Integrated Optimization of Ground Support Systems and UAV Task Planning for Efficient Forest Fire Inspection

Abstract

With the increasing frequency and intensity of forest fires driven by climate change and human activities, efficient detection and rapid response have become critical for forest fire prevention. Effective fire detection, swift response, and timely rescue are vital for forest firefighting efforts. This paper proposes an unmanned aerial vehicle (UAV)-based forest fire inspection system that integrates a ground support system (GSS), aiming to enhance automation and flexibility in inspection tasks. A three-layer mixed-integer linear programming model is developed: the first layer focuses on the site selection and capacity planning of the GSS; the second layer defines the coverage scope of different GSS units; and the third layer plans the inspection routes of UAVs and coordinates multi-UAV collaborative tasks. For planning UAV patrol routes and collaborative tasks, a goal-driven greedy algorithm (GDGA) based on traditional greedy methods is proposed. Simulation experiments based on a real forest fire case in Turkey demonstrate that the proposed model reduces the total annual costs by 28.1% and 16.1% compared to task-only and renewable-only models, respectively, with a renewable energy penetration rate of 68.71%. The goal-driven greedy algorithm also shortens UAV patrol distances by 7.0% to 12.5% across different rotation angles. These results validate the effectiveness of the integrated model in improving inspection efficiency and economic benefits, thereby providing critical support for forest fire prevention.

1. Introduction

In recent years, the frequency and intensity of forest fires have been increasing annually due to the impacts of climate change and human activities, posing significant threats to the ecological environment and social economy. Forest fires are characterized by urgency and randomness, and the lack of real-time fire information often results in significant damage [1]. Therefore, effective detection, rapid response, and timely rescue before a fire occurs are crucial for forest firefighting. The rapid development of unmanned aerial vehicle (UAV) technology offers new solutions for forest fire inspection [2]. Compared to traditional inspection methods, UAVs provide advantages such as high efficiency [3], flexibility [4], and relatively low costs [5]. They can quickly cover vast forest areas, enabling timely detection of fire hazards and monitoring, thereby significantly reducing the frequency of forest fires, economic losses, and casualties. Furthermore, by organically integrating UAVs with ground support systems (GSS), which is a composite system that includes power generation devices, sensor equipment, communication devices, monitoring devices, and combining them with intelligent control systems, highly autonomous UAV patrols can be realized, further enhancing task automation and flexibility [6]. However, the high energy consumption of GSS remains an urgent issue, especially when extensive power generation equipment is required to meet energy demands. To reduce power generation costs, the utilization of renewable energy sources such as photovoltaic systems has become a viable option [7]. Nevertheless, renewable energy generation is affected by natural resources; establishing GSS in regions with abundant sunlight may lead to an overly concentrated location of GSS, which could impact the efficiency of UAV inspections [8]. If only the efficiency of UAV patrols is considered while neglecting sunlight availability, the penetration of renewable energy within GSS will be relatively low [9]. Consequently, issues related to site selection for GSS, capacity planning for power generation devices, division of patrol areas, and coordination of multiple UAVs form a series of interconnected challenges. These problems collectively constitute a complex, integrated optimization problem that requires systematic analysis and research to ensure the optimal performance of the UAV inspection system in terms of efficiency and coordination. Therefore, comprehensive research addressing these challenges will provide vital support and guidance for future forest fire prevention efforts [10].

The UAV inspection task aims to acquire comprehensive information about specific areas or to perform full coverage operations. As a result, area coverage path planning has become a central research focus. Researchers both domestically and internationally have conducted extensive studies on the issue of UAV area coverage. For instance, Ref. [11] proposed a distributed dynamic area coverage algorithm for UAVs based on deep reinforcement learning, which improves coverage efficiency by 20% to 30% in communication-constrained environments through a coverage information fusion approach. Ref. [12] introduced a clustering-based coverage path planning method designed to develop efficient flight routes for autonomous heterogeneous UAV systems, thereby improving coverage efficiency and reducing mission duration. Additionally, Ref. [13] proposed a distributed online cooperation method for UAV coverage path planning that optimizes task completion time by 15% to 25% compared to traditional methods through environmental information map fusion technology and a distributed deep Q-learning algorithm, while effectively addressing unknown obstacles and complex emergencies. Furthermore, Ref. [14] presented a novel wildfire detection approach based on a UAV-assisted Internet of Things (UAV-IoT) network, evaluating its reliability in detecting wildfires within limited time frames and optimizing device density and UAV numbers to enhance detection probability. However, most of the existing research primarily focuses on short-term energy security strategies for UAVs, with limited consideration of long-duration operations, thereby constraining the capability of UAVs to execute extended coverage missions.

Scholars both domestically and internationally have conducted research on the use of ground support systems for UAV operations. Ref. [15] investigated the energy trade-off between ground terminals and UAVs in ground-to-UAV (G2U) communication, deriving energy consumption expressions for both circular and linear UAV trajectories, and optimizing the ground terminal transmission power and UAV trajectories to achieve Pareto optimal trade-offs. Ref. [16] proposes a coherent and cost-effective energy procurement framework aimed at powering UAVs through laser beams and local renewable energy sources, thereby reducing their overall energy costs and optimizing their positional strategies in communication. Ref. [17] designed an energy-efficient UAV relay communication scheme, jointly optimizing the transmission power of UAVs and base stations, as well as the UAV trajectories, acceleration, and speed, while introducing information causality constraints (ICC) to ensure the effectiveness of data forwarding and solving the non-convex optimization problem using iterative algorithms. Additionally, Ref. [18] examined the process of using UAVs to charge ground nodes within a radio energy transmission system, proposing two charging schemes—V-shaped and inverted trapezoidal—to maximize the energy received by ground nodes and improve the fairness of energy distribution. However, previous studies have primarily focused on task-driven approaches, such as uniformly deploying ground support systems across entire forests or in geographically advantageous areas [19], which shortens the round-trip distance for UAVs to and from the GSS, thus reducing the number of UAVs required and the overall energy consumption of the UAV system [20], while enhancing inspection efficiency. Nevertheless, these studies often overlook the characteristics of renewable energy generation devices [21]. It is well known that solar resources are abundant in mountaintop and south-facing slope areas, while wind resources are plentiful in valleys and ridges; however, these areas are often unevenly distributed. Therefore, when planning the locations of GSS, it is essential to consider the potential for renewable energy generation.

