UAV Deployment Design Under Incomplete Information with a Connectivity Constraint for UAV-Assisted Networks

Abstract

In this paper, we introduce an Unmanned Aerial Vehicle (UAV) deployment design with a connectivity constraint for UAV-assisted communication networks. In such networks, multiple UAVs are collaboratively deployed in the air to form a network that realizes efficient relay communications from ground mobile clients to the base station. We consider a scenario where ground clients are widely distributed in a target area, with their population significantly outnumbering available UAVs. The goal is to enable UAVs to collect and relay all client data to the base station by continuously moving while preserving end-to-end connectivity with the base station. To achieve this, we propose two dynamic UAV deployment methods: genetic algorithm-based and modified $\epsilon$-greedy algorithm-based methods. These methods are designed to efficiently collect data from mobile clients while maintaining UAV connectivity, based solely on local information about nearby client positions. Through numerical experiments, we demonstrate that the proposed methods dynamically form UAV-assisted networks to efficiently and rapidly collect client data transmitted to the base station.

1. Introduction

The rapid growth of wireless communication services and the widespread deployment of mobile and Internet of Things (IoT) devices have led to increasing demands for flexible and robust wireless network infrastructures [1]. In particular, scenarios such as disaster recovery, remote area access, large-scale public events, and environmental monitoring require adaptable and quickly deployable communication frameworks that can operate in the absence of fixed infrastructure [2,3,4].

Unmanned Aerial Vehicles (UAVs) have emerged as a promising solution to such requirements due to their high mobility, flexible deployment, and ability to establish line-of-sight communication links with ground clients [5,6,7]. Using UAVs, we easily realize infrastructure-free or infrastructure-augmented communication systems. Using such communication systems, in this paper, we focus on UAV-assisted communication networks that aim to enhance wireless coverage and reliability by deploying multiple UAVs as aerial relay nodes between ground clients and a central base station (Figure 1) [8].

These UAV-assisted networks are especially effective in environments where terrestrial infrastructure is unavailable, damaged, or insufficient to meet dynamic client demands. Specifically, UAV-assisted networks can be applied to scenarios involving mobile ground clients, where the network topology adapts to client mobility in real time. The literature has demonstrated the potential of UAVs to establish line-of-sight communication links, dynamically adapt to client mobility, and provide high-throughput relaying in a variety of environments [9,10,11].

Despite their potential, several challenges remain in realizing efficient UAV-assisted networks. A key issue is the connectivity constraint, i.e., UAVs must maintain a connected communication path to the base station to relay client data effectively [8]. Another challenge is the lack of accurate information about client locations. That is, it is difficult for UAVs to obtain the location information of all clients in the target area and they can only access information about nearby clients. This becomes particularly challenging when the number of UAVs is much smaller than the number of clients such as IoT devices. Especially when clients are sparsely and dynamically distributed across a large area, it is essential to appropriate strategies to develop efficient UAV-assisted networks under limited client location information. Specifically, it is essential to design deployment strategies that allow UAVs to dynamically move and adapt to client distribution in order to enhance the efficiency of client data collection while maintaining multi-hop connectivity within the network.

In this paper, we address the problem of dynamic UAV deployment for data collection in UAV-assisted networks under the connectivity constraint. We consider a scenario where mobile ground clients are sparsely and widely distributed in a target area, and UAVs must cooperatively collect and relay client data to a base station. To accomplish this, UAVs are required to move continuously while maintaining a connected aerial network that supports multi-hop data transmission. To tackle this challenge, we propose two dynamic UAV deployment methods: genetic algorithm (GA)-based method and modified $\epsilon$-greedy algorithm-based method. The GA-based method applies optimization principles, whereas the modified $\epsilon$-greedy method is based on the fundamental reinforcement learning concepts of exploration and exploitation. These methods utilize only local information about nearby clients and do not require centralized control or global knowledge of the entire network. The objective of the proposed methods is to minimize the total time needed to collect data from all mobile clients while ensuring that network connectivity is preserved throughout the process. Through numerical experiments, we demonstrate that the proposed methods can dynamically develop UAV-assisted networks that adapt to changes in client positions to relay all client data to the base station.

The contribution of this paper is as follows.

• We propose two deployment strategies based on a GA and a modified $\epsilon$-greedy algorithm, both of which allow UAVs to make movement decisions without requiring global knowledge of client locations.
• We evaluate the effectiveness of the proposed methods through extensive simulations, demonstrating that they can dynamically construct UAV-assisted networks that efficiently adapt to client mobility while maintaining multi-hop connectivity.
• We show that the proposed methods significantly reduce data collection time, even under limited location information, compared to baseline approaches, thereby validating their applicability to real-world UAV-assisted network scenarios.

