In the context of complex dynamic scenarios such as forest fire monitoring, traditional fixed monitoring systems suffer from limited coverage, significant terrain interference, and rigid resource scheduling, which cannot meet the real-time and reliability requirements of emergency response. Unmanned aerial vehicles have become a key carrier for disaster monitoring due to their mobility and flexibility. However, in the research field of unmanned aerial vehicle-assisted mobile edge computing systems, existing studies mostly focus on static or single-device mobile scenarios, ignoring the collaborative mobility of terminal devices and edge devices as well as dynamic communication links and real-time constraints on resource allocation. Moreover, most optimization objectives are single-metric, such as latency or energy consumption alone, neglecting the joint optimization of task completion time, energy efficiency, and load balancing. To address these challenges, I propose an unmanned aerial vehicle-assisted edge computing framework based on movable ends and edges, focusing on task offloading and resource scheduling optimization in forest fire monitoring scenarios.
First, I establish an edge computing model based on a parallel-moving unmanned aerial vehicle and a circular-moving mobile terminal, and implement a computation offloading strategy using a genetic algorithm. The system model integrates the unmanned aerial vehicle flight trajectory, mobile terminal movement path, computational resource allocation, and task offloading decisions. The system cost combines task completion time and energy consumption, and an optimization problem is formulated to minimize this cost. Through population initialization, fitness evaluation, selection, crossover, and mutation, the genetic algorithm dynamically allocates computational tasks under dynamic communication link constraints, safety distance constraints between unmanned aerial vehicles, and real-time resource allocation conditions, balancing latency and energy consumption.
Second, I propose an edge computing model for unmanned aerial vehicles and mobile terminals under multiple motion modes. The unmanned aerial vehicle motion modes include circular flight, zigzag flight, etc. The mobile terminal motion model includes linear and circular motions. I analyze the impacts of different motion modes on task delay, energy consumption, and coverage efficiency. A genetic algorithm is applied to encode task allocation schemes, and a fitness function is designed by considering task completion time, energy consumption, and load balancing. Tournament selection, partially mapped crossover, and targeted mutation are used to optimize task offloading and resource scheduling under multi-mode conditions.
Simulation results demonstrate that the proposed optimization strategies effectively reduce the average task execution delay, improve computational efficiency, and reduce the total system energy consumption in forest fire monitoring scenarios. The proposed work provides new ideas for end-edge collaboration in disaster monitoring and emergency communication, and also offers theoretical support for future intelligent optimization methods.
1 Introduction
The increasing frequency of extreme climate events and natural disasters has made real-time monitoring and emergency response in dynamic and complex environments a critical challenge. Forest fires, in particular, are typical because of their high occurrence and strong destructiveness. Every year, forest fires cause massive casualties, property losses, and ecological damage. Statistical data show that there are about 220,000 forest fires per year worldwide, affecting about 10 million hectares of forest, approximately 0.1% of the total forest area, and the scale and frequency have been increasing in recent decades. Forest fires not only destroy natural ecosystems but also lead to long-term environmental impacts such as air pollution and climate change. Therefore, early detection and rapid response are of great importance.
In traditional fire monitoring systems, detection equipment is usually deployed at fixed nodes in forests. These systems rely on fixed ground sensors and preset monitoring stations, such as towers, cameras, and meteorological stations, to collect environmental data in real time. Although these devices can work for a long time and provide reliable data, their fixed coverage areas are vulnerable to the dynamic propagation of fires. In complex terrain, sensor signals are easily interfered with by mountainous terrain and vegetation, leading to data transmission delays or losses, which significantly hampers real-time responses.
Cloud-based monitoring methods are also widely used, but their dependence on remote data centers causes high transmission delays and bandwidth bottlenecks, failing to meet the low-latency and high-reliability requirements of forest fire monitoring. Mobile edge computing has emerged as a new paradigm that moves computation and storage tasks to the network edge, significantly reducing data transmission delay and improving processing speed. MEC can effectively support large-scale distributed applications and provides new solutions for disaster monitoring.