To this end, this paper builds upon the existing literature and uses UAV forest fire inspection as the research object, considering the planning and design of ground support systems, and establishes a three-tier mixed-integer linear programming model. The first layer examines the site selection and capacity planning of GSS based on the consideration of renewable energy generation. The second layer, built upon the GSS established in the first layer, delineates the energy assurance range of different GSS as the inspection areas. The third layer plans the inspection routes for UAVs and coordinates multi-UAV tasks based on the inspection areas defined in the second layer. These three layers of the model are not independent of one another; rather, they are interconnected and inseparable, requiring simultaneous optimization. Compared to previous research, the main contributions of this paper can be summarized as follows:

• A comprehensive mixed planning model is established, comprising the GSS site selection model, generation device capacity allocation model, inspection area division model, inspection route planning model for each inspection area, and multi-UAV collaborative task planning model. This model aims to optimize the overall efficiency of UAV inspection tasks and enhance the economic benefits of resource allocation within the energy assurance system.
• A hybrid solving strategy is proposed, employing an integer programming algorithm to address the upper-layer site selection and capacity determination problem formulated as an integer linear programming model, while k-means clustering, the boundary function, and the Douglas–Peucker algorithm are used to address the inspection area division problem. A goal-driven greedy algorithm (GDGA) is applied to tackle the multi-UAV collaborative task planning issue.
• Extensive simulation experiments are conducted to verify the effectiveness of the proposed model. Additionally, comparative algorithm experiments are executed to demonstrate the enhanced solution achieved through the proposed algorithm.

The remainder of this paper is organized as follows. Section 2 provides a detailed introduction to the research problem addressed in this paper and describes the conceptual framework for establishing the three-tier mixed-integer linear programming model. Section 3 formulates the specific mathematical planning models for each layer and provides detailed explanations for each model. Section 4 presents corresponding solution methods for the models developed in Section 3, including several improved algorithms proposed in this paper. Section 5 presents simulation experiments and analyzes the results. Finally, Section 6 summarizes the research contributions and suggests directions for future research.

2. Problem Description

This paper primarily focuses on the planning and application of UAV systems for forest fire prevention patrols. The overall framework of the problem is illustrated in Figure 1A, depicting the scene of forest fire prevention inspection. The entire forest area can span hundreds to tens of thousands of square kilometers, necessitating division into several zones. Each zone is equipped with a GSS to support UAV patrol tasks, furnished with relevant inspection equipment and a certain number of UAVs. The patrol task planning for each zone is shown in Figure 1B, where multiple UAVs perform coordinated inspections, executing a ’Z-shaped’ back-and-forth pattern according to predefined patrol missions. Planning involves defining the patrol trajectory, the UAV’s flight direction, and the collaboration strategy among multiple UAVs. The configuration details of the GSS within each zone are shown in Figure 1C, which includes energy supply devices such as renewable energy generation units, energy storage systems (ES), and diesel generators (DG), as well as UAV control centers, UAV monitoring equipment, and data processing units.

After introducing the aforementioned system, the subsequent question is how to plan the entire UAV inspection system. The solution framework proposed in this paper is illustrated in Figure 2, and the entire strategy is divided into three stages. The first stage primarily focuses on the site selection of the GSS and the capacity configuration of power generation devices. The site selection problem for the GSS mainly involves considering both the renewable energy generation capacity and the efficiency of UAV inspections, choosing a reasonable construction site for the GSS in a trade-off between the two. The capacity configuration problem for power generation devices primarily involves determining the capacity of renewable energy generation equipment based on local renewable resources, alongside configuring appropriate energy storage devices for charging and discharging, as well as a certain number of diesel generators to address any inadequacies in renewable power supply. The second stage mainly concerns the division of UAV inspection areas and the planning of UAV flight trajectories. Based on the positions and capacities determined for the GSS in the first stage, it is assumed that each area has only one GSS, and the size of the divided areas is determined according to the GSS’s renewable energy generation capacity—the greater the renewable energy output, the larger the area, which corresponds to a greater workload. Once the area has been divided, the flight trajectories of the UAVs can be determined based on the polygonal characteristics of the area. Since UAVs consume more energy while turning, the optimal flight direction should be planned to minimize the number of turns, a point that will be elaborated on in the subsequent model development. The third stage focuses on configuring the number of UAVs and planning their collaborative tasks. Building on the foundations established in the first two stages, a task-level study can then be conducted for the established GSS and task areas, ensuring that the number of UAVs deployed precisely meets the inspection task requirements while minimizing energy production costs without risking unmet load demands. While the UAVs are executing inspection tasks, it is essential to coordinate the responsibilities of each UAV to ensure the entire inspection mission is completed efficiently while minimizing the total energy consumption of all UAVs.

It is important to note that these three stages are not independent but are interconnected. Specifically, the output of each stage determines the input for the next stage, and the results of the subsequent stage influence the total cost of the overall planning scheme, thereby in turn affecting the output of the previous stage. The results of the first stage, involving GSS site selection and capacity planning, determine how the region is divided and the routing direction is planned in the second stage. Conversely, the principle of regional division affects the total cost of the overall scheme, which in turn influences the decision-making in the first stage. Similarly, the regional division and routing direction planned in the second stage determine the number of UAVs to be deployed and their task allocation in the third stage. Different planning outcomes in the third stage result in varying energy consumption costs, which in turn feedback into the second stage to influence its planning decisions. Therefore, a simultaneous optimization of all three stages is essential in the overall system design to achieve the minimum total planning cost.

