code and input parameters) in bits; C m Indicates A m The computational complexity is the number of CPU cycles required to calculate each bit of input data, in cycles / bit. m Indicates A m The size of the calculation result of is in bits; D m Indicates A m ​The maximum tolerable delay is in seconds. The characteristics of the computing task are determined by the device that generates it, that is, the input data size, computing complexity, computing result size and maximum tolerable delay of each computing task are different. In addition, in order to ensure the working efficiency and service quality of ground equipment, the task execution time exceeding the maximum tolerable delay is not allowed.

[0027] Assume that the computing task of each ground device can be divided into two parts, which are performed by the ground device and the UAV respectively. The unloading ratio is λ m Indicates that the calculation task A m There is λ m I m bits of input data are offloaded to the drone for execution, with (1-λ m )I m The input data of bits is executed on the ground equipment. Obviously, λ m The size needs to satisfy the following constraints

[0028]

[0029] Considering that drones can provide edge computing services for ground equipment, the computing tasks of ground equipment can be calculated in two ways: local computing on the ground equipment and offloading to drones.

[0030] Since local computation at the ground device does not require radio resources such as bandwidth, each ground device can perform local computation and computation offloading simultaneously. The CPU clock frequency during the execution of the computing task is used (in Hz) indicates that the computing task A m The local computation delay of input data is

[0031]

[0032] When the ground equipment offloads part of the input data of the computing task to the UAV for execution, the delay generated is composed of three parts: (1) the communication delay generated by the transmission of the computing task input data from the ground equipment to the UAV; (2) the computing delay generated by the execution of the computing task input data on the UAV; (3) the communication delay generated by the calculation result from the UAV to the ground equipment. In particular, compared with the input data, the size of the calculation result is often very small, and the communication delay generated by the output calculation result is very small, so we ignore the communication delay generated by this process. Ignoring the return process of the calculation result can greatly reduce the complexity of the model, which has been adopted by many studies. Therefore, the computing task A m The total delay of the partial input data calculated on the drone is

[0033]

[0034] where λ m I m / R m,n represents the transmission delay of the mission input data from the ground device m to the UAV n; λ m I m C m / f m,n Represents computing task A m Execution delay on the drone; f m,n Indicates that drone n performs mission A m The CPU clock frequency when inputting data. To simplify the model, we assume that each drone distributes computing resources evenly to the received computing tasks, that is,

[0035]

[0036] in Indicates the maximum CPU clock frequency of drone n.

[0037] In summary, the calculation task A m The execution completion time is

[0038]

[0039] The average task response time is defined as the average completion time of all computing tasks in the system, that is,

[0040]

[0041] In this method, given the system parameters ( A,f L ,u GD ,φ0,B,P,σ 2 ,N max ,f max ), we expect to deploy the UAV at position u UAV , the ground equipment access relationship ξ and the computing task offloading ratio λ are optimized to minimize the average task response time. The above joint optimization problem can be formally defined as follows:

[0042]

[0043] Constraint C1 means that the computing task of each ground device must be completed before its maximum tolerable delay; constraints C2 and C3 respectively represent the computing task offloading ratio and the value range of the access variable between the ground device and the UAV; constraint C4 means that each ground device only offloads the computing task to one UAV for execution; constraint C5 means that the number of tasks received by each UAV cannot exceed its maximum parallel processing number.

[0044] The method of the present invention proposes an alternating iterative algorithm based on block coordinate descent (BCD) and successive convex approximation (SCA) to solve the UAV deployment and computational offloading problems in a multi-UAV enabled mobile edge computing system. The algorithm decomposes the above problem into three sub-problems of UAV deployment optimization, ground equipment access optimization, and computational task offloading optimization through BCD, and obtains the approximate optimal solution of the original problem by alternately solving the three sub-problems.