The rest of this paper is organized as follows. In Section 2, we describe related works. In Section 3, we explain the system model and problem formulation. Section 4 discusses the proposed UAV deployment methods. In Section 5 provides simulation results and performance analysis. Section 6 concludes the paper and discusses future research directions.

2. Related Works

In the past, various approaches have been proposed to address UAV deployment and path planning problems for UAV-assisted networks. In general, related works on UAV deployment and network design can be broadly categorized into two major approaches: machine learning-based (especially, reinforcement learning-based) approaches and optimization-based approaches.

2.1. Machine Learning-Based Approach

For example, the following works represent machine learning-based approaches. In [12], the authors have addressed the problem of multi-UAV area coverage in urban environments where each UAV has access to only local and partial information. They have developed an event-triggered hierarchical reinforcement learning framework, enabling a UAV swarm to autonomously learn efficient 3D space coverage despite limited global knowledge. The authors in [13] have proposed a multi-UAV path planning method based on multi-agent reinforcement learning with centralized training and decentralized execution. By using recurrent neural networks and a joint reward function, the approach enables efficient cooperative navigation under partial observability and multiple constraints. In [14], the authors have proposed a learning-based resource allocation method for ultra-dense UAV networks with time-varying user demands. They have modeled the interactions among UAVs as a stochastic game and developed a model-free reinforcement learning algorithm to solve the problem. The authors in [15] have proposed a dynamic and energy-efficient path planning framework for 5G-assisted multi-UAV communication networks in disaster scenarios. The method incorporates lightweight gated recurrent units for weather prediction, a density-based clustering algorithm for reliable communication with IoT devices, a soft actor-critic algorithm for positioning UAVs, and a shuffled optimization approach for path planning. In [16], the authors have proposed an energy-efficient control method based on deep reinforcement learning for managing UAVs serving as aerial base stations. This method jointly optimizes communication coverage, fairness, energy consumption, and connectivity by learning environmental dynamics and making decisions through deep neural networks. In [17] the authors have proposed a reinforcement learning-based method for multi-agent control of UAVs in ground communication relay tasks. This method is based on the $\epsilon$-greedy strategy and multi-agent proximal policy optimization algorithm. In [18], the authors have addressed the problem of sensing data storage in autonomous UAV crowdsensing without edge server support, focusing on optimizing replica distribution to balance data availability and energy consumption. They have proposed a deep reinforcement learning algorithm with centralized training and decentralized execution, based on the actor-critic framework. The authors in [19] have proposed an online deployment algorithm for UAVs to provide wireless connectivity to partially observable mobile ground users in low-altitude platform networks. The method is formulated as a partially observable decision-making problem and solved using a tree search algorithm with deep neural network guidance and policy optimization.

2.2. Optimization-Based Approach

Similarly, various optimization-based approaches have been proposed in the past. The authors in [20] have proposed an optimal deployment strategy for UAVs in disaster scenarios, aiming to provide wireless communication services with the minimum number of aerial units. They formulated the problem as a mixed-integer linear programming model that determines the three-dimensional positions of UAVs while considering constraints such as coverage, connectivity, and user distribution. In [21] the authors have focused on a wireless relaying system in which multiple UAVs assist communication between multiple source–destination pairs using a shared spectrum. To mitigate interference, they have proposed a method to maximize the minimum throughput across all links by jointly optimizing the three-dimensional trajectories of UAVs and the transmit power of both sources and relays. In [22], the authors have addressed the three-dimensional deployment problem of multiple UAVs in a space–air–ground integrated network, aiming to maximize coverage while considering connection capacity limits and network robustness. They have proposed a multi-stage approach combining initial placement via clustering, a fairness-based connection strategy, an improved GA for horizontal position optimization, and a height adjustment algorithm. The authors in [23] have focused on a single-cell cellular network where multiple UAVs upload sensing data to a base station using either direct communication or relay communication via neighboring UAVs. They have proposed a cooperative sense-and-send protocol and formulated a joint optimization problem for subchannel allocation and UAV speed to maximize uplink throughput. The authors in [24] have investigated the integration of UAVs into cellular networks, focusing on UAVs as mobile users served by ground base stations. They formulated a trajectory optimization problem to minimize mission completion time while ensuring continuous connectivity with the cellular network based on a minimum signal quality requirement. In [25], the authors have considered a wireless powered communication network assisted by a UAV, where the UAV simultaneously charges ground devices and collects their data. They have formulated a joint optimization problem for power allocation and three-dimensional trajectory planning to maximize coverage, improve time efficiency, and reduce flight distance. In [26], the authors have proposed a mobile edge computing system enabled by multiple UAVs, where UAVs act as computing servers for task offloading from ground users. To minimize user energy consumption, they have introduced a two-layer optimization framework that jointly optimizes task scheduling, data allocation, and aerial trajectories. The authors in [27] have investigated a multi-hop relaying system using UAVs to enhance wireless connectivity between distant users. They have formulated a joint optimization problem for UAV trajectories and transmit power, subject to mobility, collision avoidance, and energy constraints. An iterative algorithm combining alternating maximization and convex approximation has been proposed to solve the problem. In [8], the authors have addressed the problem of UAV deployment for data collection in scenarios where the number of UAVs is limited compared to ground client nodes. To ensure full data collection, they have proposed two deployment methods: integer linear programming-based method and sequential deployment-based method.