However, even though MEC offers lower latency and efficient data processing, its resources are relatively limited compared to traditional cloud computing. How to efficiently manage these limited resources has become a key problem. Many works have been done on MEC resource management, aiming to optimize system latency, energy consumption, or the total cost of both. For example, joint optimization of unmanned aerial vehicle positions, communication and computational resource allocation has been studied to reduce service delays. Some researchers investigated task offloading in ultra-dense networks to minimize task duration under energy constraints. Others proposed resource allocation methods in multi-unmanned aerial vehicle MEC vehicular networks to optimize task processing latency. However, most of these works assume that edge resources are connected via wired or dedicated wireless links and that these resources are either statically deployed with sufficient bandwidth or only consider the mobility of a single device. These assumptions often do not hold in dynamic and complex disaster search and military reconnaissance scenarios where the number of mobile users increases sharply or network infrastructure is sparse.
Unmanned aerial vehicles, especially low-cost multirotor drones, have been widely used in traffic monitoring, public safety, and disaster reconnaissance due to their high mobility and flexibility. They have become an important tool for forest fire monitoring. UAVs have the advantages of rapid deployment, programmable operation, and scalability. They can cover large areas and carry various payloads such as cameras, small-cell bases, and embedded computing modules to perform different sensing, communication, and computing tasks. Moreover, UAVs can serve as wireless relays or aerial base stations to improve connectivity and extend coverage for ground wireless devices because their high altitude enables effective line-of-sight communication links, mitigating signal blockage and shadowing. If deployed and operated correctly, UAVs can provide reliable and cost-effective wireless communication solutions for many real-world scenarios.
Nevertheless, despite the advantages of UAV-assisted edge computing, several challenges still need to be solved. First, traditional fixed sensors may not respond quickly to changing fire areas in dynamic scenarios. Second, forest fire monitoring systems need to maximize monitoring efficiency and reduce energy consumption under limited resources and energy constraints. UAVs have limited endurance, and continuous large-scale monitoring tasks pose severe challenges. Existing research lacks a joint optimization of task offloading, trajectory planning, and resource allocation when both mobile terminals and mobile edge nodes are moving.
To address these gaps, I develop a collaborative work model in which both mobile terminals and mobile edge nodes are moving. The model aims to improve the system’s dynamic adaptability and coverage efficiency, achieving flexible task scheduling and resource management in fire monitoring. To optimize the task allocation problem, I also improve the genetic algorithm to solve a complex binary integer programming problem, minimizing time delay and energy consumption under limited resources. Compared with traditional methods, the proposed approach can flexibly adjust task allocation and resource scheduling according to real-time fire conditions and environmental changes, ensuring efficient and economical operation of the fire monitoring system in emergency situations.
2 Related Work
With the rapid development of mobile edge computing and especially in the field of UAV-assisted computation offloading, more and more research focuses on optimizing performance metrics such as offloading efficiency, energy consumption, and latency in resource-limited and complex dynamic environments. According to the mobility of devices and application scenarios, existing research can be classified into three categories: static edge and static terminal, only terminal mobile, and only edge mobile.
2.1 Static Edge and Static Terminal
In early MEC research, many works assumed that both edge devices and terminal devices are statically fixed. These works mainly focus on computation offloading, resource allocation, and task scheduling in fixed networks. For example, some researchers proposed efficient transmission-aware task scheduling and resource allocation algorithms under power-domain non-orthogonal multiple access. Others built deep Q-learning based autonomous computation offloading frameworks for IoT applications. Joint optimization of computation offloading and uplink/downlink resource allocation was also studied in time-division multiple access based MEC systems. However, these works often ignore device mobility and cannot effectively deal with dynamic environments. Some works attempted to include high interference and limited resources, but they still concentrated on static scenarios.
2.2 Only Terminal Mobile
With the continuous advancement of edge computing and mobile terminals, researchers have started to focus on scenarios where only the terminal device is mobile. These studies mainly address task offloading and resource allocation problems faced by mobile terminals in MEC systems. For instance, dynamic resource allocation algorithms based on Lyapunov optimization were proposed for heterogeneous IoT services with time-sensitive task demands. In NOMA-based MEC systems, online energy minimization offloading algorithms were developed to determine the optimal energy and data transmission time allocation. Some researchers jointly minimized the transmission and computation energy in NOMA NB-IoT networks. Learning-based intent-aware task offloading methods were also introduced. However, these studies generally ignore the mobility of edge devices, which is critical for fully exploiting the potential of MEC in dynamic environments.