[0045] The first sub-problem P2 of the original problem P1 is to solve the optimal UAV deployment plan u under the given ground equipment access relationship ξ and the computing task offloading plan λ. UAV In this subproblem, the optimization variable u in the original problem UAV , ξ and λ no longer exist, and the local execution time of the calculation task is known. The problem can be formalized as follows:

[0046]

[0047] For the above problem P2, since R m,n About variable u UAV is non-convex, so its objective function and constraint C6 are non-convex. The problem is still about the variable u UAV In order to solve this problem, we first introduce a non-negative auxiliary variable μ = {μ m |m∈M}, where represents the computing task completion time of ground equipment m, and rewrites problem P2 as

[0048]

[0049] Obviously, the problem P 2.1 The objective function is a convex function of the variable μ, and the constraint C8 is a convex constraint on the variable μ. Next, in order to transform the non-convex constraint C7 into a convex constraint, another non-negative auxiliary variable z = {z m,n |m∈M,n∈N}, let problem P 2.1 Convert to

[0050]

[0051] In question P 2.2 In the example, the original non-convex constraint C7 is transformed into constraint C9, and constraint C11 is added. Constraint C9 is a convex constraint for both variables μ and z, while for constraint C11, parameter R m,n About variable u UAV The non-convex problem is still not solved. In order to further transform the constraint condition C11 into a convex constraint, based on SCA, we m,n Perform a first-order Taylor expansion on the given UAV deployment plan to obtain R m,n The lower bound value of is expressed as

[0052]

[0053] in represents R obtained by first-order Taylor expansion m,n Lower bound value, represents the position vector of the mth GD, C m,n (t) and D m,n (t) respectively represent the transmission speed R in the tth iteration m,n The first-order coefficient and constant term coefficient of the Taylor expansion are specifically expressed as:

[0054]

[0055]

[0056] in is the deployment position of UAV n given in the tth iteration, and its size depends on the deployment position of UAV n obtained in the previous iteration.

[0057] By taking the lower bound Replacement constraint R in C11 m,n , we can solve the problem P 2.2 Convert to

[0058]

[0059] Transformed question P 2.3 is about the variable u UAV , the convex optimization problem of μ and z can be solved using existing toolkits (such as the CVX toolkit).

[0060] The second sub-problem of P1, P3, is to solve the UAV deployment position u obtained by solving P2. UAVGiven the computing task offloading ratio λ in P2, solve the optimal access relationship ξ between ground equipment and UAVs. Under this condition, the local execution time of the computing task And the transmission rate R between any UAV n and ground device m m,n is known, so the optimization variable u in the original problem UAV The coupling relationship between ξ and λ no longer exists, and the problem can be formalized as follows:

[0061]

[0062] However, since the variable to be optimized ξ is a discrete binary variable, this problem is a non-convex optimization problem about the optimization variable ξ. To further solve this problem, we first relax the binary optimization variable ξ into a continuous variable And transform problem P3 into problem P as follows 3.1

[0063]

[0064] The above question P 3.1 It's about variables The convex optimization problem can be solved using existing tools (such as the CVX toolkit). It should be noted that solving the problem P 3.1 The obtained access matrix does not satisfy constraint C14 in P3. To solve this problem, we use a meta-integration algorithm based on a greedy strategy to solve problem P 3.1 The obtained access matrix Transformed into an access matrix that satisfies all constraints in P3 The detailed steps of the meta-integration algorithm based on the greedy strategy are shown in Algorithm 1.

[0065]

[0066]

[0067] The main steps of the greedy strategy-based meta-integration algorithm are as follows. First, the access matrix Initialized to a size The same zero matrix (row 1); then according to the original access matrix Iterate in units of row vectors to find The position corresponding to the maximum value in each row will be The value of this position in is set to 1 (lines 2-6); after the above steps are executed, it can be guaranteed Constraints C16 and C17 of problem P3 are satisfied. Next, check in column vector units Whether constraint C18 is satisfied. When the constraints are not met, that is, when a UAV is overloaded, the ground equipment connected to the overloaded UAV is switched to other UAVs with lower loads (lines 7-17); finally, the access matrix is ​​returned (Line 18).