In this paper, we consider a situation similar to the work in [8]. Specifically, we address the UAV deployment problem to form UAV-assisted networks where UAVs relay the communication of client nodes to a base station. However, in [8], the authors have considered a static scenario where client nodes are stationary and their location are fully known. Furthermore, they have not considered any mobility constraints of UAVs, assuming that UAVs can move freely within a target area at any time. On the other hand, in this paper, we consider a dynamic scenario where client nodes move over time and only limited location information is available. Additionally, we incorporate a mobility constraint on UAVs, which restricts their movement range per time step. In order to tackle the dynamic scenario, we propose two methods: the GA-based method and modified $\epsilon$-greedy method. The GA-based method represents a metaheuristic optimization strategy. On the other hand, the modified $\epsilon$-greedy method selects actions based on exploration and exploitation principles, which are fundamental to reinforcement learning. In what follows, we explain the system model and these methods.

3. System Model

3.1. System Model and Problem Formulation

Figure 2 shows the system model assumed in this paper. We consider an $I\times J$ closed area $\mathcal{A}$, which consists of multiple hexagonal cells (i.e., $\mathcal{A}=\left\{\right(i,j)\mid 1\le i\le I,1\le j\le J\}$). There is one base station in the area. Let $\mathcal{U}=\{1,2,\dots U\}$ and $\mathcal{N}=\{1,2,\dots ,N\}$ denote the sets of UAVs and clients nodes, respectively, in the area. Each client node has a communication request to the Internet.

In this paper, we assume that each client node is located on one of the cells and can access the Internet through the base station. However, due to their limited communication range, each client node is assumed to be unable to communicate beyond its own cell. In other words, even if a client node is located in a cell adjacent to the base station’s cell, it cannot communicate directly with the base station. Instead, UAVs relay the communication from client nodes to the base station. Each UAV can communicate only with the clients located in the same cell where the UAV hovers, assuming that it is equipped with an omnidirectional antenna that covers the cell. Additionally, UAVs are assumed to be able to communicate with other UAVs or the base station located in adjacent cells, assuming that they are also equipped with directional antennas. The objective of this paper is to establish connections for each client through UAVs’ relay to the base station. However, since the number of UAVs is assumed to be significantly smaller than the number of client nodes and the area size, it is difficult to cover all the client nodes simultaneously.

In order to address this limitation, we assume a scenario where UAVs dynamically move and develop an efficient UAV-assisted network at each time step t ($t=0,1,2,\dots$) as shown in Figure 3. In the UAV-assisted network, UAVs are deployed on cells in such a way that each UAV has a connection to the base station via other UAVs, meaning that each UAV is adjacent to at least one other UAV or directly to the base station. At most one UAV can be deployed in each cell. We assume that each UAV can move up to K cells in a single time step, which is defined as the movement range. On the other hand, at each time step, each client node either remains in its current cell or randomly moves to one of the adjacent cells. At each time step, UAVs do not have access to the location information of all client nodes. Instead, each UAV can only obtain the number of client nodes in adjacent cells and shares this information with other UAVs. We define these cells from which client information can be obtained as the observation range.

At each time step, each UAV can accommodate at most M clients’ communication requests. It is important to note that the value of M is influenced by some factors such as radio interference. For instance, under strong radio interference, the throughput of each communication decreases, thereby reducing the number of communication requests that a UAV can complete within a single time slot. Such situations can be indirectly considered by appropriately setting the value of M. In this paper, we treat M as a given parameter, without detailed considerations of such factors. This is because the main objective of this paper is to discuss a general method for developing UAV-assisted networks that can accommodate all communication requests under various conditions.

