Enhancing Unmanned Aerial Vehicle Task Assignment with the Adaptive Sampling-Based Task Rationality Review Algorithm

Abstract

As the application areas of unmanned aerial vehicles (UAVs) continue to expand, the importance of UAV task allocation becomes increasingly evident. A highly effective and efficient UAV task assignment method can significantly enhance the quality of task completion. However, traditional heuristic algorithms often perform poorly in complex and dynamic environments, and existing auction-based algorithms typically fail to ensure optimal assignment results. Therefore, this paper proposes a more rigorous and comprehensive mathematical model for UAV task assignment. By introducing task path decision variables, we achieve a mathematical description of UAV task paths and propose collaborative action constraints. To balance the benefits and efficiency of task assignment, we introduce a novel method: the Adaptive Sampling-Based Task Rationality Review Algorithm (ASTRRA). In the ASTRRA, to address the issue of high-value tasks being easily overlooked when the sampling probability decreases, we propose an adaptive sampling strategy. This strategy increases the sampling probability of high-value targets, ensuring a balance between computational efficiency and maximizing task value. To handle the coherence issues in UAV task paths, we propose a task review and classification method. This method involves reviewing issues in UAV task paths and conducting classified independent auctions, thereby improving the overall task assignment value. Additionally, to resolve the crossover problems between UAV task paths, we introduce a crossover path exchange strategy, further optimizing the task assignment scheme and enhancing the overall value. Experimental results demonstrate that the ASTRRA exhibits excellent performance across various task scales and dynamic scenarios, showing strong robustness and effectively improving task assignment outcomes.

1. Introduction

Nowadays, unmanned aerial vehicles (UAVs) have become crucial tools for performing various tasks, including data collection, monitoring, inspection, and communication relay [1,2,3]. The widespread use of UAVs has not only significantly enhanced efficiency and flexibility [4,5] but also reduced the costs associated with human labor. However, with the increasing number of UAVs and the complexity of their missions, how to effectively allocate tasks for UAVs has become a crucial issue [6,7].

The goal of multi-UAV task assignment is to allocate tasks to suitable UAVs based on mission requirements and UAV capabilities, ensuring optimal mission completion [8,9]. This process involves considering multiple factors such as UAV flight performance, task priority, resource constraints, and environmental interference, making the multi-UAV task assignment a complex combinatorial optimization problem [10,11]. Essentially, it is more complicated than the multi-traveling salesman problem (MTSP) [12] and is classified as an NP-hard [13] problem. Currently, the two main methods for solving task assignment problems are heuristic-based methods and auction-based methods.

Heuristic algorithms are experience-based algorithms that provide feasible solutions to instances of combinatorial optimization problems within reasonable cost limits. Common heuristic algorithms include genetic algorithm (GA) [14], particle swarm optimization (PSO) [15], simulated annealing (SA) [16], and gray wolf optimizer (GWO) [17]. These algorithms simulate natural evolution and group behaviors to effectively solve complex optimization problems [18]. Genetic algorithms explore a wide solution space through operations such as selection, crossover, and mutation to find near-optimal task assignment solutions [19,20]. Particle swarm optimization simulates a bird flock’s foraging behavior to achieve information sharing and global search among individuals [21,22]. However, heuristic algorithms have significant drawbacks, such as slow convergence, tendency to get trapped in local optima, and requiring extensive parameter tuning [23,24]. These issues are particularly pronounced in complex and dynamic environments, limiting the application of traditional heuristic algorithms in UAV task assignment.

To overcome the shortcomings of heuristic methods, market auction-based algorithms have emerged [25,26,27]. These methods dynamically assign tasks to the most suitable UAVs through competitive bidding mechanisms, maximizing task benefits and efficiency [28,29]. Auction-based methods can more flexibly adapt to changes in external environments, quickly adjusting task assignment plans, and exhibit high real-time performance and adaptability.