[0068] The third sub-problem P4 of problem P1 is to solve the UAV deployment position u obtained by solving P2. UAV Under the conditions of solving P3 and the access matrix ξ between ground equipment and UAVs, the optimal computing task offloading ratio λ is solved. Under this condition, any UAV n allocates computing resources f to ground equipment m. m,n And the transmission rate R between the two m,n is known, so the optimization variable u in the original problem UAV The coupling relationship between ξ and λ no longer exists, and the problem can be formalized as follows:

[0069]

[0070] The above problem P4 is a convex optimization problem about the variable λ. However, since the objective function of this problem contains a non-differentiable piecewise linear function, the commonly used Lagrangian method is not applicable to this problem. Sometimes Right now is the non-differentiable point of the objective function and also the minimum point of the objective function. Therefore, by solving the equation The optimization variable λ can be obtained m The general expression of is:

[0071]

[0072] Based on the solution of the above sub-problems, we propose an alternating optimization algorithm based on BCD and SCA (Alternating Optimization empowered BCD and SCA, AO-BS) to quickly solve the original problem P1 to obtain its approximate optimal solution. In this algorithm, by alternately solving the sub-problems P2, P3 and P4 of P1, the deployment position u of the drone is realized. UAV , ground equipment access relationship ξ and optimization of computing task offloading ratio λ. The specific implementation steps of the algorithm are shown in Algorithm 2.

[0073]

[0074] The algorithm first initializes the ground equipment access relationship according to the principle of the closest spatial distance (line 2), and randomly sets the offloading ratio of each computing task (line 4). Next, the three sub-problems of the original problem are solved, including: First, using ξ and λ obtained in the previous iteration as input, and solving problem P2 to obtain u UAV (Line 9); Secondly, u is obtained from the previous iteration UAV and λ as input, ξ is obtained by solving problem P3 (line 10), and is converted into an access matrix that meets the constraints through Algorithm 1 (lines 11-12); then, u is obtained by the above UAV and ξ are input, and λ is obtained by solving problem P4 (line 13); finally, u UAV , ξ, λ and formula (10) to calculate the average task response time. The condition for the end of the loop is that the difference between the results of two loops is less than the accuracy threshold ε or the number of loops reaches the maximum value iter max (Line 15). The algorithm finally returns the minimum average task response time found (Line 16).

[0075] The present invention has advantages in algorithm convergence, algorithm execution efficiency and system performance. It can generate a joint optimization solution within a few seconds and can be used in a drone-assisted mobile edge computing system composed of multiple drones and multiple ground devices. It can make quick decisions on the deployment location of the drone and the task offloading plan of ground users to reduce the average response time of computing tasks of various ground devices in the system.

[0076] In order to verify the effectiveness of the AO-BS algorithm proposed in this invention, a simulation experiment was conducted in a simulation environment. In particular, the following research questions were verified through simulation experiments:

[0077] 1. Whether AO-BS converges when solving the target optimization problem.

[0078] 2. Whether AO-BS has performance advantages over other advanced algorithms when solving target optimization problems.

[0079] 3. When using AO-BS to solve the target optimization problem, is the optimization solution of the three sub-problems effective?

[0080] In the simulation experiment, consider a block of size 200×200m 2The CPU clock frequency of the ground users distributed in this area is 0.8-1.2 GHz, and the maximum CPU clock frequency of all drones is set to 2.5 GHz. The input data size of all computing tasks in the system meets the random distribution within 10-15 Mbit, and the computational complexity and maximum tolerable delay of the computing tasks are set to 80-120 cycle / bit and 2s respectively. Other system parameter settings are shown in Table 1.

[0081] Table 1 Simulation parameter settings

[0082]

[0083] exist Figure 2 The results of the average system response time obtained by the proposed AO-BS algorithm as a function of iterations are shown in Figure 2. It can be seen that no matter what system scenario, the AO-BS proposed in this invention can quickly converge to an approximate optimal solution for the average task response time. Specifically, from Figure 2 From the curves corresponding to the 9 system scenarios (a)-(c), it can be seen that when the number of ground devices is fixed and the number of drones changes, the proposed alternating optimization algorithm can converge to an approximate optimal solution. Figure 2 It can be seen from (d)-(f) that when the number of UAVs is fixed and the number of ground equipment changes, the proposed alternating optimization algorithm can still converge to an approximate optimal solution. The above experimental results well verify the proof of algorithm convergence in Chapter 4.