2.3 Only Edge Mobile
Scenarios where only the edge device is mobile are another important research direction. In these works, UAVs are often used as mobile edge platforms, performing computation offloading, task assignment, and resource scheduling. For example, a task offloading scheme was proposed where UAVs provide offloading services only at specific times or positions, optimizing the overall energy consumption. Some researchers proposed a two-stage strategy to jointly optimize UAV trajectories, CPU frequencies, and offloading time allocations to minimize weighted energy consumption. Others optimized UAV trajectories and task offloading via optimal transport theory. Deep reinforcement learning methods have also been used to control offloading decisions. Despite these advances, most of these methods do not consider the simultaneous mobility of both the terminal and the edge devices, which is essential for fully dynamic environments.
3 Cooperative Optimization with Translation Edge and Circular Terminal
3.1 System Model
I consider a mobile edge computing system consisting of a set of unmanned aerial vehicles (UAVs) and a set of mobile ground sensor terminals. The ground sensor nodes acquire geographic information in real time and transmit the environmental data to UAVs. UAVs process the information during flight to construct a real-time map containing detailed terrain topology, assisting post-disaster prediction and emergency handling.
The system uses a decentralized scheduling strategy with precomputed global scheduling results. At the initial planning stage, a scheduling device randomly deploys nodes in a rectangular monitoring area to ensure no blind spots and stable data transmission. The scheduling device computes the task assignment and transmission paths for each node before deployment, and stores the scheduling results in the node memory. After deployment, the nodes only need to follow the preset scheduling scheme for data transmission and communicate seamlessly with UAVs.
Let \(\mathcal{M} = \{1,2,\ldots,M\}\) be the set of mobile terminals, \(\mathcal{U} = \{1,2,\ldots,U\}\) the set of UAVs, and \(\mathcal{T} = \{1,2,\ldots,T\}\) the set of time periods. UAVs execute a translation movement along a horizontal line and hover at the beginning of each time period.
| Symbol | Meaning |
|---|---|
| \(\mathcal{M}\) | Set of mobile terminals |
| \(\mathcal{U}\) | Set of UAVs |
| \(\mathcal{T}\) | Set of time periods |
| \(\theta_{step}\) | Angle increment of the terminal circular motion |
| \(t_u\) | Flight time of UAV |
| \(r_u\) | Coverage radius of UAV |
| \(q_u(t)\) | Horizontal coordinate of UAV \(u\) |
| \(p_u(t)\) | Propulsion power of UAV \(u\) |
| \(E_u^{fly}(t)\) | Propulsion energy of UAV \(u\) |
| \(L_m(t)\) | Data size of task generated by terminal \(m\) |
| \(C_m\) | Number of CPU cycles required for the task |
| \(f_{m,u}(t)\) | Computing resource allocated by UAV \(u\) to terminal \(m\) |
| \(z_{m,u}(t)\) | Binary variable indicating whether terminal \(m\) is connected to UAV \(u\) |
| \(d_{m,u}(t)\) | Distance between terminal \(m\) and UAV \(u\) |
| \(g_{m,u}(t)\) | Wireless channel power gain between terminal \(m\) and UAV \(u\) |
| \(r_{m,u}(t)\) | Transmission rate from terminal \(m\) to UAV \(u\) |
| \(D_{m,u}^{comm}(t)\) | Transmission delay for offloading task from terminal \(m\) to UAV \(u\) |
| \(E_{m,u}^{comm}(t)\) | Communication energy consumption for offloading |
| \(D_{m,u}^{comp}(t)\) | Computation time of UAV \(u\) for terminal \(m\) |
| \(D_{u,m}^{down}(t)\) | Downlink transmission time of the result |
| \(D_{u,m}^{wait}(t)\) | Waiting time for UAV to reconnect with terminal |
| \(D_{m,i}^{gene}(t)\) | Generation time of task \(i\) at terminal \(m\) |
| \(D_{m,i}(t)\) | Completion time of task \(i\) at terminal \(m\) |
| \(D_m(t)\) | Total completion time of all tasks on terminal \(m\) |
| \(D_{total}(t)\) | Total completion time of all tasks |
| \(E_{total}(t)\) | Total system energy consumption |
3.2 Mobile Terminal Model
Each mobile terminal moves in a circular path confined within a global rectangular area. The lower-left corner of the global rectangle is \((x_{min},y_{min})\) and the upper-right corner is \((x_{max},y_{max})\).