Under these assumptions, we consider the dynamic UAV deployment problem, which aims to minimize the completion time T required for UAVs to accommodate the communication requests from all mobile client nodes. Formally, the completion time T is defined as

$$T=inf\left\{t\mid \mathcal{R}\left(t\right)=\varnothing \right\},$$

(1)

where $\mathcal{R}\left(t\right)$ denotes the set of client nodes whose communication requests have not yet been served at time step t (initially $\mathcal{R}\left(0\right)=N$). Note that to ensure communication via the base station at every time step, the connectivity constraint must be satisfied such that UAVs form a connected graph, i.e., UAV-assisted network. The objective of the dynamic UAV deployment problem is the completion time T is minimized, while meeting the connectivity constraint.

3.2. Modeling Assumptions and Justification

In our model, we assume a two-dimensional hexagonal cell structure, where each cell can be covered by at most one UAV with omnidirectional coverage. These simplifications allow for a structured, tractable, and scalable evaluation of UAV deployment strategies under connectivity constraints. Hexagonal cell structures are widely used in network simulations due to their ability to represent uniform coverage and neighbor relations with minimal distortion. Furthermore, we assume omnidirectional communication coverage per cell to approximate real-world UAVs equipped with circular coverage antennas operating at a fixed altitude. The assumption of at most one UAV per cell avoids potential coordination conflicts and reflects a conservative scheduling model where UAVs avoid overlapping coverage. Instead of explicitly modeling energy or altitude constraints, we assume that flight and coverage limitations are implicitly reflected in the connectivity and per-cell movement constraints. While these factors are critical in real-world applications, our aim in this paper is to isolate and evaluate the effectiveness of the proposed algorithms (i.e., GA-based and modified $\epsilon$-greedy) under limited information conditions. We recognize that extending the model to incorporate energy constraints, heterogeneous coverage patterns, and altitude control is an important direction for future work.

In addition, our model abstracts the communication process using a single parameter M, which limits the number of clients that can simultaneously transmit data to a UAV. While this simplification omits detailed factors such as wireless interference, link quality, and multi-hop routing, it allows us to isolate the effects of spatial distribution and connectivity constraints on UAV deployment decisions. A more realistic communication model incorporating these elements is left as future work.

In this paper, we adopt a simplified random mobility model for client nodes, where each node either remains in its current position or moves randomly to one of the adjacent cells at each time step. This assumption enables tractable analysis and facilitates a general evaluation of the proposed UAV deployment methods. However, it does not fully reflect realistic mobility patterns observed in actual environments, such as hotspot-driven movement, group behavior, or location preferences. These factors can impact network connectivity and task completion efficiency. Incorporating more realistic mobility models is an important direction for future work to enable a more comprehensive evaluation of the adaptability and robustness of the proposed algorithms in practical scenarios.

4. Proposed Method

To achieve the above objective, this paper proposes two methods: the GA-based method and the modified $\epsilon$-greedy method. In what follows, we first explain the common procedure of the proposed methods, and then discuss the details of these methods.

4.1. Procedure of the Proposed Method

We here explain the common procedure of the proposed methods. The proposed method dynamically determines the UAV deployment at each time step in response to client movements, while satisfying the following constraints.

Constraints

• Each UAV can move up to K cells in a single time step (i.e., within the movement range).
• UAVs know the location of client nodes only in adjacent cells (i.e., within the observation range).
• At most one UAV is placed in each cell.
• UAVs must maintain a connected communication path to the base station (i.e., the connectivity constraint).

While satisfying these constraints, the proposed method determines the UAV deployment according to the following procedure.

Common procedure:

Step 1.

$t\leftarrow 0$ and $\mathcal{R}\left(0\right)\leftarrow \mathcal{N}$.

Step 2.

The initial deployment is determined as follows. The first UAV is placed in the cell adjacent to the base station that contains the largest number of client nodes. Subsequently, each UAV is placed in the adjacent cell of either the base station or already deployed UAVs that has the largest number of client nodes.

Step 3.

Each UAV accommodates the communication requests of up to M clients located within the cell where it hovers. Let $S\left(t\right)$ denote the set of client nodes accommodated by UAVs at time step t.

Step 4.