Choi et al. [30] proposed the consensus-based bundle algorithm (CBBA), which served as the starting point for many derivative auction algorithms. The CBBA achieved consistency in task assignment through local information and limited communication, resolving conflicts in the task assignment process and ensuring 50% optimality. Zhang et al. [31] built on the CBBA and proposed a task sequence maintenance method. This method ensured conflict-free task assignment solutions by evaluating task sequence consistency and introducing task contribution. Shin et al. [32] proposed decentralized sample-based task allocation (DSTA), which incorporated a task sampling process during initialization to form specific task sample sets for each UAV, reducing computational complexity and ensuring optimality for both monotonic and non-monotonic objective functions. Wang et al. [33] expanded the multi-UAV cooperative task assignment model under multiple constraints, establishing a two-stage task assignment algorithm framework and proposing a time window cooperative task assignment algorithm. This algorithm effectively addressed the cooperative task assignment problem for heterogeneous UAVs within different mission execution time windows. Cao et al. [34] proposed a dynamic adjustment strategy based on a task-trigger mechanism. This strategy allowed UAVs to dynamically adjust task assignment results based on time-triggered requests, meeting the real-time and dynamic requirements of multi-task assignment in actual air combat competitions. Yan et al. [35] improved the bundle structure, consensus strategy, and system grouping method, proposing new internal and external conflict resolution consensus methods. These methods effectively reduce the number of communication events required to reach consensus while maintaining the robust convergence characteristics of the baseline CBBA. Kim et al. [36] proposed a systematic method for grouping UAVs based on initial task preferences, increasing communication efficiency among UAV swarms in large-scale scenarios by reducing the total number of information exchanges before converging to conflict-free solutions. Cui et al. [37] integrated time window constraints into a decentralized framework based on pi, associating effective time windows with task importance to minimize task completion time without adding additional communication burdens, achieving more reasonable task assignment. Xu et al. [38] evaluated the overall efficiency of task allocation by incorporating robot status information into the factors influencing task completion and introduced an adjustment step for the task execution sequence, thereby achieving a good balance between high execution efficiency and low motion costs. Buckman et al. [39] reduced team communication burdens by re-planning the team’s size and resetting a portion of previously assigned tasks in each bidding round to balance response time and solution quality.

Despite the advantages of the aforementioned algorithms, they still face several limitations in practical applications. Some algorithms fail to fully consider the complexity of real-world environments in their model designs, others do not achieve the expected overall task assignment benefits, and some struggle with high computational complexity, making them unsuitable for large-scale task scenarios. Therefore, this paper proposes a new algorithm, the Adaptive Sampling-Based Task Rationality Review Algorithm (ASTRRA), to address the complex and changing real-world environment.

The main contributions of this paper are as follows:

• Introducing task path decision variables and incorporating real-world constraints such as collaborative action constraints into the traditional model, improving the rigor and completeness of the task assignment mathematical model.
• Proposing an adaptive sampling strategy with dynamically adjusted sampling probabilities based on task importance, effectively avoiding the loss of high-value tasks due to low sampling probabilities, and ensuring a balance between computational efficiency and maximizing task value.
• Presenting a task review and classification method to address coherence issues in UAV task paths that are common in existing auction algorithms, significantly enhancing overall task benefits.
• Proposing a crossover path exchange strategy to reduce crossovers between UAV task paths, further optimizing the task assignment scheme and improving overall benefits.

The remainder of this paper is organized as follows. Section 2 introduces variable definitions and the basic symbols used in this paper. Section 3 establishes the mathematical model for UAV task assignment. Section 4 details the principles of the proposed ASTRRA. Section 5 validates the effectiveness of the proposed method through extensive simulation experiments. Section 6 summarizes this paper.

2. Preliminary

This section covers the preparatory work. Section 2.1 covers variable definitions, Section 2.2 introduces symbol descriptions, and Section 2.3 introduces the assumptions.

2.1. Variable Definitions

Definition 1. 

The number of tasks actually undertaken by UAV a, denoted as $n_a$, is given by:

$$n_a=\sum _{j=1}^N\sum _{i=0}^N{y}_{ij}^a$$

(1)

where i and j are task indices, a is the UAV index, and N is the total number of tasks. $y_{ij}^a$ is the task path decision variable (see Section 3 for details). If the task path of UAV a includes the path from task i to task j, then $y_{ij}^a=1$; otherwise, $y_{ij}^a=0$.