The initial position of terminal \(m\) is randomly generated as:
$$x_{center} = x_{min} + rand()*(x_{max}-x_{min})$$
$$y_{center} = y_{min} + rand()*(y_{max}-y_{min})$$
All terminals move at a constant speed \(v_m\). Each terminal follows a circular path with radius \(r\) around its initial position. The angular increment is
$$\theta_{step} = \frac{2\pi}{movesteps}$$
At each time step, the new position is computed by:
$$x_{next} = x_{center} + r \cos(\theta_{current})$$
$$y_{next} = y_{center} + r \sin(\theta_{current})$$
where \(\theta_{current}\) is updated by \(\theta_{current} = \theta_{current} + \theta_{step}\). This process is repeated until the required number of steps is reached.
3.3 UAV Movement Model
At the beginning of each time period, the UAV hovers at its current position and provides services to mobile terminals. The horizontal coordinate of UAV \(u\) at time \(t\) is defined as:
$$q_u(t) = (x_u(t), y_u(t))$$
The UAV has a coverage radius \(r_u\), a constant flight height \(H\), and a speed \(v_u\). The flight angle \(\alpha_u(t)\) is adjusted when the UAV reaches the boundary of the rectangular area so that it remains within the area. The position update equations are:
$$x_u(t) = x_u(t-1) + v_u t_u \cos(\alpha_u(t))$$
$$y_u(t) = y_u(t-1) + v_u t_u \sin(\alpha_u(t))$$
In the baseline model, translation motion is used: \(\alpha_u(t)=0^\circ\) for left-to-right flight and \(\alpha_u(t)=180^\circ\) for right-to-left flight. To maximize coverage, odd-numbered UAVs fly from left to right, while even-numbered UAVs fly from right to left.
3.4 Communication and Computation Models
The distance between mobile terminal \(m\) and UAV \(u\) is:
$$d_{m,u}(t) = \sqrt{H^2 + \|S_m(t) – q_u(t)\|^2}$$
The wireless channel power gain is:
$$g_{m,u}(t) = \beta d_{m,u}(t)^{-2}$$
where \(\beta\) is the channel power gain at reference distance \(d_0=1\) m.
The uplink transmission rate from terminal \(m\) to UAV \(u\) is:
$$r_{m,u}(t) = \frac{B_M}{M} \log_2\left(1+\frac{P_M g_{m,u}(t)}{\sigma^2}\right)$$
where \(B_M\) is the total bandwidth, \(P_M\) is the terminal transmit power, and \(\sigma^2\) is the noise power.
The offloading transmission time is:
$$D_{m,u}^{comm}(t) = \frac{z_{m,u}(t) L_m(t)}{r_{m,u}(t)}$$
The communication energy consumption of the terminal is:
$$E_{m,u}^{comm}(t) = D_{m,u}^{comm}(t) P_M$$
After computation, the UAV sends the result back to the terminal. The downlink transmission rate is:
$$r_{u,m}(t) = \frac{B_U}{M} \log_2\left(1+\frac{P_U g_{m,u}(t)}{\sigma^2}\right)$$
The downlink transmission time is:
$$D_{u,m}^{down}(t) = \frac{D_{m,i}^{result}(t)}{r_{u,m}(t)}$$
The downlink energy consumption is:
$$E_{u,m}^{down}(t) = D_{u,m}^{down}(t) P_U$$
If the UAV has already left the terminal’s coverage area after computing, a waiting time occurs. The waiting time is calculated based on the UAV flying to the boundary and returning:
$$D_{u,m}^{wait}(t) = 2 \cdot \frac{d_{toboundary}}{v_u}$$
where \(d_{toboundary}\) is the distance from the current horizontal coordinate to the right or left boundary of the region.