It updates $\mathcal{R}\left(t\right)$ as follows: $\mathcal{R}(t+1)\leftarrow \mathcal{R}\left(t\right)\setminus S\left(t\right)$. If $\mathcal{R}(t+1)=\varnothing$, the procedure terminates.

Step 5.

Each mobile client nodes randomly moves to one of adjacent cells with a probability of $\beta$ and stays in its current cell with a probability of $1-\beta$, where $\beta$ ($0\le \beta \le 1$) is a parameter.

Step 6.

Each UAV observes the movement of client nodes within the observation range.

Step 7.

$t\leftarrow t+1$.

Step 8.

A new UAV deployment is determined while satisfying the constraints. Then, the procedure returns to Step 3.

In Step 2, UAVs are deployed on cells as an initial position. Then, UAVs accommodate up to M client nodes in Step 3. In Step 5, each client node moves to another cell. In Step 8, each UAV moves to another cell within its movement range in response to the user movement observed in Step 6. In Step 8, we use GA-based methods or modified $\epsilon$-greedy method to deploy the UAV.

4.2. GA-Based Method

The GA is one of metaheuristic algorithms used for solving optimization problems. The GA is inspired by the process of natural selection. It iteratively evolves a population of candidate solutions using operations such as selection, crossover, and mutation to search for near-optimal solutions to complex problems.

In the GA-based method, the GA is applied to determine the UAV deployment at each time step, aiming to find a deployment that can serve the maximum number of client nodes at that time. At each time step, the GA is used to find a solution following a greedy approach. Specifically, in Step 8 in the common procedure, we use the GA to determine the location of UAVs. The objective function of the GA at each time step is to maximize the number of client nodes accommodated by UAVs (i.e., $max\left|\mathcal{S}\right(t\left)\right|$) while satisfying the constraints discussed above. The detailed procedure of the GA-based method is as follows.

GA-based method:

Step 1.

It generates an initial population of UAV deployment patterns (i.e., sets of UAV positions), ensuring that all constraints are satisfied.

Step 2.

For each deployment pattern, it evaluates the fitness based on the number of client nodes that can be accommodated.

Step 3.

It selects high-performing deployment patterns (individuals) from the population to serve as parents for the next generation, based on their fitness scores using a selection method such as roulette wheel selection.

Step 4.

It generates new UAV deployment patterns (offspring) by combining portions of two parent deployments (e.g., exchanging UAV positions).

Step 5.

It applies small random changes to UAV positions (e.g., move a UAV to a neighboring cell).

Step 6.

It forms a new generation by selecting individuals from the combined pool of parents and offspring, based on fitness scores.

Step 7.

If a termination condition is met (e.g., a fixed number of generations), the algorithm terminates and outputs the best UAV deployment; otherwise, it returns to Step 2.

Note that in each step, UAV deployment patterns should satisfy the constraints discussed above. Furthermore, in the GA, cells without client information are excluded from the search space because UAVs know the location of client nodes only within the observation range.

Figure 4 illustrates an example of the procedure of the GA-based method, where the number in each cell represents the number of client nodes located in that cell. Figure 4a shows the initial states of client nodes and Figure 4b shows the initial deployment of UAVs determined by Step 2 in the common procedure discussed in Section 4.1. As shown in Figure 4c, in the GA-based method, we observe that UAVs tend to gather in cells within their observation range that have a higher number of client nodes, while satisfying the constraints. From Figure 4d, a similar tendency can also be observed in the following time step.

4.3. Modified $\epsilon$-Greedy Method

The $\epsilon$-greedy algorithm is an algorithm that balances exploration and exploitation based on a probability parameter $\epsilon$ ($0\le \epsilon \le 1$). Specifically, the exploration, i.e., random action, is performed with the probability $\epsilon$. On the other hand, with probability $1-\epsilon$, the best action at that time, i.e., greedy action, is selected. As mentioned in the GA-based method, the greedy action in this case is to maximize the number of client nodes accommodated by UAVs. However, since each UAV can only obtain the location information of client nodes in adjacent cells, the search space for the greedy action is inherently limited.

Thus, in this paper, we modify the exploration phase from random exploration to strategic exploration. Specifically, instead of moving randomly with probability $\epsilon$, UAVs move to the farthest reachable cell within the movement range from their current positions. By employing this strategy, the proposed method aims to efficiently expand the exploration area even under the constraint of limited client location information. The detailed procedure of the modified $\epsilon$-greedy method is as follows.

Modified $\epsilon$-greedy method:

Step 1.

${\mathcal{U}}_t\leftarrow \mathcal{U}$.

Step 2.