3. Mathematical Model

3.1. First Stage Planning Model

This section primarily focuses on the modeling of the site selection and capacity planning problem for GSS, which is divided into two parts. The first part involves the site selection problem, where several alternative locations must be determined as potential sites. Then, based on the optimization objectives, a number of these alternative locations are selected as sites for constructing the GSS. The second part is the capacity planning problem, which involves determining the capacity allocation scheme for the generating equipment based on demand load [22]. Simulations are then conducted based on this scheme to model power generation over time scales and calculate relevant costs to evaluate the effectiveness of the capacity allocation scheme, allowing for adjustments towards an optimal configuration. The specific model is as follows:

$$\begin{array}{cc}\hfill \min F_1=& \sum _{i\in B}\left(\sum _{u_k\in U}{c}_{u_k}^{\mathrm{inv}}·N_{u_k}^i\right)·x_i+\sum _{i\in B}\sum _{t\in T}\sum _{u_k\in U}{c}_{u_k}^{\mathrm{op}}·P_{u_k}^{i,t}\hfill \end{array}$$

(1)

$$U=\{PV,ES,DG\}$$

(2)

$$c_{u_k}^{\mathrm{inv}}={\displaystyle \frac{ϵ{(1+ϵ)}^{{\tau }_{u_k}}}{{(1+ϵ)}^{{\tau }_{u_k}}-1}}·c_{u_k}^{\mathrm{buy}}$$

(3)

$$0\le N_{u_k}^i\le N_{u_k}^{\max }$$

(4)

In this context, Equation (1) represents the objective function of the first-stage model. The first half of the equation indicates the planning cost, which refers to the cost required to deploy generating units. Here, B denotes the set of alternative locations, and $x_i$ is a binary variable that takes the value of 1 if GSS is established at that location and 0 otherwise. U represents the set of all generating units, as shown in Equation (2). $c_{u_k}^{\mathrm{inv}}$ denotes the annualized investment cost for each generating unit $u_k$, while $c_{u_k}^{\mathrm{buy}}$ represents the unit acquisition cost of the power generation equipment. $N_{u_k}^i$ indicates the number of generating units equipped at the $i^{th}$ location, with constraints outlined in Equation (4). Equation (3) is used to calculate the investment cost of the generation device, where ${\tau }_{u_i}$ refers to the lifespan of device $u_i$, $ϵ$ is the discount rate, and $T_{\mathrm{inv}}$ indicates the planning time scale of the microgrid. By utilizing Equation (3), it is possible to the calculate the investment cost of the generation device $u_i$ over the time scale $T_{\mathrm{inv}}$, accounting for factors such as wear, maintenance, and upkeep.

$$P_{PV}^{i,t}+P_{DG}^{i,t}+P_{E{S}_{dis}}^{i,t}=P_L^{i,t}+P_{E{S}_{ch}}^{i,t}\forall i,t=1,2,\dots ,24$$

(5)

$$P_L^{i,t}=\left({\displaystyle \frac{k_0+a·k_0^2}{b·k_0+c·k_0^3}}\right)·P_{UAV}^{i,t}$$

(6)

The second half of Equation (2) represents the operational costs over the planning time scale T, where $c_{u_k}^{\mathrm{op}}$ denotes the unit operational cost of the generating unit $u_k$, also referred to as the unit generation cost, and $P_{u_k}^{i,t}$ represents the corresponding power output. The power balance constraint is presented in Equation (5), where the left-hand side denotes the power generation, including photovoltaic generation $P_{PV}^{i,t}$, diesel generator output $P_{DG}^{i,t}$, and energy storage discharge $P_{E{S}_{dis}}^{i,t}$; the right-hand side indicates the power consumption, comprising load $P_L^{i,t}$ and energy storage charging $P_{E{S}_{ch}}^{i,t}$. The Equation (6) indicates the method for calculating the $P_L^{i,t}$, where $k_0$, a, b, and c represent the correlation coefficients, and $P_{UAV}^{i,t}$ denotes the load of the UAV. This formula demonstrates a positive correlation between the total load and the load of the UAV. As the energy consumed by the UAV within a GSS increases, the power consumption of the associated equipment also rises. This indicates that the total load is related to the inspection workload of the UAV.

$$P_{PV}=I·A_{PV}·{\eta }_{PV}$$

(7)

$${\eta }_{PV}={\eta }_0·\left(1-\varphi ·(T-T_{\mathrm{ref}})\right)$$

(8)

Equation (7) illustrates the calculation method for photovoltaic generation, where I represents the irradiance, $A_{PV}$ denotes the area of the photovoltaic panels, and ${\eta }_{PV}$ indicates the conversion efficiency. The calculation method is outlined in Equation (8), where ${\eta }_0$ is the conversion efficiency at standard temperature, $\varphi$ is the temperature coefficient, and $T_{\mathrm{ref}}$ is the reference temperature.

$$SOC(t+\Delta t)=SOC\left(t\right)+\left({\eta }_{{ES}_{ch}}·{\displaystyle \frac{P_{E{S}_{ch}}^{i,t}}{E_{\max }}}-{\displaystyle \frac{P_{E{S}_{dch}}^{i,t}}{E_{\max }·{\eta }_{{ES}_{dch}}}}\right)·\Delta t$$

(9)

$$0\le P_{E{S}_{ch}}^{i,t}\le P_{E{S}_{ch}}^{max}$$

(10)

$$0\le P_{E{S}_{dch}}^{i,t}\le P_{E{S}_{dch}}^{max}$$

(11)

$$SO{C}_{min}\le SOC\le SO{C}_{max}$$

(12)

The calculation method for the state of charge (SOC) of the ES is shown in Equation (9), where ${\eta }_{E{S}_{ch}}$ and ${\eta }_{E{S}_{dch}}$ represent the charging and discharging efficiencies, respectively, and $E_{\max }$ is the maximum capacity of the ES, with its charging and discharging constraints illustrated in Equations (10)–(12).

$$P_{DG}={\eta }_{DG}·m_g·H_g$$

(13)

$$0\le |P_{DG}^{i,t}-P_{DG}^{i,t-1}|\le r_{DG}$$

(14)

$$0\le P_{DG}^{i,t}\le P_{DG}^{max}$$

(15)

The calculation method for the DG is specified in Equation (13), where ${\eta }_{DG}$ indicates the conversion efficiency of the DG, $m_g$ represents the amount of diesel used, and $H_g$ denotes the heating value. The constraints for DG are detailed in Equations (14) and (15), where $r_{DG}$ is the maximum ramp rate of the DG, and $P_{DG}^{max}$ indicates the maximum power output of the DG.