The computation time at the UAV is:
$$D_{m,u}^{comp}(t) = \frac{L_m(t) C_m z_{m,u}(t)}{f_{m,u}(t)}$$
The total completion time for task \(i\) on terminal \(m\) is:
$$D_{m,i}(t) = D_{m,i}^{gene}(t) + D_{m,u}^{comm}(t) + D_{m,u}^{comp}(t) + D_{u,m}^{down}(t) + D_{u,m}^{wait}(t)$$
For each terminal, the completion time is the maximum over its tasks:
$$D_m(t) = \max\{D_{m,1}(t), D_{m,2}(t), \ldots, D_{m,I}(t)\}$$
3.5 Optimization Problem
The total system cost is defined as the weighted sum of the total task completion time and the total system energy consumption:
$$C_{total} = \omega_D D_{total}(t) + \omega_E E_{total}(t)$$
where \(D_{total}(t) = \max_{m \in \mathcal{M}} D_m(t)\) and
$$E_{total}(t) = \sum_{m=1}^{M}\sum_{u=1}^{U} \left( E_{m,u}^{comm}(t) + E_u^{fly}(t) + E_{u,m}^{down}(t) \right)$$
The optimization problem is formulated as:
$$\min_{\{z_{m,u}(t)\}, \{f_{m,u}(t)\}} \quad \omega_D D_{total}(t) + \omega_E E_{total}(t)$$
subject to:
- \(0 \le \alpha_u(t) \le 2\pi, \forall u \in \mathcal{U}\)
- \(z_{m,u}(t) \in \{0,1\}, \sum_{u=1}^{U} z_{m,u}(t) \le 1, \forall m \in \mathcal{M}, \forall t \in \mathcal{T}\)
- \(f_{m,u}(t) \ge 0, \sum_{m \in \mathcal{M}} f_{m,u}(t) \le f_u^{max}, \forall u \in \mathcal{U}\)
- \(\|d_u(t) – d_{u’}(t)\| \ge d_{min}, \forall u, u’ \in \mathcal{U}, u \ne u’\)
The first constraint limits the flight angle. The second ensures that each terminal can connect to at most one UAV at any time. The third limits the allocated computing resources to the UAV’s capacity. The fourth enforces a minimum safety distance between UAVs.
3.6 Genetic Algorithm Design
I adopt a genetic algorithm to solve the optimization problem. Each individual in the population is a three-dimensional matrix of size \(T \times M \times U\), encoding the task allocation decisions.
Population initialization randomly assigns each terminal to one UAV or to no UAV at each time step, satisfying the connection constraint.
The fitness function is exactly the system cost:
$$Fitness = \omega_D D_{total}(t) + \omega_E E_{total}(t)$$
Selection uses roulette wheel selection, where the selection probability is proportional to the inverse of the fitness value, so better individuals have higher chances.
Crossover uses single-point crossover. A random crossover point is chosen, and the genetic material before and after the point is exchanged between two parents. The crossover rate is set to 0.8.
Mutation randomly changes the UAV assignment for a terminal at a certain time step, with a mutation rate of 0.2. This introduces new solutions and prevents premature convergence.
The evolution process runs for 200 generations. The algorithm is summarized as follows:
| Algorithm 1 | Genetic Algorithm for Task Offloading |
|---|
Input: number of terminals \(M\), number of UAVs \(U\), number of steps \(movesteps\), population size, generations, crossover rate, mutation rate.
Output: best individual and its fitness (minimum system cost).
- Initialize population randomly.
- For each generation:
- Evaluate fitness of each individual.
- Select parents using roulette wheel.
- Apply single-point crossover.
- Apply mutation.
- Create new population.
- Return the best individual.
3.7 Experimental Results
I simulate a rectangular area of 100m × 100m with 40 mobile terminals, 10 UAVs, and 25 movement steps. The terminal circular motion radius is 20m, UAV coverage radius is 50m. The algorithm is run for 50 generations.
Fig. 1 in the original thesis showed the fitness value change over generations. Over 30 independent runs, the fitness value decreases with the generation number, demonstrating the convergence and stability of the genetic algorithm. The average fitness per generation is shown below.
Table below shows a partial optimal task allocation scheme for the first 10 time steps and 20 terminals. The value indicates the UAV index connected to each terminal.