[0084] In addition, from Figure 2 It can also be seen that no matter what system scenario, AO-BS can converge to a stable solution after about 6 iterations. Therefore, in the following simulation experiments, unless otherwise specified, AO-BS executes 6 iterations by default.

[0085] In order to verify the performance advantages of AO-BS, we introduce the following advanced algorithms from related research works for comparison:

[0086] One2One: This algorithm is similar to AO-BS. It also decomposes the target optimization problem into three sub-problems: UAV deployment, ground equipment access, and computing task offloading. It uses the following three sub-algorithms to optimize and solve them: ① One-to-one exchange matching method to achieve UAV deployment position optimization ② Lagrangian dual decomposition method to achieve ground equipment access optimization ③ Greedy algorithm to achieve computing task offloading rate optimization.

[0087] K-PSO-GA: In this algorithm, the deployment plan of the drones is determined by the K-means algorithm, and the access relationship and computational offloading ratio are optimized by PSO-GA. The relevant parameters are set as follows: the population size and the maximum number of iterations are 50 and 1000, respectively; the maximum and minimum values ​​of the inertia weight are 0.8 and 0.2, respectively; the maximum and minimum values ​​of the individual cognitive factor and the global cognitive factor are 0.9 and 0.2, respectively.

[0088] Figure 3 The average task response time comparison between AO-BS and other advanced algorithms for comparison in different system scenarios is shown. Figure 3 It can be seen from (a)-(c) that when the number of UAVs in the system (i.e., N) is constant, the average task response time will increase as the number of ground devices increases. This is because when the total number of ground devices in the system increases, each UAV needs to provide computing services for more ground devices. According to equation (8), this will result in less computing resources allocated by the UAV to a single ground device, which in turn increases the computing time of the computing task, ultimately affecting the average task response time. Figure 3 The simulation results shown in (a)-(c) show that, when the number of UAVs is fixed, AO-BS reduces the average task response time by 15.27% and 5.97% respectively compared with One2One and K-PSO-GA. AO-BS has obvious performance advantages in the above cases.

[0089] In addition, from Figure 3 From (d)-(f), we can see that when the number of ground devices in the system (i.e., M) is constant, the average task response time decreases as the number of drones increases. The reason for this phenomenon is that when the number of ground devices that need computing services in the system remains unchanged and the total number of deployed drones increases, the number of ground devices that a single drone needs to serve decreases. From equation (8), we can see that drones can allocate more computing resources to ground devices, so in this case the computing time of the computing task is reduced, which ultimately affects the average task response time. Figure 3 The simulation results shown in (d)-(f) show that, when the number of ground equipment is fixed, AO-BS reduces the average task response time by 15.29% and 5.90% compared with One2One and K-PSO-GA, respectively.

[0090] Specifically, when deploying UAVs, the One2One algorithm only uses the center of each sub-area as a candidate deployment point. Although this greatly reduces the solution space, it also affects the quality of the solution. In addition, when making decisions on computing task offloading, the strategy adopted by the One2One algorithm cannot fully consider the utilization of computing resources. Although the K-PSO-GA algorithm optimizes UAV deployment, ground equipment access relations, and computing task offloading, the optimization of average task response time is still slightly inferior to AO-BS because both K-Means and PSO-GA have the disadvantage of being easily trapped in local optimality. Compared with One2One and K-PSO-GA, AO-BS jointly optimizes UAV deployment, ground equipment access relations, and computing task offloading while ensuring convergence, fully considering the mutual influence between optimization variables, and can obtain an approximate optimal solution to the target problem. Figure 3 The experimental results in also prove this point.

[0091] Figure 4 The execution time comparison between AO-BS and other advanced algorithms for comparison in different system scenarios is shown. From the simulation results shown in the figure, it can be seen that the execution time of K-PSO-GA in the same system scenario is much longer than that of AO-BS, while the execution time of One2One is close to that of AO-BS. When deploying drones, One2One divides the target area evenly and only uses the center of the divided sub-area as the candidate deployment point, which greatly reduces the number of possible deployment plans, so its algorithm complexity is low. The PSO-GA algorithm in K-PSO-GA is a meta-heuristic search algorithm, which requires multiple iterations to ensure the quality of the solution, so its execution time is much longer than One2One and K-PSO-GA.