3.2. Second Stage Planning Model

Building upon the completion of the GSS location and capacity planning in the first phase, this section primarily focuses on modeling the division of inspection regions [23]. After determining the location and capacity of each GSS, the power supply capacity can be calculated. To maximize the utilization of power generation resources and reduce overall costs, this section adopts a principle for regional division: the larger the power supply capacity, the larger the area of the inspection region it serves. First, ensure that each GSS is responsible for a single inspection sub-region, with no overlap between sub-regions; the union of all sub-regions constitutes the entire inspection area [24]. The specific model developed is as follows:

$$max{F}_2=\sum _{s\in S}\sum _{j\in J}{C}_s·A_j·x_{sj}$$

(16)

$$C_s={\displaystyle \frac{{\displaystyle \sum _{u_k\in U}}{p}_{u_k}^{max}·N_{u_k}^s}{{\displaystyle \sum _{u_k\in U}}{p}_{u_k}^{max}·N_{u_k}^{max}}}$$

(17)

Among these, Equation (16) represents the objective function for the second phase, where S denotes the collection of GSS selected in the first phase, J indicates the collection of divided inspection regions, and $C_s$ represents the power supply capacity of the s-th GSS. The specific calculation method is provided in Equation (17). The variable $A_j$ denotes the area of the j-th inspection region. Using the product of $C_s$ and $A_j$ as the objective function signifies that a larger power supply capacity corresponds to a larger area of the inspection region being served, thus maximizing the objective function. The variable $x_{sj}$ is a binary variable indicating whether the s-th GSS provides power to the j-th sub-region; it is equal to 1 if power is supplied and 0 otherwise. Equation (17) illustrates the calculation method for the power supply capacity of a GSS, based on the ratio of the maximum power generation capacity of the GSS to its power generation capacity under maximum configuration conditions. In simpler terms, this is the ratio of the GSS’s maximum power supply capacity to the maximum power supply capacity stipulated for a single GSS in this study. Here, $p_{u_k}^{max}$ denotes the maximum power output of a single generating unit $u_k$, $N_{u_k}^s$ represents the number of that type of generating unit configured within the GSS, and $N_{u_k}^{max}$ indicates the maximum allowable number of generating units $u_k$ that can be configured in a single GSS as stipulated in this study.

$$\sum _{j\in J}{A}_j=A_{\mathrm{total}}$$

(18)

$$0\le A_j\le A_{\mathrm{total}},\forall j\in J$$

(19)

$$\sum _{s\in S}{x}_{sj}=1,\forall j\in J$$

(20)

The relevant constraints of this model are presented in Equations (18)–(20). Equation (18) states that the union of all sub-regions constitutes the inspection area, Equation (19) asserts that the area of each sub-region must fall within a reasonable range, and Equation (20) indicates that each GSS supplies power to only one sub-region, which exclusively represents the inspection area for that GSS.

3.3. Third Stage Planning Model

After the models for the above two stages have been established, the remaining problem is how UAVs conduct inspections within each sub-region [25]. Specifically, this involves how multiple UAVs can collaborate efficiently to complete the inspection tasks. Previously, it was mentioned that UAVs perform inspections using a “Z-shaped” back-and-forth flight pattern, and their inspection routes have been determined. However, because the sub-region areas are still relatively large, a single UAV cannot complete the inspection task alone. Therefore, multiple UAVs are needed to collaborate in inspection. The proposed plan in this paper is to partition the UAV inspection route into several segments, with each UAV responsible for inspecting one segment. Consequently, each segment has a start and end point, and the entire route can be represented as a collection of inspection points, $P=\left(p_1,\dots ,p_i{p}_j\dots \right)$. However, traveling back and forth between the inspection points from the GSS consumes a certain amount of energy, which is not directly related to the inspection task itself. Therefore, it is essential to plan these inspection points carefully to minimize this energy consumption and improve inspection efficiency. The model in this section aims to find the optimal inspection point plan. The specific model is as follows:

$$min{F}_3=\sum _{v_i\in V}\sum _{p_j\in P}{P}_{UAV}^{p_j{p}_{j+1}}·x_{v_i,p_j{p}_{j+1}}$$

(21)

$$P_{UAV}^{p_j{p}_{j+1}}=P_{prop}·{\displaystyle \frac{d_{p_j{p}_{j+1}}}{v_f^u}}$$

(22)

$$d_{p_j{p}_{j+1}}=d\left((x_0,y_0),p_j\right)+d(p_j,p_{j+1})+d(p_{j+1},(x_0,y_0))$$

(23)

Equation (21) represents the objective function of the third stage, where V denotes the set of UAVs within the sub-region. $P_{UAV}^{p_j{p}_{j+1}}$ indicates the total power consumed by UAV $v_i$ for inspecting the route segment $\{p_j,p_{j+1}\}$. The variable $x_{v_i,p_j{p}_{j+1}}$ is a binary indicator of whether the UAV inspects this route segment. Equation (22) describes the calculation method for the UAV’s power, where $P_{prop}$ is the propulsion power, $v_f^u$ is the straight-line speed, and $d_{p_j{p}_{j+1}}$ is the total distance flown for inspecting the segment. As shown in Equation (23), this includes the distance from the GSS to the inspection start point $p_j$, the inspection distance itself, and the return distance from $p_{j+1}$ back to the GSS.

$$P_{prop}=P_0+P_i$$

(24)

$$P_0={\displaystyle \frac{\delta }{8}}\rho s{A}_{UAV}{\Omega }^3{R}^3$$

(25)

$$P_i=(1+k_{UAV}){\displaystyle \frac{W^{3/2}}{\sqrt{2\rho A_{UAV}}}}$$

(26)

The calculation of $P_{prop}$ is detailed in Equation (24), with $P_0$ representing the UAV’s profile power and $P_i$ representing the induced power of the rotor blades. Equations (25) and (26) provide methods for calculating these powers, involving parameters such as the profile drag coefficient $\delta$, air density $\rho$, rotor solidity s, rotor radius R, swept area $A_{UAV}$, angular velocity $\mathrm{\Omega }$, induced power correction factor $k_{UAV}$, and UAV weight W.

$$\sum _{p_j\in P}{x}_{v_i,p_j{p}_{j+1}}=1,\forall v_i\in V$$

(27)

$$d_{p_j{p}_{j+1}}\le d_{\max },\forall p_j\in P$$

(28)

The model includes constraints shown in Equations (27) and (28), where the former stipulates that each UAV is assigned only one inspection route and performs the task once, with no repetitions, and the latter restricts each UAV’s flight distance to not exceed the maximum flight range $d_{max}$.