| Terminal | t0 | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 | t9 |
|---|---|---|---|---|---|---|---|---|---|---|
| m0 | 0 | 2 | 4 | 1 | 1 | 4 | 1 | 0 | 0 | 0 |
| m1 | 4 | 4 | 4 | 0 | 2 | 2 | 4 | 0 | 2 | 3 |
| m2 | 3 | 0 | 2 | 3 | 2 | 2 | 1 | 0 | 1 | 3 |
| m3 | 4 | 2 | 0 | 1 | 1 | 3 | 0 | 0 | 3 | 4 |
| m4 | 2 | 0 | 2 | 0 | 4 | 3 | 1 | 4 | 3 | 3 |
| m5 | 0 | 3 | 0 | 0 | 1 | 1 | 1 | 2 | 0 | 0 |
| m6 | 2 | 1 | 2 | 4 | 0 | 2 | 3 | 4 | 1 | 3 |
| m7 | 1 | 0 | 1 | 3 | 3 | 3 | 4 | 1 | 3 | 0 |
| m8 | 2 | 0 | 4 | 4 | 1 | 4 | 2 | 0 | 3 | 4 |
| m9 | 4 | 4 | 2 | 1 | 3 | 1 | 1 | 4 | 0 | 2 |
| m10 | 2 | 1 | 1 | 4 | 2 | 2 | 0 | 1 | 1 | 2 |
| m11 | 2 | 2 | 4 | 2 | 2 | 0 | 2 | 1 | 3 | 2 |
| m12 | 0 | 1 | 4 | 4 | 4 | 4 | 3 | 3 | 0 | 3 |
| m13 | 2 | 0 | 4 | 4 | 3 | 0 | 2 | 3 | 3 | 0 |
| m14 | 0 | 4 | 1 | 0 | 4 | 2 | 1 | 2 | 2 | 1 |
| m15 | 0 | 3 | 3 | 0 | 1 | 0 | 2 | 3 | 4 | 4 |
| m16 | 0 | 2 | 1 | 1 | 2 | 1 | 3 | 1 | 0 | 4 |
| m17 | 4 | 4 | 4 | 3 | 0 | 2 | 0 | 0 | 2 | 3 |
| m18 | 1 | 0 | 4 | 3 | 2 | 2 | 1 | 1 | 1 | 3 |
| m19 | 3 | 0 | 0 | 3 | 1 | 3 | 3 | 0 | 1 | 1 |
I also performed sensitivity analysis. The following table summarizes the impact of the number of mobile terminals, UAVs, and movement steps on completion time, energy, runtime, and total cost.
| Parameter | Range | Effect on Completion Time | Effect on Energy | Effect on Runtime | Effect on Total Cost |
|---|---|---|---|---|---|
| Number of terminals | 5 – 40 | Increases non-linearly | Increases significantly | Increases | Increases |
| Number of UAVs | 5 – 25 | Decreases (with minor fluctuation) | Decreases | Almost constant | Decreases |
| Movement steps | 1 – 10 | Increases | Increases | Increases | Increases |
Finally, I compared the genetic algorithm with a signal-strength-based greedy scheme. The comparison is shown in the table below for different terminal numbers with 5 UAVs.
| Terminals | GA Total Cost | Signal-Strength Total Cost |
|---|---|---|
| 5 | 48 | 3607 |
| 10 | 2608 | 10013 |
| 15 | 23120 | 16489 |
| 20 | 21163 | 22751 |
| 25 | 47921 | 37188 |
| 30 | 59959 | 36046 |
| 35 | 58480 | 44805 |
| 40 | 65972 | 53862 |
These results show that the genetic algorithm significantly outperforms the greedy approach, especially when the number of terminals grows, because it balances the load among UAVs and minimizes the overall cost.
4 Collaborative Optimization under Multiple Edge and Terminal Mobility Modes
4.1 Introduction
In practice, UAVs and terminals can move in many ways. For example, in mountainous terrain, UAVs may use zigzag flight to avoid obstacles and cover different areas. In urban environments, terminals may follow circular or linear paths depending on traffic conditions. Therefore, I extend the previous model to consider multiple movement modes for both UAVs and mobile terminals.
4.2 UAV Movement Modes
I define three UAV movement modes:
- Translation motion: The UAV moves along a straight line:
$$P_u(t) = (x_0 + v t \cos\theta, y_0 + v t \sin\theta)$$
- Circular motion: The UAV moves along a circle with radius \(R_{uav}\):
$$x_u(t) = x_u^{center} + R_{uav} \cos(\omega_{uav} t + \varphi_0)$$
$$y_u(t) = y_u^{center} + R_{uav} \sin(\omega_{uav} t + \varphi_0)$$
- Zigzag motion: The UAV moves with a sinusoidal path in the x-direction and a constant speed in the y-direction:
$$x_u(t) = x_0 + A \sin\left(\frac{2\pi}{T_{zigzag}} t\right)$$
$$y_u(t) = y_0 + v_y t$$
These modes offer different trade-offs in coverage and energy. The flight energy for zigzag motion can be expressed as:
$$E_{u}^{fly} = \int_0^{t} P_{flight} \sqrt{\left(\frac{dx_u(t)}{dt}\right)^2 + \left(\frac{dy_u(t)}{dt}\right)^2} dt$$
4.3 Terminal Movement Modes
The mobile terminal can also move in linear or circular patterns. The circular motion has been defined previously. The linear motion is:
$$x_m(t) = x_0 + v_m t \cos\theta$$
$$y_m(t) = y_0 + v_m t \sin\theta$$
Both modes affect the distance to UAVs and thus the communication performance.