Definition 2. 

The cumulative distance for task j, denoted as $D_j^a$, represents the total distance UAV a flies from the starting point to task j along the assigned task path:

$$D_j^a=d_{0j}{y}_{0j}^a+\sum _{i=1}^N\left(D_i^a+d_{ij}\right)y_{ij}^a,\forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M$$

(2)

where $d_{ij}$ is the distance from task point i to task point j, $d_{0j}{y}_{0j}^a$ is the distance from the starting point to the first task point for UAV a, and M is the total number of UAVs.

Definition 3. 

The flight speed of UAV a, denoted as $v_a$, is the average speed at which UAV a flies. In this paper, we assume that each UAV maintains a constant speed $v_a$ without external influences.

Definition 4. 

The cumulative execution time for task j, denoted as $T_j^a$, represents the total time consumed by UAV a to execute the tasks up to and including task j (excluding flight time):

$$T_j^a=t_{aj}{y}_{0j}^a+\sum _{i=1}^N\left(T_i^a+t_{aj}\right)y_{ij}^a,\forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M$$

(3)

where $t_{aj}$ represents the time consumed by UAV a to execute task j, and $t_{aj}{y}_{0j}^a$ represents the time consumed by UAV a to execute the first task.

Definition 5. 

The time discount factor ${\tau }_j$ indicates the extent to which the revenue from task j is affected by the arrival time of the UAV. The longer the UAV flight time, the higher the discount, and the lower the revenue. This influence is expressed as:

$${{\tau }_j}^{D_j^a/v_a+T_j^a}$$

(4)

Definition 6. 

The fitness factor ${\lambda }_{aj}$ indicates the degree of match between UAV a and task j, with a value between zero and one. A higher value indicates a better match and higher task revenue.

Definition 7. 

The task importance factor ${\xi }_j$. This factor indicates the importance of task j, with a value between zero and one. A higher value indicates a higher importance and a higher priority for execution.

Definition 8. 

UAV task sequence $\left\{P^a\right\}$ is a set that represents the task path of UAV a, describing the complete flight route of UAV a and including the execution order of all task points:

$$P^a=\{P_1^a,P_2^a,\dots ,P_{n_a}^a\}$$

(5)

where $P_m^a=(x_m,y_m)$ represents the coordinates of the mth task point (including the starting point) in the task path of UAV a.

2.2. Symbol Descriptions

In order to facilitate the reading of the mathematical model developed in this paper, the definitions of the symbols involved and their descriptions are presented in

Table 1. The basic symbol definitions and descriptions.

Symbol	Description
M	Total number of UAVs
N	Total number of tasks
$x_{aj}$	Indicates whether UAV a performs task j
$y_{ij}^a$	Indicates whether UAV a flies from task i to task j
$n_a$	Total number of tasks assigned to UAV a
$d_{ij}$	Distance from task point i to task point j
$D_j^a$	Cumulative distance flown by UAV a to task j
$v_a$	Average speed of UAV a
$t_{aj}$	Time consumed by UAV a to perform task j
$T_j^a$	Cumulative time consumed by UAV a to reach task j
${\tau }_j$	Degree to which the benefit of task j is affected by the arrival time of UAVs
${\lambda }_{aj}$	Matching degree of UAV a to task j
${\xi }_j$	Importance level of task j
R	Total benefit value of the UAV task allocation result
$c_j$	Number of times task j needs to be performed
$L_a$	Maximum task load of UAV a
$D_a$	Maximum flight range of UAV a
$t_a$	Takeoff waiting time of UAV a
$t_{\mathrm{start}}$	Official start time of UAV cooperative action
$T_a$	Maximum flight time of UAV a

.

2.3. Assumptions

(1)

The distance between tasks is assumed to be Euclidean.

(2)

All UAVs and tasks are considered in a two-dimensional plane.

(3)

UAV flight speeds are assumed to remain constant.