4. Optimization Methodology

4.1. Optimization Method for Area Partitioning

This section aims to address the problem of partitioning inspection zones, specifically by assigning corresponding sub-regions to each GSS, allowing them to undertake the inspection assurance tasks for those areas [26]. The principle for zone partitioning is that GSS with greater power capacity should cover larger sub-regions. To achieve this, the study employs a clustering method and designs a distance function to guide the clustering process. The distance function consists of two components: the first measures the spatial distance between discrete points and different GSS, while the second assesses the power capacity of various GSS, as shown in Equation (29). Here, $D(q,G_i)$ represents the combined distance from discrete point q to GSS $G_i$, $d(q,G_i)$ is the Euclidean distance between point q and GSS $G_i$, and $C\left(G_i\right)$ denotes the power capacity of GSS $G_i$, with $\alpha$ and $\beta$ being weight coefficients used to adjust the influence of the two components. During the clustering process, we first uniformly discretize the map into several discrete points. We then utilize the aforementioned distance function to cluster the discrete points, resulting in an initial zone partition. It is important to note that the regions generated by this method are irregular curved shapes, which adds complexity to subsequent processing. To address this issue, we introduce a boundary fitting function to fit each clustered area into a polygonal shape. Although this polygonal representation can more clearly delineate zone partitions, the initially generated polygons often have numerous edges and complex shapes. Therefore, we further apply the Douglas–Peucker algorithm to simplify the polygons, reducing their complexity and obtaining the final zone partition results. This approach not only maintains the rationality of the zone partitioning but also facilitates subsequent analysis and processing.

$$D(q,G_i)=\alpha ·d(q,G_i)-\beta ·C\left(G_i\right)$$

(29)

The detailed optimization process is illustrated in Algorithm 1. It begins with distance calculation and region division based on the previously defined distance function, resulting in an initial partition of sub-regions. Subsequently, for each clustered region, the boundary fitting function is applied to approximate it as a polygon. The Douglas–Peucker algorithm is then employed to simplify the polygons according to specified rules, reducing the number of edges while preserving the essential shape, which results in polygonal regions that conform to the initial partitioning principles and exhibit lower complexity, thereby facilitating subsequent computational processing. The preliminary results after clustering are shown in Figure 3a. Although these sub-regions strictly adhere to the partitioning rules proposed in this section, they are irregular curvilinear shapes, posing significant challenges for subsequent processing. The results after applying the boundary fitting function are shown in Figure 3b. Clearly, this approach produces distinct polygonal sub-regions; however, the polygons contain many edges, and their complexity remains high. The results after further simplification using the Douglas–Peucker algorithm are presented in Figure 3c. As can be seen from the figures, the partitioned sub-regions not only conform to the principles proposed but also significantly reduce polygon complexity, making subsequent calculations more efficient. These methods ensure accurate partitioning while markedly improving the operational feasibility and efficiency of the process.

Algorithm 1 Inspection Zone Partitioning Algorithm

1: Input: Map data, GSS power capacities 2: Output: Final zone partition results 3: Discretize the map into a set of discrete points Q 4: Initialize the distance function $D(q,G_i)$ 5: for each discrete point $q\in Q$ do 6:     for each GSS $G_i$ do 7:         Calculate the Euclidean distance $d(q,G_i)$ 8:         Calculate the power capacity $C\left(G_i\right)$ 9:         Compute the combined distance $D(q,G_i)=\alpha ·d(q,G_i)-\beta ·C\left(G_i\right)$ 10:     end for 11: end for 12: Apply clustering algorithm to the discrete point set Q based on the distance function 13: Obtain initial zone partitions 14: for each clustered area do 15:     Use boundary fitting function to fit the area as a polygon 16: end for 17: for each generated polygon do 18:     Apply Douglas—Peucker algorithm to simplify the polygon 19: end for 20: Output final zone partition results

4.2. Optimization Method for Inspection Direction Selection

As mentioned earlier, this paper employs a “Z-shaped” reciprocal coverage path planning method for unmanned aerial vehicles. To improve the efficiency of coverage operations, the first step is to determine the flight direction for coverage [27]. According to investigation and research, UAVs typically need to fly out of the coverage area to execute turns and then return to the coverage zone. The frequency of such turning behavior is generally proportional to the total path length; therefore, reducing the number of turns can significantly shorten the operation time. Consequently, the optimization goal of this section is to select a flight direction that minimizes the number of turns. Specifically, after determining the coverage width of the UAV, a set of parallel lines, spaced at intervals equal to the coverage width, are used to intersect the region to be covered at various angles. By traversing different orientations, the coverage direction that intersects the fewest nodes within the polygonal region is identified as the optimal coverage flight direction for the UAV. The process of determining the coverage flight direction is illustrated in Figure 4.

The coverage maps under different inspection directions indicate that when the rotation angles are 30° and 50°, the UAV requires at least eight turns to complete the inspection task. However, at a rotation angle of 60°, the UAV needs only seven turns, thereby saving both turning energy and time, which enhances inspection efficiency. Consequently, identifying the optimal inspection direction is of great importance. To rapidly identify the optimal inspection direction for this polygonal area, a coordinate transformation method can be employed. By applying Equation (30) to combine the rotation angle with the original coordinates, the coordinates in the rotated coordinate system can be obtained. Using these new coordinates, the path covering the polygon can be calculated to determine the optimal rotation angle efficiently. Subsequently, Equation (31) can be used to revert the coordinates back to the original coordinate system, thereby revealing the optimal inspection direction.

$$\left[\begin{array}{c}{x}_n^{\prime }\\ y_n^{\prime }\end{array}\right]=\left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]\left[\begin{array}{c}{x}_n\\ y_n\end{array}\right]$$