It selects the UAV $u\in {\mathcal{U}}_t$ that is deployed in the cell closest to the base station.

Step 3.

For UAV u, it generates a real number a between 0 and 1 at random.

Step 4.

According to the value of a, the following step is performed to select a next cell.

Step 4-a.

If $a>\epsilon$, UAV u selects the cell with the highest number of client nodes among cells that are both within its observation range and movement range, while meeting the connectivity constraint. Note that if the number of client nodes within the observation range is 0, a cell is randomly selected from the UAV’s movement range.

Step 4-b.

If $a\le \epsilon$, UAV u selects the farthest reachable cell from its current position while maintaining the connectivity constraint. In this case, cells outside the observation range are also considered for selection. If there are multiple candidates, a cell is randomly selected.

Step 5.

UAV u moves to the selected cell. Then, ${\mathcal{U}}_t\leftarrow {\mathcal{U}}_t\setminus \left\{u\right\}$. If ${\mathcal{U}}_t=\varnothing$, the procedure terminates; otherwise, it returns to Step 2.

In this paper, the value of $\epsilon$ is initially set to 0.3. It is halved every 20 time steps in the common procedure discussed in Section 4.1 with a minimum value of 0.05. This is because, in the early stages, it is important to explore a wide area in order to discover client nodes as broadly as possible. To improve coverage efficiency in the later stages, the value of $\epsilon$ is gradually decreased over time.

Figure 5 illustrates an example of the procedure of the modified $\epsilon$-greedy method. Note that the initial state and the initial deployment of UAVs are the same as the case of the GA-based method. Therefore, those figures are omitted in this example. As shown in Figure 5a, at the first time step, UAVs gather in areas with a high number of client nodes, similar to the GA-based method. Note that this behavior results from the probabilistic nature of the $\epsilon$-greedy algorithm. As we can see from Figure 5b, in the following time step, unlike the GA-based method, UAVs move over a wide area that includes cells beyond the observation range. By doing so, the modified $\epsilon$-greedy method is expected to efficiently discover client nodes that locate outside of the current observation range.

4.4. Computational Complexity of Each Method

In order to evaluate the scalability, we analyze the computational complexity of the proposed GA-based and modified $\epsilon$-greedy methods at each time step.

The GA-based method involves the iterative evolution of a population of solutions, where each solution represents a UAV deployment pattern over the candidate cells. Let P denote the population size, G denote the number of generations, and C denote the number of candidate cells within the movement range of each UAV. At each generation, for each of the P individuals, the method evaluates a fitness score by simulating the deployment of U UAVs over a subset of the C candidate cells. This involves operations such as selection, crossover, and mutation. Thus, the computational complexity per time step is approximately $\mathcal{O}\left(PGUC\right)$. This reflects that for every generation, the algorithm evaluates P individuals, each of which considers U UAVs with C candidate cells.

In contrast, the modified $\epsilon$-greedy method is a lightweight heuristic designed for real-time decision-making. At each time step, each UAV independently selects its next cell from among C candidates. Since this selection process is executed independently for each UAV and does not require iterative optimization, the overall complexity is linear with respect to U and C. Thus the computational complexity per time step is approximately $\mathcal{O}\left(UC\right)$. These results indicate that while the GA-based method can potentially achieve higher-quality solutions due to its global optimization nature, the modified $\epsilon$-greedy method offers significantly lower computational overhead, making it more suitable for large-scale or real-time applications.

5. Performance Evaluation

5.1. Model

To evaluate the performance of the proposed method, we conduct numerical experiments using three closed areas consisting of $7\times 7$, $9\times 9$, or $11\times 11$ hexagonal cells. There are N client nodes and U UAVs are deployed at each time step. The base station is located at the center of the areas. Each UAV can move up to K cells in a single time step. Each UAV can accommodate up to $M=5$ client nodes at each time step. We consider two scenarios as the initial positions of the client nodes: a random scenario and an uneven scenario. In the random scenario, the initial number of client nodes in each cell is randomly assigned such that the total number of client nodes is equal to $N=200$ for the $7\times 7$ hexagonal cell area, $N=400$ for the $9\times 9$ hexagonal cell area, and $N=600$ for the $11\times 11$ hexagonal cell area. Figure 6 shows an example of the client node distribution in the random scenario where the number in each cell represents the number of client nodes in the cell. On the other hand, in the uneven scenario, client nodes are concentrated in only a subset of the cells, as illustrated in Figure 7. Specifically, client nodes initially exist only in the upper-left and lower-right cells. The number of client nodes in those cells is randomly assigned such that the total number of client nodes is equal to $N=100$ for the $7\times 7$ hexagonal cell area, $N=200$ for the $9\times 9$ hexagonal cell area, and $N=300$ for the $11\times 11$ hexagonal cell area. The movement probability $\beta$ of each client node at each time step is set to 0.8 discussed in Section 4.1.