4.4 Optimization with Genetic Algorithm
In the multi-mode version, each individual encodes not only the task allocation matrix but also the movement mode of each UAV and each terminal. I assign integer codes to the modes: 0 for circular, 1 for zigzag (UAV) or linear (terminal), 2 for translation (UAV). The fitness function now includes a load balancing term to prevent overloading any individual UAV:
$$Fitness = \alpha \frac{\sum_{i=1}^{m} T_{i}^{completion}}{\max_{i} T_{i}^{completion}} + \beta \frac{\sum_{j=1}^{u} E_{j}^{uav}}{\max_{j} E_{j}^{uav}} + \gamma \frac{\sum_{k=1}^{u} |L_{k}^{uav} – \bar{L}|}{\max_{k} |L_{k}^{uav} – \bar{L}|}$$
where \(\alpha\), \(\beta\), and \(\gamma\) are weighting coefficients, \(T_i^{completion}\) is the completion time of task \(i\), \(E_j^{uav}\) is the energy of UAV \(j\), \(L_k^{uav}\) is the load of UAV \(k\), and \(\bar{L}\) is the average load.
Selection uses tournament selection with tournament size \(s\). Crossover uses partially mapped crossover (PMX) to preserve the feasibility of task allocation. For movement mode variables, I use a simple one-point crossover. Mutation randomly changes a task assignment or a movement mode with probability \(p_m\).
4.5 Experimental Results
I simulate a 100m × 100m area with 20 or 50 terminals and 4 or 10 UAVs. The iteration number is 30 or 50. All results are averaged over 30 independent runs.
First, I verify the convergence of the genetic algorithm for various movement modes. The average fitness decreases over generations, confirming stable convergence.
Then I obtain the optimal task allocation schemes for circular UAV motion, zigzag UAV motion, and linear terminal motion. An example for zigzag UAV motion with 20 terminals and 4 UAVs is shown below (only 10 time steps).
| Terminal | t0 | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 | t9 |
|---|---|---|---|---|---|---|---|---|---|---|
| m0 | 1 | 0 | 2 | 2 | 3 | 1 | 1 | 3 | 0 | 0 |
| m1 | 1 | 1 | 3 | 2 | 0 | 3 | 3 | 2 | 2 | 1 |
| m2 | 3 | 3 | 1 | 0 | 0 | 0 | 1 | 3 | 0 | 2 |
| m3 | 3 | 2 | 0 | 3 | 3 | 1 | 2 | 1 | 1 | 1 |
| m4 | 2 | 3 | 1 | 0 | 2 | 1 | 3 | 3 | 1 | 1 |
| m5 | 1 | 3 | 1 | 1 | 3 | 0 | 2 | 3 | 1 | 0 |
| m6 | 0 | 2 | 0 | 3 | 3 | 1 | 0 | 2 | 1 | 1 |
| m7 | 3 | 1 | 1 | 2 | 2 | 2 | 0 | 3 | 0 | 1 |
| m8 | 1 | 1 | 2 | 0 | 3 | 2 | 2 | 1 | 2 | 0 |
| m9 | 0 | 0 | 1 | 3 | 1 | 2 | 0 | 1 | 2 | 3 |
| m10 | 2 | 3 | 0 | 1 | 2 | 2 | 2 | 2 | 3 | 1 |
| m11 | 0 | 0 | 2 | 3 | 0 | 3 | 1 | 1 | 0 | 2 |
| m12 | 1 | 3 | 1 | 0 | 2 | 2 | 1 | 3 | 3 | 3 |
| m13 | 0 | 1 | 0 | 3 | 0 | 3 | 1 | 1 | 0 | 2 |
| m14 | 2 | 3 | 1 | 0 | 3 | 2 | 0 | 2 | 2 | 1 |
| m15 | 3 | 2 | 1 | 1 | 1 | 0 | 2 | 0 | 2 | 0 |
| m16 | 2 | 2 | 2 | 1 | 3 | 1 | 2 | 0 | 3 | 1 |
| m17 | 1 | 2 | 0 | 3 | 1 | 3 | 0 | 1 | 2 | 3 |
| m18 | 0 | 3 | 0 | 0 | 2 | 0 | 2 | 0 | 1 | 1 |
| m19 | 1 | 3 | 3 | 0 | 0 | 0 | 0 | 3 | 1 | 1 |
I also compared the genetic algorithm against the signal-strength-based scheme for different movement modes. The following tables show the total cost values for circular UAV motion, zigzag UAV motion, and linear terminal motion.