(30)

$$\left[\begin{array}{c}{x}_n\\ y_n\end{array}\right]=\left[\begin{array}{cc}cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}\right]\left[\begin{array}{c}{x}_n^{\prime }\\ y_n^{\prime }\end{array}\right]$$

(31)

4.3. Optimization Method for UAV Task Planning

One issue to address in this section is how to reasonably allocate inspection tasks to each UAV based on the already planned inspection route, in order to minimize the total flight distance of all UAVs while ensuring the completion of the inspection within that sub-region [28]. Traditionally, most studies adopt a greedy algorithm strategy: if the UAV performing the current inspection task continues to operate, its remaining energy may be insufficient to support its return. In this case, the UAV marks this point as a return point and then returns, while the next UAV starts its inspection from the GSS to the previous UAV’s return point. According to Equation (23), the distances from the GSS to the inspection point and from the completed inspection back to the GSS are represented by $d\left((x_0,y_0),p_j\right)$ and $d(p_{j+1},(x_0,y_0))$, respectively. Since these paths do not include inspection, it is possible to introduce a mutually constraining weight between these two distances and the inspection distance $d(p_j,p_{j+1})$. This adjustment allows the inspection distance to be shortened while simultaneously reducing the flight distance needed for UAVs to return. Consequently, the next UAV would also travel a shorter distance to the previous UAV’s return point, leading to an overall reduction in the total flight distance of the UAV fleet. This approach constitutes the goal-driven greedy algorithm proposed in this section. As illustrated in Figure 5, which depicts an extreme case to better demonstrate the effectiveness of the proposed algorithm, the left panel shows that under the traditional greedy algorithm, UAV1’s return distance is excessively large, resulting in a longer travel distance for UAV2 to reach the inspection point. If UAV2’s return distance is also substantial, the sum of $d\left((x_0,y_0),p_j\right)$ and $d(p_{j+1},(x_0,y_0))$ becomes very large. Conversely, as shown in the right panel of Figure 5, the proposed algorithm results in a reduced return distance for UAV1, which in turn shortens the distance UAV2 must travel to the inspection point. Therefore, the sum of these two distances in this case is comparatively smaller.

The goal-driven greedy algorithm’s pseudocode is presented in Algorithm 2. The algorithm aims to reasonably allocate inspection tasks to UAVs while minimizing the total flight distance of all UAVs, ensuring coverage of the inspection area. It begins by initializing each UAV’s current position and remaining energy (i.e., maximum feasible flight distance). Subsequently, the initial maximum inspection distance is determined using an original greedy approach, which involves calculating the distance from each UAV to its next inspection point. If, after completing the task, the UAV can safely return to the GSS, it executes the inspection and updates its position and remaining energy; otherwise, it returns to the nearest GSS. The next UAV then departs from the GSS to inspect the previous UAV’s return point. Unlike the original greedy algorithm, this method introduces a weighted mechanism that constrains both the initial maximum inspection distance and the round-trip distance to the GSS. By allocating weights to each component, the approach balances these factors, striving to maximize the inspection distance while reducing the UAV’ total round-trip flying distances. This significantly lowers the overall flight distance of the UAV fleet. The method effectively combines task allocation and energy management, ensuring efficient and feasible UAV inspection operations.

Algorithm 2 Goal-Driven Greedy Algorithm for UAV Inspection (GDGA)

1: Input: Inspection route with points $P=\{p_1,p_2,\dots ,p_n\}$, GSS $(x_0,y_0)$, UAVs $U_{uav}=\{u_1,u_2,\dots ,u_m\}$ 2: Output: Allocated inspection tasks for each UAV 3: for each UAV $u_i\in U_{uav}$ do 4:     $current\_position\leftarrow (x_0,y_0)$ 5:     $remaining\_energy\leftarrow \mathrm{initial}\mathrm{energy}\mathrm{of}{u}_i$ 6:     for each inspection point $p_j\in P$ do 7:         $distance\_to\_next\leftarrow d(current\_position,p_j)$ 8:         if $distance\_to\_next+distance\_to\_GSS\le remaining\_energy$ then 9:              $u_i$ performs inspection at $p_j$ 10:            $remaining\_energy\leftarrow remaining\_energy-distance\_to\_next$ 11:            $current\_position\leftarrow p_j$ 12:         else 13:            $return\_point\leftarrow current\_position$ 14:            $u_i$ returns to GSS 15:            $next\_UAV\leftarrow \mathrm{next}\mathrm{UAV}\mathrm{in}{U}_{uav}$ 16:            $next\_UAV$ starts inspection from GSS to $return\_point$ 17:            break 18:         end if 19:         $distance\_return\leftarrow d(p_j,(x_0,y_0))$ 20:         $inspection\_distance\leftarrow d(p_j,p_{j+1})$ 21:         Adjust distances: 22:         $weight\leftarrow \mathrm{mutually}\mathrm{constraining}\mathrm{weight}\mathrm{between}distance\_return,inspection\_distance$ 23:         $inspection\_distance\leftarrow inspection\_distance-weight$ 24:     end for 25: end for

5. Case Study

5.1. Parameter Setting

This paper focuses on the planning of power supply assurance under UAV-based forest fire patrols. Therefore, the current section begins by approaching the issue from the perspective of forest fire prevention, selecting a real wildfire case for in-depth study and simulating the region accordingly [29]. The case selected is a forest fire that occurred in Turkey on 22 July 2025, specifically in the Sehitgazi district of Eskisehir Province in central Turkey. Investigations indicate that the primary causes of the fire were prolonged high temperatures, drought, and strong winds [30].

Regular inspections using UAV-based forest fire patrol systems could potentially detect critical information in areas that might otherwise be neglected, enabling timely suppression of potential hazards and thereby reducing casualties and property damage [31]. Consequently, this research uses this case for analysis, collecting geographic and meteorological data of the region, and conducting a detailed examination of a rectangular area measuring 30 km by 40 km within the forest (see Figure 6).

Following the delineation of the research area, this section uniformly distributes twelve candidate sites within the region, each representing a potential location for GSS construction (see Figure 7). Due to economic constraints, it is infeasible to establish GSSs at all candidates; hence, the previously developed site selection and capacity planning model is employed for simulation to determine the optimal configuration. Recognizing the strong correlation between GSS placement and renewable energy generation, the study systematically collects and analyzes annual solar radiation data for these sites.

