Multi-objective Optimization for Multi-UAV-assisted Mobile Edge Computing

1 INTRODUCTION

• Multi-UAV-assisted MEC offers flexible, low-cost offloading through UAV maneuverability, fast deployment, and line-of-sight links.Terrestrial MEC infrastructure can be inflexible to deploy because of installation costs and environmental limitations.Source: §1 · p. 1
• The design must accommodate heterogeneous user requirements while allocating limited UAV computing resources and managing finite onboard energy and flight endurance.The paper also identifies multi-objective optimization and the convergence and training burden of machine-learning methods as challenges.Source: §1 · pp. 1–2
• The optimization jointly minimizes total task completion delay and UAV energy consumption while maximizing offloaded tasks through task offloading, resource allocation, and trajectory control.The problem is formulated as non-convex and mixed-integer nonlinear.Source: §1 · p. 2
• JTORATC splits the coupled decisions into three sub-problems, using distributed splitting and threshold rounding for offloading, KKT for resource allocation, and SCA for trajectory control.The paper states that this approach reduces problem complexity and improves solution efficiency.Source: §1 · p. 2
• JTORATC outperforms benchmark schemes in objective value, total task completion delay, and total UAV energy consumption, with better scalability in the considered scenarios.The paper reports simulation results for these comparisons.Source: §1 · p. 2

2 RELATED WORK

• The related-work review covers MEC, UAV-assisted MEC, task offloading, resource allocation, trajectory control, and optimization approaches.Table 1 is identified as comparing related works with this work.Source: §2 · p. 2, Table 1 · p. 3
• Earlier MEC studies considered fixed edge infrastructure, while cited UAV-assisted MEC studies often focused on single-server systems.These settings may not apply to remote or large-scale scenarios with many users.Source: §2 · p. 2
• Some multi-UAV MEC studies optimized offloading and resource allocation while keeping UAVs stationary or on predetermined trajectories.The paper notes this may not suit dynamic or cooperative flight scenarios.Source: §2 · p. 3
• Other work incorporated trajectory control, but some studies focused on UAV deployment rather than trajectory optimization.The paper argues that this may limit real-time control in dynamic and complex environments.Source: §2 · p. 3
• The paper notes that existing optimization methods can have high computational complexity, especially in large-scale systems or complex dynamic environments.It adopts distributed splitting, threshold rounding, KKT, and SCA to reduce complexity.Source: §2 · p. 3
• The paper identifies prior-work gaps in single-objective optimization, partial decision-variable coverage, and high algorithmic complexity.Its proposed formulation jointly minimizes delay and UAV energy consumption while maximizing offloaded tasks.Source: §2 · p. 3

3 SYSTEM MODEL AND PROBLEM FORMULATION

• The section presents the system model, followed by mobility, communication, and computation models.Source: §3 · p. 4
• It then formulates the multi-objective optimization problem.Source: §3 · p. 4
• Table 2 lists system-model notation for readability.Source: §3 · p. 4

3.1 System Model

• The system contains M rotary-wing UAVs and U users, with one or more MEC servers on each UAV.Source: §3.1 · p. 4
• The continuous timeline is divided into N equal-duration slots, and each user may generate a task per slot for local execution or UAV offloading.Source: §3.1 · p. 4
• Each task is characterized by its size in bits, computation intensity in cycles per bit, and deadline.Source: §3.1 · p. 4

3.2 Mobility Model

• UAVs fly at constant altitude H, with horizontal position, acceleration, and velocity specified for each time slot.Users are represented by horizontal coordinates in a 3D Cartesian coordinate system.Source: §3.2 · p. 4
• The mobility constraints cover position and velocity updates, speed limits, safe separation, identical initial and final positions, and a maximum flight distance per time slot.The maximum per-slot travel distance is Dmax = Vmaxδt.Source: §3.2 · p. 4

3.3 Communication Model

• The channel power gain for uplink communication incorporates probabilistic LoS transmission and accounts for small- and large-scale fading.The model distinguishes LoS and NLoS links and their respective channel gains.Source: §3.3 · p. 5
• Small-scale fading is modeled with a Nakagami distribution, using separate fading parameters for LoS and NLoS links.The fading parameter is denoted w in the Nakagami model.Source: §3.3 · p. 5
• The link model also includes LoS/NLoS path loss and zero-mean Gaussian shadowing, with separate shadowing deviations for each link type.Path loss depends on carrier frequency and user–UAV distance; the model uses reference distance and LoS/NLoS path-loss exponents.Source: §3.3 · p. 5
• The uplink data rate is defined from the communication model using channel bandwidth, user transmit power, and noise power.The supplied passage identifies these rate parameters but does not provide the full rate expression.Source: §3.3 · p. 5

3.4.1 Service Delay

• UAV-assisted service delay combines task transmission and processing delay, while local service delay depends on the user's computing capability.The total task completion delay aggregates user delays across time slots; result download delay is ignored because results are typically much smaller than input data [32].Source: §3.4.1 · p. 5

3.4.2 Energy Consumption

• UAV energy consumption includes energy for task execution and flight across the time slots.The model separately describes local-computing energy, UAV task-processing energy, and propulsion power.Source: §3.4.2 · pp. 5–6