[0092] Combination Figure 3 and Figure 4 From the simulation results, we can see that although the optimization effect of K-PSO-GA on the average task response time is close to that of AO-BS, the execution time of the algorithm is too long, which is not conducive to its application in practical environments; the execution time of One2One in each system scenario is close to that of AO-BS, but the optimization effect on the average task response time is poor. In summary, AO-BS has obvious performance advantages over the advanced algorithms used for comparison.

[0093] In addition, in order to verify the effectiveness of the three optimization stages in AO-BS, we compare AO-BS with several of its variant algorithms. The variant algorithms of AO-BS used for comparison are:

[0094] Variant algorithm 1 (VA1): In this variant algorithm, for problem P2, a random deployment strategy is used to give a UAV deployment plan. The optimization solutions for problems P3 and P4 are consistent with AO-BS. The specific process of this variant algorithm is as follows: first, a UAV deployment plan is randomly given, then the ground equipment access plan is initialized using the nearest access principle, and finally P3 and P4 are solved alternately according to the relevant steps in Algorithm 2. Due to the randomness of this plan, we take the average of 100 repeated experimental results as the final result.

[0095] Variant algorithm 2 (VA2): In this variant algorithm, for problem P3, the nearest access principle is used to give a computing task offloading deployment plan. The optimization solutions for problems P2 and P4 are consistent with AO-BS. The specific process of this variant algorithm is as follows. First, the UAV deployment plan is randomly initialized, and then the ground equipment access plan is initialized using the nearest access principle. Finally, the following steps are looped: 1) P2 and P4 are solved alternately according to the relevant steps in Algorithm 2; 2) The ground equipment access plan is given using the nearest access principle; 3) P4 is solved alternately according to the relevant steps in Algorithm 2.

[0096] Variant algorithm 3 (VA3): In this variant algorithm, for problem P4, a binary offloading strategy is used to give a computing task offloading deployment plan. The optimization solutions for problems P2 and P3 are consistent with AO-BS. The specific process of this variant algorithm is as follows. First, the UAV deployment plan is randomly initialized, and then the ground equipment access plan is initialized using the nearest access principle. Finally, the following steps are executed in a loop: 1) According to the relationship between the execution time of the computing task locally and on the UAV, a computing task offloading plan is given; 2) P2 is solved alternately according to the relevant steps in algorithm 2; 3) P3 is solved alternately according to the relevant steps in algorithm 2; 3) According to the relationship between the execution time of the computing task locally and on the UAV, a computing task offloading plan is obtained.

[0097] Figure 5 The comparison of average task response time obtained by AO-BS and its variant algorithms in different system scenarios is shown. Figure 5 In the corresponding multiple system scenarios, AO-BS reduces the average task response time by 13.62% compared with VA1. This is because in VA1, the UAV deployment plan is obtained by a random deployment strategy. Although it also optimizes the ground equipment access and computing task offloading, it can only reflect the average level of all UAV deployment plans. This also verifies that AO-BS is effective in optimizing UAV deployment. Figure 5In the corresponding multiple system scenarios, AO-BS can reduce the average task response time by 5.09% and 42.94% respectively compared with VA2 and VA3, with significant performance improvement. In VA2, ground equipment is connected to the UAV based on the principle of nearest access. Although the algorithm jointly optimizes and solves the UAV deployment and computing task offloading, the nearest access principle may cause the UAV to overload and reduce the task processing efficiency. In VA3, the computing tasks are only offloaded as a whole, and the computing resources of GD and UAV cannot be fully utilized. By comparing with VA2 and VA3, it is verified that AO-BS is effective in optimizing ground equipment access and computing task offloading.