To enhance computational efficiency and reduce complexity, a stochastic optimization method is adopted, wherein the annual solar radiation data are used to estimate scenario probabilities and their expected values, leading to the extraction of representative daily solar radiation profiles. The resulting typical daily solar radiation data for the twelve GSSs are presented in Figure 8.

In this study, to effectively simulate the actual operating conditions of UAVs in forest fire inspection tasks, the simulation environment is set as follows: The flight altitude of the UAV is set at 200 m to ensure effective coverage of a wide inspection area. Regarding meteorological conditions, various environmental factors are considered, with wind speed set to a maximum of 10 m per second to minimize its impact on the stability of the UAV. Additionally, the temperature is set between 15 ℃ and 30 ℃ to simulate common forest climate conditions, while humidity is set between 40% and 70% to reflect a range from humid to dry climate conditions. In addition, this section selects the DJI Matrice 350 RTK (DJI Enterprise, Shenzhen, China) UAV as the research subject, with a variable table showing some parameters of the power generation devices and the UAV, as presented in

Table 1. Key parameters, definitions and settings.

Parameters	Definition	Setting
$N_{PV}$	Installed quantities of PV	[0, 10]
$N_{ES}$	Installed quantities of ES	[0, 8]
$N_{DG}$	Installed quantities of DG	[0, 8]
$c_{PV}^{\mathrm{buy}}$, $c_{PV}^{\mathrm{op}}$	Investment and operation cost of PV (USD)	6150,0.11
$c_{ES}^{\mathrm{buy}}$, $c_{ES}^{\mathrm{op}}$	Investment and operation cost of ES (USD)	12,100,0.89
$c_{DG}^{\mathrm{buy}}$, $c_{DG}^{\mathrm{op}}$	Investment and operation cost of DG (USD)	9600,0.53
$SO{C}_{min}$, $SO{C}_{max}$	Upper and lower bounds of SOC for the ES	0.2, 0.8
$P_{E{S}_{ch}}^{max}$, $P_{E{S}_{dch}}^{max}$	Maximum charging and discharging power (kW)	10
$P_{DG}^{max}$	Maximum generation power of DG (kW)	15
$k_0$, a, b, c	correlation coefficient of load calculation	0.121, 1.879, 0.157, 0.186
$ϵ$	Discount rate	0.06
${\tau }_{u_i}$	Service life cycle of equipment $u_i$ (year)	6
$A_{PV}$	Area of photovoltaic panels (m2)	10
$T_{ref}$	the reference temperature	25 °C
${\eta }_0$	Conversion coefficient of PV at $T_{ref}$	17%
${\eta }_{DG}$	Conversion coefficient of DG	36.4%
$H_g$	the calorific value (kWh/m3)	9.78
$r_{DG}$	Maximum ramp-up power of DG (kW)	5
$\delta$	the profile drag coefficient	0.012
s	the rotor solidity of UAV	0.16
R	the rotor radius of UAV (m)	0.81
$A_{UAV}$	the swept area of UAV (km2)	2.061
$k_{UAV}$	the power correction factor of UAV	0.1
W	the Weight of the UAV (N)	64.7
$\rho$	Air density (kg/m3)	1.225
$d_{max}$	the maximum flight range (km)	26.4

[32].

5.2. Simulation Result

5.2.1. Analysis of Model Effectiveness

By applying the model proposed in this paper to solve the problem, the GSS site selection and capacity planning scheme can be obtained. To verify the effectiveness of the model, this section sets up three models for comparative analysis: Model A (Proposed) is the three-layer planning model proposed in this paper; Model B (Take-Only) only considers the site selection and capacity planning at the task level, without accounting for renewable energy generation. Specifically, Model B first divides the inspection area evenly, then establishes GSS at the geometric center of each sub-region, followed by capacity planning. Model C (Renewable-Only) only considers site selection under renewable energy generation conditions, ignoring the inspection task layer; it first establishes GSS at locations rich in renewable resources, then conducts regional division and task planning based on these results.

Table 2. The costs of the power supply system planning.

Model (Type)	Annual Total Cost (USD)	Annual Planning Cost (USD)	Annual Operation Cost (USD)	Penetration Rate of Renewable Energy
A (Proposed)	$4.321\times {10}^5$	$2.672\times {10}^5$	$1.649\times {10}^5$	68.71%
B (Take-Only)	$6.014\times {10}^5$	$3.171\times {10}^5$	$2.843\times {10}^5$	37.23%
C (Renewable-Only)	$5.15\times {10}^5$	$2.874\times {10}^5$	$2.276\times {10}^5$	55.96%

presents the cost comparison results of each model, while

Table 3. Site selection and capacity planning.

Model (Type)	Site Selection	Capacity Planning (PV, ES, DG)
A (Proposed)	GSS2 GSS4 GSS9 GSS11	GSS2: [4 1 3] GSS4: [6 2 2]
		GSS9: [5 2 2] GSS11: [3 0 3]
B (Take-Only)	GSS5 GSS6 GSS7 GSS8	GSS5: [4 0 5] GSS6: [5 3 3]
		GSS7: [4 0 5] GSS8: [3 0 6]
C (Renewable-Only)	GSS4 GSS5 GSS6 GSS9	GSS4: [4 1 1] GSS5: [5 1 1]
		GSS6: [10 0 4] GSS9: [5 2 3]

displays the planning scheme outcomes.