For the modified $\epsilon$-greedy method, the value of $\epsilon$ is initially set to 0.3. The hyperparameters for the GA-based method are configured as follows: the population size P is set to 30 and the number G of generations is 20. For the selection strategy, tournament selection is used: two individuals are randomly selected from the top half of the population. For crossover, uniform crossover is used, in which the position of each UAV is randomly selected from one of the two parents. The mutation rate is set to 0.2.

We use two performance metrics. The first is the completion time T, as defined in (1). The second is the number of time steps required to accommodate the communication requests of 95% of the client nodes. In each experiment, we perform 30 independent runs and show the average result with 95% confidence intervals.

For the sake of comparison, we adopt three methods. The first method is the random method. In this method, UAVs are deployed on randomly selected cells within their movement range at each time step, while satisfying the connectivity constraint. The second method is the standard $\epsilon$-greedy method. In this method, instead of applying Step 4-b in the modified $\epsilon$-greedy procedure discussed in Section 4.3, UAVs are deployed to randomly selected cells in the same manner as in the random method. In this method, we set the value of $\epsilon$ is to 0.3 as in our modified $\epsilon$-greedy method. The third method is the extended GA-method, which assumes that the locations of all client nodes are fully known. Note that this method uses the same hyperparameter setting as the proposed GA-based method. In this method, the GA searches for UAV deployment strategies by optimizing the coverage of client nodes based on complete location information. This approach serves as an upper-performance baseline, providing an approximate reference for the best possible performance when full knowledge of the environment is available. By comparing the proposed methods against this baseline, we can evaluate how effectively the proposed algorithms operate under incomplete information scenarios.

5.2. Results

5.2.1. Random Scenario

First, we examine the performance of the proposed methods in the random scenario shown in Figure 6.

Figure 8 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $7\times 7$ hexagonal cell area, where $U=7$ and $K=3$. Figure 8a represents the number of time steps required for UAVs to accommodate 95% of the client nodes (i.e., 190 client nodes). Note that, for the random method, the results are omitted beyond a certain time step, as it requires significantly more time steps compared to the other methods. As we can see from this figure, the random method does not work well because UAVs move without considering the number of client nodes in cells in the observation range. We also observe that the proposed GA-based achieves the result close to that of the extended GA-based method, despite utilizing only limited location information about client nodes. The modified $\epsilon$-greedy method reduces the time steps required to cover 95% of the client nodes more efficiently than the standard $\epsilon$-greedy method. This improvement is due to the ability of the modified $\epsilon$-greedy method in which UAVs probabilistically explore distant cells beyond the observation range, thereby enhancing the discovery of client nodes.

Figure 8b shows the number of time steps required for UAVs to accommodate 100% of the client nodes (i.e., the completion time T). The completion time of the random method is much higher than that of the other methods. As we can see from this figure, the proposed GA-based method achieves the shortest completion time, except for the extended GA-method. This is because the GA-based method gradually expands its exploration area, thereby reducing the likelihood of missing the remaining 5% of client nodes. On the other hand, in the modified $\epsilon$-greedy method, UAVs probabilistically move to cells without client nodes, leading to delayed discovery of the remaining 5% of client nodes. Furthermore, as discussed earlier, the computational complexity of the GA-based method is significantly higher than that of the modified $\epsilon$-greedy method. Therefore, if faster computation with reasonably good results is required, the modified $\epsilon$-greedy method is preferable. Conversely, if more time is acceptable in exchange for better performance, the GA-based method is more suitable. Note that the computational complexity of the standard $\epsilon$-greedy method is the same as that of the modified $\epsilon$-greedy method.

Figure 9 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $9\times 9$ hexagonal cell area, where $U=9$ and $K=5$. Figure 9a represents the number of time steps required for UAVs to accommodate 95% of the client nodes (i.e., 380 client nodes). From this figure, we observe that similar results are obtained as in the case of $7\times 7$ hexagonal cell area shown in Figure 8a. Figure 9b represents the number of time steps required for UAVs to accommodate 100% of the client nodes. As we can see from the figure, the GA-based method has the best performance in covering all client nodes, similar to the results shown in Figure 8b.