[0098] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A joint optimization method for UAV deployment and computation offloading based on convex optimization, characterized in that: The joint optimization problem is decomposed into three sub-problems: UAV deployment optimization, ground equipment access optimization, and computing task offloading optimization. The approximate optimal solution of the joint optimization problem is obtained by alternately solving the three sub-problems to minimize the average task response time. The specific implementation of this method is as follows: Given the system parameters, it is expected that the UAV deployment position u UAV , the ground equipment access relationship ξ and the computing task offloading ratio λ are optimized to minimize the average task response time; The joint optimization problem of UAV deployment, ground user access, and computing task offloading can be formally defined as follows: Constraint C1 means that the computing task of each ground device must be within its maximum tolerable delay D m Constraints C2 and C3 represent the computing task offloading ratio and the value range of the access variable between the ground equipment and the UAV respectively; Constraint C4 means that each ground equipment only offloads the computing task to one UAV for execution; Constraint C5 means that the number of tasks received by each UAV cannot exceed its maximum parallel processing number N max ; and and represent all ground devices and UAVs in the multi-UAV-enabled mobile edge computing system, respectively. M is the total number of ground devices and N is the total number of UAVs. The deployment locations of all UAVs in the multi-UAV-enabled mobile edge computing system are represented by express, is the deployment location of UAV n, and It is used to indicate the deployment position of UAV n on the horizontal plane, and H represents the flight altitude of the UAV; ξ m,n ∈{0,1} represents the access relationship between ground device m and UAV n. When ground device m decides to offload the computing task to UAV n for execution, ξ m,n =1, otherwise ξ m,n =0; Ground equipment The unloading ratio is λ m Indicates ground equipment The computational task is A m Represents; computing task A m The execution completion time is t m express, Represents computing task A m The local computation latency of the input data, Represents computing task A m The total delay of computing some input data on the drone; The joint optimization problem P1 is decomposed into three sub-problems: UAV deployment optimization, ground equipment access optimization, and computing task offloading optimization, namely P2, P3, and P4; P2 is to solve the optimal UAV deployment plan u under the conditions of given ground equipment access relationship ξ and computing task offloading ratio λ UAV ; In P2, the variable u in P1 is optimized UAV , ξ and λ no longer exist, and is known; P2 can be formalized as follows: represents the transmission delay of the mission input data from the ground device m to the UAV n, represents the execution delay of the computing task Am on the drone; fm,n represents the CPU clock frequency when drone n executes the input data of task Am; R m,n represents the transmission rate of the wireless channel between ground device m and UAV n; B represents the bandwidth of the wireless channel, Pm represents the transmission power of the mth ground device, σ 2 is the Gaussian white noise power in the wireless channel; represents the spatial distance between the ground device m and the UAV n, φ0 represents the wireless channel gain per unit spatial distance; For P2, due to R m,n About variable u UAV is non-convex, so its objective function and constraint C6 are non-convex. The problem is still about the variable u UAV non-convex optimization problem; To solve P2, we first introduce a non-negative auxiliary variable μ = {μ m |m∈M}, where represents the computing task completion time of ground equipment m, and P2 is rewritten as: Obviously P 2.1 The objective function is a convex function of the variable μ, and the constraint C8 is a convex constraint on the variable μ. In order to transform the non-convex constraint C7 into a convex constraint, another non-negative auxiliary variable z = {z m,n |m∈M,n∈N}, P 2.1 Translates to: In P 2.2 In the example, the original non-convex constraint C7 is transformed into constraint C9, and constraint C11 is added; constraint C9 is a convex constraint for both variables μ and z, and for constraint C11, parameter R m,n About variable u UAV The non-convex problem is still not solved. To further transform the constraint C11 into a convex constraint, based on SCA, the transmission speed R m,n Perform a first-order Taylor expansion on the given UAV deployment plan to obtain R m,n The lower bound value of is specifically expressed as: in represents R obtained by first-order Taylor expansion m,n Lower bound value, represents the position vector of the mth ground device, C m,n (t) and D m,n (t) respectively represent the transmission speed R in the tth iteration m,n The first-order coefficient and constant term coefficient of the Taylor expansion are specifically expressed as: in is the deployment position of UAV n given in the tth iteration, and its size depends on the deployment position of UAV n obtained in the previous iteration; By taking the lower bound Replacement constraint R in C11 m,n , P 2.2 Convert to The transformed P 2.3 is about the variable u UAV , convex optimization problem of μ and z; P3 is the UAV deployment position u obtained by solving P2 UAV Given the computing task offloading ratio λ in P2, solve the optimal access relationship ξ between ground equipment and UAVs; in P3, And the transmission rate R between any UAV n and ground device m m,n is known, and the optimization variable u in P1 UAV The coupling relationship between ξ and λ no longer exists; P3 can be formalized as follows: However, since the variable to be optimized ξ is a discrete binary variable, P3 is a non-convex optimization problem about the optimization variable ξ. To further solve P3, we first relax the binary optimization variable ξ into a continuous variable And transform P3 into the following problem P 3.1 : The transformed P 3.1 It's about variables Convex optimization problem; since solving P 3.1 The obtained access matrix does not satisfy the constraint C14 in P3, so a meta-integration algorithm based on a greedy strategy is used to solve the problem P 3.1 The obtained access matrix Transformed into an access matrix that satisfies all constraints in P3 P4 is the UAV deployment position u obtained by solving P2 UAV Under the conditions of solving the access matrix ξ between the ground equipment and the UAV obtained in P3, solve the optimal computing task offloading ratio λ; in P4, any UAV n allocates computing resources f to the ground equipment m m,n And the transmission rate R between the two m,n is known, and the optimization variable u in P1 UAV , ξ and λ no longer exist; P4 can be formalized as follows: The above P4 is a convex optimization problem about the variable λ. Since the objective function of P4 contains a non-differentiable piecewise linear function, by solving the equation The optimization variable λ can be obtained m The general expression of is: Based on the above solutions to P2, P3, and P4, an alternating optimization algorithm AO-BS based on BCD and SCA is proposed to quickly solve P1 to obtain its approximate optimal solution; in AO-BS, the sub-problems P2, P3, and P4 of P1 are alternately solved to achieve the optimal solution of the UAV deployment position u UAV , ground equipment access relationship ξ, and optimization of computing task offloading ratio λ to minimize the average task response time.