| UAV Mode | Terminals | GA Total Cost | Signal-Strength Total Cost |
|---|---|---|---|
| Circular | 5 | 8077.87 | 32252.60 |
| Circular | 10 | 15957.11 | 58382.02 |
| Circular | 15 | 24373.42 | 98602.91 |
| Circular | 20 | 32879.02 | 124396.44 |
| Circular | 25 | 41403.66 | 153066.91 |
| Circular | 30 | 48729.30 | 181462.19 |
| Zigzag | 5 | 8200.65 | 5800.16 |
| Zigzag | 10 | 18000.68 | 12700.39 |
| Zigzag | 15 | 23800.64 | 35000.43 |
| Zigzag | 20 | 31900.75 | 60000.74 |
| Zigzag | 25 | 40100.87 | 85000.38 |
| Zigzag | 30 | 47500.47 | 115000.76 |
For terminal linear motion with 10 UAVs, the comparison is:
| Terminals | GA Total Cost | Signal-Strength Total Cost |
|---|---|---|
| 5 | 6385.03 | 982.12 |
| 10 | 14691.55 | 8149.79 |
| 15 | 23365.86 | 17059.74 |
| 20 | 31755.55 | 23200.50 |
| 25 | 39140.42 | 42298.84 |
| 30 | 50158.80 | 59476.22 |
| 35 | 56681.93 | 72638.53 |
| 40 | 67544.38 | 97609.73 |
Finally, I compared the total costs of six combinations of UAV and terminal movement modes. The results are shown in the following tables for 20 terminals and 10 UAVs.
| Combination | Average Total Cost after 30 generations |
|---|---|
| UAV zigzag + terminal circular | ≈ 10-70 (decreasing) |
| UAV zigzag + terminal linear | ≈ 10-70 (decreasing) |
| UAV circular + terminal circular | ≈ 10-70 (decreasing) |
| UAV circular + terminal linear | ≈ 10-70 (decreasing) |
| UAV translation + terminal circular | ≈ 440-580 (decreasing from 580 to 440) |
| UAV translation + terminal linear | ≈ 440-580 (decreasing from 580 to 440) |
When the number of terminals increases to 50, the total costs increase significantly. The UAV translation modes still yield the highest costs, indicating that fixed linear paths are less efficient in complex environments. In contrast, zigzag and circular UAV movements provide better coverage and flexibility, resulting in lower total costs.
Based on these experiments, I conclude that for forest fire monitoring, the combination of UAV zigzag or circular motion with mobile terminal circular or linear motion is preferable over pure translation motion of UAVs. The genetic algorithm effectively optimizes task offloading and resource scheduling across multiple movement modes, decreasing task completion time, reducing energy consumption, and balancing the computational load among unmanned aerial vehicles.
5 Conclusion
In this thesis, I have addressed the joint optimization of task offloading and resource scheduling in unmanned aerial vehicle-assisted mobile edge computing systems where both end devices and edge devices are moving. I first proposed a cooperative optimization model for translation-moving UAVs and circular-moving terminals. By formulating the system cost as a weighted sum of task completion time and energy consumption, I applied a genetic algorithm to solve the resulting integer programming problem. The simulation results showed that the algorithm converges effectively and significantly outperforms the traditional signal-strength-based greedy scheme, especially in high-load scenarios.
I then extended the model to multiple movement modes for both UAVs and mobile terminals. The genetic algorithm was enhanced with tournament selection, partially mapped crossover, and targeted mutation, and the fitness function integrated a load-balancing metric. Through extensive simulations, I analyzed the impact of different movement mode combinations. I found that UAV zigzag and circular motion modes provide better adaptability in complex environments than translation motion, and the proposed algorithm effectively minimizes the total system cost across all tested combinations.
The research provides new insights and practical guidelines for deploying unmanned aerial vehicles in disaster monitoring and emergency communication scenarios. Future work may consider more realistic environmental factors such as terrain variations, dynamic obstacles, and device failures. Furthermore, combining the genetic algorithm with other metaheuristics or deep reinforcement learning could improve scalability and convergence speed for large-scale systems. The proposed framework lays a solid foundation for intelligent resource management in UAV-assisted mobile edge computing.