Based on the analysis presented in Table 2, although the planning costs across the three models are similar, Model A incurs a notably lower total cost compared to Models B and C. This difference is primarily attributed to significant variations in operational costs among the models. As shown in Table 3, Models A and C feature relatively balanced generation capacity configurations, whereas Model B has a less developed ES, with some GSS lacking storage devices. To gain deeper insights into these results, we analyzed the regional division outcomes. Figure 9 illustrates that Model A’s regional division is relatively regular; notably, GSS4 is equipped with more generation units, resulting in higher power generation capacity and a larger area share. In contrast, GSS2 has fewer units and occupies a smaller area, but the difference between them is not substantial. Model B’s regional division displays a highly uniform pattern, with each inspection sub-region having equal area. Conversely, Model C’s inspection regions differ significantly, with GSS6’s area being substantially larger than the others—mainly because GSS6 is equipped with the most generation units. To further understand the reasons behind the differences in operational costs, we examined the power outputs of the key GSSs on a typical day—specifically GSS4 in Model A, GSS8 in Model B, and GSS6 in Model C—as shown in Figure 10. The results reveal that renewable energy generation and ES dominate in Model A, with DG playing a compensatory role only during peak load periods. Conversely, Model B relies more heavily on DG due to limited renewable energy output, primarily because it only considers task-level regional divisions without accounting for renewable resource siting. This results in a power system with scarce renewable resources, a lower proportion of renewable energy generation, and no need for ES to store excess electricity. The reliance on DG, which has higher operational costs, explains why Model B’s operational costs are higher than those of the other models. Observations of Model C’s power generation indicate that, despite higher renewable energy output, its load is significantly greater than that of the other models. This is due to an unreasonable regional division; the excessively large area of GSS6 increases the round-trip distance for UAV inspections. Although the actual inspection path length is short, frequent deployment of multiple UAVs is necessary, leading to higher total energy consumption. Consequently, GSS6’s total load remains high, which significantly raises operational costs.

5.2.2. Analysis of Algorithm Performance

To validate the effectiveness of the proposed goal-driven greedy algorithm, this section presents a series of comparative experiments. Different inspection paths were generated by varying the rotation angles of the path directions. Both the standard greedy algorithm and the goal-driven greedy algorithm were employed to solve each path, resulting in task planning schemes for the UAVs under various inspection directions. The experimental results are detailed in

Table 4. Comparison of algorithm performance.

Rotation Angle	Distance from Greedy Algorithm (km)	Distance from Goal-Driven Greedy Algorithm (km)
0°	29.9893	27.873
30°	54.9226	52.4558
60°	65.9073	59.9575
90°	32.9951	29.9679
120°	7.9921	6.9991
150°	20.009	17.9853

and Figure 11. Table 4 presents the total inspection path distances obtained using the two algorithms under different rotation angles. Figure 11 provides a visual comparison of the inspection routes produced by the two algorithms under various path configurations, demonstrating that different strategies have a significant impact on the efficiency and effectiveness of UAV-based inspection tasks.

Figure 11 provides a visual representation of the task planning schemes for the two algorithms under various path configurations, where the different schemes significantly impact the efficiency and effectiveness of the UAVs in inspection tasks. It is evident that the inspection route generated by the goal-driven greedy algorithm for the round trip to GSS is shorter, whereas the route obtained using the greedy algorithm is relatively longer. As shown in Table 4, there are significant differences in the total distances of the inspection paths calculated using the two algorithms at different rotation angles. The data indicate that the task planning distances for the goal-driven greedy algorithm are consistently shorter than those for the greedy algorithm at all tested angles, demonstrating its superior performance.

To validate the performance of the proposed algorithm in terms of solving efficiency, four sets of comparative experiments were designed, corresponding to UAV flight distances of 10 km, 20 km, 50 km, and 100 km. For each scenario, the greedy algorithm, goal-driven greedy algorithm, and Genetic Algorithm (GA) were employed to obtain the solution times for each specific algorithm, as shown in

Table 5. Comparison of algorithm solution time.

UAV Flight Distance (km)	Solution Time of Greedy Algorithm (s)	Solution Time of Goal-Driven Greedy Algorithm (s)	Solution Time of GA Algorithm (s)
10	0.0165	0.0138	3.2406
20	0.8082	0.6657	5.7323
50	1.5473	1.1369	11.2110
100	3.4201	3.5760	16.2035

. An analysis of the results indicates that there is no significant difference in solving speed between the greedy algorithm and the goal-driven greedy algorithm. However, compared to the GA, both algorithms are significantly faster, demonstrating that greedy algorithms are a rapid solving strategy for such problems, with speeds far surpassing those of heuristic algorithms. Furthermore, by considering the results in Table 4, it can be confirmed that the proposed goal-driven greedy algorithm exhibits both fast solving speed and high-quality results, making it particularly suitable for the problems studied in this paper.

5.3. Discussion

The analysis of the comparative experimental results of the models indicates that, in considering the energy security of UAV inspections, it is essential not only to plan the task allocation and area division of the UAVs reasonably but also to fully consider the utilization of renewable resources. To minimize the total cost while ensuring task completion, it is necessary to integrate both aspects to construct an effective site selection and capacity planning model. Furthermore, the comparative results of the algorithms demonstrated the effectiveness of the goal-driven greedy algorithm in optimizing path planning. This algorithm significantly reduces the distance that UAVs travel to and from GSS, a factor that directly affects the total energy consumption of all UAVs.

6. Conclusions and Future Work

In this study, we propose a comprehensive planning model for a UAV forest fire inspection system, aimed at optimizing the site selection and capacity configuration of the GSS and effectively assigning inspection tasks to UAVs. By establishing a three-layer mixed-integer linear programming model, we systematically address key issues such as GSS site selection and capacity planning, division of inspection regions, and collaborative UAV task planning. The results demonstrate that the proposed model offers significant advantages in reducing overall costs and enhancing resource utilization efficiency. Through extensive simulation experiments, we validated the effectiveness of the model and algorithm, and compared them with several existing methods, showing that our approach consistently outperformed these alternatives in multiple aspects.

Despite the achievements of this study, several limitations remain. Firstly, the model’s complexity is relatively high, involving multiple layers of mixed-integer linear programming, which results in longer solving time, particularly in large-scale instances, where practical applications may face computational efficiency issues. Secondly, although the model takes into account the utilization of renewable energy, its adaptability regarding energy generation capabilities under varying climatic conditions and the actual operational environments for UAVs require further validation. Furthermore, the optimization strategies for task allocation and path planning in the model are primarily based on theoretical derivations and do not account for actual obstacles or environmental factors such as wind speed. Lastly, future research could consider integrating more influencing factors, such as meteorological data, to enhance the model’s adaptability and practicality.