3.4.3 Total Amount of Offloaded Tasks

• The total amount of offloaded tasks is treated as a measure of the service quality provided by UAVs.The passage introduces a calculation for this quantity.Source: §3.4.3 · p. 6

3.5 Problem Formulation

• The objective minimizes total task completion delay and UAV energy consumption while maximizing the total amount of offloaded tasks through joint optimization of offloading, resource allocation, and trajectories.The formulation includes task deadlines, UAV computing-resource limits, and mobility constraints.Source: §3.5 · p. 6
• Problem P is a non-convex, NP-hard MINLP involving binary task-offloading decisions and continuous resource-allocation and trajectory variables.The proof attributes non-convexity to constraints (1c) and (1d), making an optimal solution difficult to find and motivating JTORATC.Source: §3.5 · p. 6

4 THE PROPOSED JTORATC

• JTORATC alternates among task offloading, computation resource allocation, and UAV trajectory control, using distributed splitting and threshold rounding, KKT, and SCA, respectively.The block alternate descent method iteratively solves the three coupled subproblems.Source: §4 · p. 6

4.1 Problem Reformulation

• The right-of-use coefficient method combines delay, energy consumption, and offloaded-task amount into a single objective with adjustable non-negative weights.The reformulation is intended to reduce difficulty, avoid differences between metrics, and allow flexible objective trade-offs.Source: §4.1 · pp. 6–7

4.2 Task Offloading

• For task offloading, distributed splitting relaxes binary decisions into continuous variables, and threshold rounding converts the relaxed decisions back to binary values.With resource allocation and UAV trajectory fixed, the transformed task-offloading problem is a convex NLP.Source: §4.2 · p. 7

4.3 Computation Resource Allocation

• The computation-allocation subproblem is convex and is solved using KKT conditions, with a bisection algorithm used to obtain the resource allocation.The objective is convex with respect to the allocated computation resource.Source: §4.3 · p. 8

4.4 UAV Trajectory Control

• Successive convex approximation transforms the non-convex UAV trajectory subproblem into a convex problem using lower bounds and auxiliary variables.The transformed problem is stated not to change the subproblem's optimality.Source: §4.4 · p. 9

4.5 Main Steps of JTORATC and Analysis

• JTORATC initializes decisions and alternately solves task-offloading, resource-allocation, and trajectory subproblems to obtain updated decisions.The paper also states that it proves convergence and analyzes computational complexity.Source: §4.5 · p. 9

4.5.1 Convergence and Computation Complexity

• The objective is non-increasing after each iteration and finitely lower-bounded, with the paper reporting polynomial convergence for JTORATC.The non-increasing property is attributed to the subproblem updates and the sub-optimality of UAV trajectory control.Source: §4.5.1 · pp. 9–10

5.1 Simulation Setup

• Simulations in MATLAB R2022b evaluate a multi-UAV-assisted MEC system serving 8 users in a 2500 × 3000 m2 rectangular area, with 2, 4, or 6 UAVs over 100 s divided into 50 time slots.Benchmarks include random offloading and nearest-UAV offloading, with resource allocation and trajectory control based on JTORATC.Source: §5.1 · p. 10

5.2.1 System Performance

• As UAV count rises, objective value and UAV energy consumption increase for all approaches except NOJRATC, which simplifies scheduling and reduces trajectory conflicts.The authors link the general increase to more complex scheduling, resource competition, and trajectory conflicts.Source: §5.2.1 · pp. 10–11
• JTORATC maintains superior overall performance as the number of UAVs increases, while ERJOTC uses less energy but performs worse on objective value and delay.The authors attribute JTORATC’s advantage to jointly adapting offloading, resources, and trajectories; fixed circular and predefined trajectories also perform worse.Source: §5.2.1 · p. 11

5.2.2 Performance Evaluation

• With UAV computation capacity below 400 MHz, ERJOTC has a lower objective value; as capacity increases, JTORATC is superior on that metric.Below 600 MHz, ROJRATC also achieves lower total task completion delay than JTORATC; offloaded-task totals stay constant as capacity varies.Source: §5.2.2 · p. 11
• As task computation intensity rises, the approaches show upward trends in objective value, delay, and energy, while JTORATC outperforms them on objective value.ERJOTC performs best on UAV energy; all approaches maintain constant offloaded-task totals across varying intensity.Source: §5.2.2 · p. 12
• As task size increases, seven approaches trend upward; ERJOTC outperforms JTORATC in objective value and completion delay, but performs worst above 3 MB and best in UAV energy consumption.Offloaded-task totals also rise with task size.Source: §5.2.2 · pp. 12–13
• As the number of users increases, all four reported metrics rise; JTORATC has the best objective value, while ROJRATC leads on delay but performs relatively poorly on energy and offloaded tasks.ERJOTC reduces UAV energy through even resource allocation, with a delay trade-off.Source: §5.2.2 · pp. 13–14

• JTORATC demonstrates superior performance in total task completion delay and total UAV energy consumption.Source: §6 · p. 14
• The optimization aims to minimize total task completion delay and UAV energy consumption while maximizing the amount of offloaded tasks.Source: §6 · p. 14
• The approach formulates a multi-objective problem and transforms it into a single-objective problem before applying JTORATC at lower cost.Source: §6 · p. 14
• JTORATC shows better adaptability with varying UAV computing capacities and superior scalability in light- and heavy-workload scenarios.Source: §6 · p. 14