Figure 10 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $11\times 11$ hexagonal cell area, where $U=11$ and $K=5$. From this figure, we observe that even when the area size is increased to $11\times 11$, the overall trend remains consistent with the results obtained for the $7\times 7$ and $9\times 9$ areas. In particular, the proposed GA-based method and the modified $\epsilon$-greedy method work well, demonstrating the scalability and robustness of the proposed methods in larger deployment scenarios.

Figure 11a,b show the number of time steps required to cover 95% client nodes and 100% client nodes, respectively, as a function of U in the $9\times 9$ hexagonal cell area, where $K=5$. When U is small, the modified $\epsilon$-greedy method can reduce the required number of time steps more effectively than the standard $\epsilon$-greedy method. However, as the value of U increases, the performance difference between these methods diminishes. This is because, when U is large, the impact of differences in the client node exploration procedures among these methods becomes negligible. We also observe that the GA-based method consistently demonstrates the best performance, regardless of the value of U.

Figure 12a,b show the number of time steps required to cover 95% client nodes and 100% client nodes, respectively, as a function of K in the $9\times 9$ hexagonal cell area, where $U=9$. From these figures, we observe that increasing the value of K has little impact on the overall performance. This is likely because the limited observation range of UAVs reduces the benefit of increasing K.

We also examined the effects of other parameters, including $\beta$ and M, and confirmed that the proposed methods consistently outperform the baseline methods under these settings. To keep the paper concise, we omit the detailed results and discussions here. Overall, these findings further validate the effectiveness of the proposed methods.

5.2.2. Uneven Scenario

Next, we examine the performance of the proposed methods in the uneven scenario shown in Figure 7.

Figure 13 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $7\times 7$ hexagonal cell area, where $U=7$ and $K=3$. Figure 13a represents the number of time steps required for UAVs to accommodate 95% of the client nodes (i.e., 95 client nodes). Figure 13b represents the number of time steps required for UAVs to accommodate 100% of the client nodes. As shown in these figure, unlike in the random scenario, the modified $\epsilon$-greedy method does not work well. This inefficiency arises from the fact that, under a biased initial distribution of client nodes, the modified $\epsilon$-greedy method tends to explore areas where no client nodes exist. In contrast, the GA-based method tends to avoid expanding its search into areas without client nodes, thereby enabling effective accommodation of client nodes.

Figure 14 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $9\times 9$ hexagonal cell area, where $U=9$ and $K=5$. Figure 14a shows the number of time steps required for UAVs to accommodate 95% of the client nodes (i.e., 190 client nodes). Also, Figure 14b shows the number of time steps required for UAVs to accommodate 100% of the client nodes. These figures indicate that similar trends are observed as in the case of $7\times 7$ hexagonal cell area, i.e., the GA-based method works well.

Figure 15 shows the number of remaining client nodes that have not been accommodated by any UAV as a function of the time step t in the $11\times 11$ hexagonal cell area, where $U=11$ and $K=5$. From this figure, we observe that the gap in the required number of time steps between the extended-GA method and the proposed GA-based method is relatively large. This is because the extended GA-method has full knowledge of all client locations, allowing it to operate more efficiently, especially in scenarios where client distributions are highly uneven and the target area is large. However, among the remaining methods, the proposed GA-based method achieves the best performance.

Figure 16 shows the number of time steps required to cover client nodes as a function of U in the $9\times 9$ hexagonal cell area. Figure 16a shows the number of time steps required to cover 95% client nodes. Also, Figure 16b shows the number of time steps required to cover 100% client nodes. As we can see from these figures, in each case, the GA-based method exhibits the excellent performance, regardless of the value of U. These results indicate that the GA-based method is the most suitable in the uneven scenario.

6. Conclusions

In this paper, we addressed the problem of dynamic UAV deployment for data collection in UAV-assisted networks under the connectivity constraint. We proposed two dynamic UAV deployment methods: the GA-based method and modified $\epsilon$-greedy algorithm-based method. Through numerical experiments, we demonstrated that the GA-based method is effective for achieving full coverage, while the modified $\epsilon$-greedy method provides a good balance between performance and computational efficiency.

While our model simplifies various aspects such as UAV coverage, energy constraints, and communication realism to facilitate tractable analysis, these assumptions limit direct applicability to real-world deployments. As future work, we plan to extend the model to incorporate realistic coverage patterns, energy consumption, and communication models. In addition, we aim to integrate more realistic client mobility models and evaluate the proposed methods in larger-scale and more diverse scenarios to enhance their robustness and generalizability.