2. The joint optimization method for UAV deployment and computation offloading based on convex optimization according to claim 1 is characterized in that: The joint optimization problem is decomposed into three sub-problems: UAV deployment optimization, ground equipment access optimization and computing task offloading optimization through the block coordinate descent method.

3. The joint optimization method for UAV deployment and computation offloading based on convex optimization according to claim 1 is characterized in that: P 2.3 , P 3.1 The CVX toolkit is used for solving.

4. The joint optimization method for UAV deployment and computation offloading based on convex optimization according to claim 1 is characterized in that: The implementation steps of the greedy strategy-based meta-integration algorithm are as follows: first, the access matrix Initialized to a size The same zero matrix; then according to the original access matrix Iterate in units of row vectors to find The position corresponding to the maximum value in each row will be The value of this position in is set to 1; next, check in units of column vectors Whether constraint C18 is satisfied; when When the constraints are not met, that is, when a drone is overloaded, the ground equipment connected to the overloaded drone is switched to other drones with lower loads; finally, the access matrix is ​​returned.

5. The joint optimization method for UAV deployment and computation offloading based on convex optimization according to claim 1 is characterized in that: The implementation steps of the AO-BS are as follows: first, the ground equipment access relationship is initialized according to the principle of the shortest spatial distance, and the offloading ratio of each computing task is randomly set; then, the three sub-problems of P1 are solved, specifically including: first, taking ξ and λ obtained in the previous iteration as input, u is obtained by solving P2 UAV ; Secondly, the u obtained in the previous iteration UAV and λ as input, ξ is obtained by solving problem P3, and is converted into an access matrix that meets the constraints through a greedy strategy-based meta-integration algorithm; then, the obtained u UAV and ξ are input, and λ is obtained by solving P4; finally, u UAV , ξ, λ calculate the average task response time; the condition for the end of the loop is that the difference between the results of two loops is less than the accuracy threshold ε or the number of loops reaches the maximum value iter max ; The algorithm finally returns the minimum average task response time solved.

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