3. Problem Formulation

This section establishes the UAV task assignment model in complex environments. Section 3.1 describes the decision variables, Section 3.2 formulates the objective function, Section 3.3 outlines the constraints, and Section 3.4 provides a summary of the model.

3.1. Decision Variables

(1)

Task assignment decision variable $x_{aj}$ indicates whether or not UAV a performs task j:

$$x_{aj}=\left\{\begin{array}{cc}0\hfill & \\ 1\hfill \end{array}\right.j=1,2,\dots ,N,a=1,2,\dots ,M$$

(6)

When $x_{aj}=1$, it means UAV a is assigned to execute task j; when $x_{aj}=0$, task j is not assigned to UAV a.

(2)

Task path decision variable $y_{ij}^a$ indicates whether UAV a flies from task i to task j:

$$y_{ij}^a=\left\{\begin{array}{cc}0\hfill & \\ 1\hfill \end{array}\right.i,j=1,2,\dots ,N,a=1,2,\dots ,M$$

(7)

Here, $y_{ij}^a=1$ indicates that UAV a flies from task i to task j; $y_{ij}^a=0$ indicates no such path exists.

3.2. Objective Function

The objective of UAV task allocation is to maximize the total benefit value obtained after completing all tasks. To distinguish between high- and low-reward tasks, the objective function incorporates a non-linear term. The normalization process ensures the final reward value is between zero and one. The final objective function R is to maximize the total benefit:

$$R=max{\displaystyle \frac{{{\displaystyle \sum _{a=1}^M}{\displaystyle \sum _{j=1}^N}\left({\lambda }_{aj}{\xi }_j{\tau }_j^{\frac{D_j^a}{v_a}+T_j^a}{x}_{aj}\right)}^2}{{\displaystyle \sum _{j=1}^N}{max}_a{\lambda }_{aj}{\xi }_j{\tau }_j^{\frac{D_{0j}^a}{v_a}+T_j^a}}}$$

(8)

3.3. Constraints

(1)

Task execution constraint: Each task j needs to be executed $c_j$ times by UAVs:

$$\sum _{a=1}^M\sum _{i=0}^N{y}_{ij}^a=c_j,\forall j=1,2,\dots ,N$$

(9)

For each task j, $c_j$ UAVs are required to execute the task. Each independent task point is assigned to only one UAV in this study.

(2)

Path uniqueness constraint: Each UAV has only one start and end point, and all task points must form a complete path:

$$\sum _{j=1}^N{y}_{0j}^a=1,\sum _{i=1}^N{y}_{i(N+1)}^a=1,\forall a=1,2,\dots ,M$$

(10)

where $y_{0j}^a$ represents the task path decision variable for UAV a flying from the start point to task j, with $y_{0j}^a=1$ indicating the existence of such a path. Similarly, $y_{i(N+1)}^a$ represents the decision variable for UAV a flying from task i to the end point, with $y_{i(N+1)}^a=1$ indicating the existence of such a path.

(3)

Path connectivity constraint: Each task point must be entered and exited, forming pairs:

$$\sum _{j=0}^{N+1}{y}_{ij}^a=\sum _{z=0}^{N+1}{y}_{jz}^a,\forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M$$

(11)

where for UAV a and task j, if there is a path from task i (including the start point) to task j, there must also be a path from task j (including the end point) to task z. Thus, entry into a task point is always accompanied by an exit from that point.

(4)

Decision consistency constraint: Path decision variables and task execution decision variables must be consistent:

$$\sum _{i=1}^N{y}_{ij}^a\le x_{aj},\forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M$$

(12)

where when $x_{aj}=1$, it indicates that task j is assigned to UAV a. Therefore, there must exist a path from task i (including the start point) to task j within UAV a’s task path.

(5)

UAV load constraint: Each UAV has a limited task load:

$$\sum _{j=1}^N\sum _{i=0}^N{y}_{ij}^a\le L_a,\forall a=1,2,\dots ,M$$

(13)

where $L_a$ is the maximum task load of UAV a, indicating that the total number of tasks performed by UAV a cannot exceed its maximum task load.

(6)

UAV range constraint: UAVs have a limited maximum flight distance:

$$\sum _{j=1}^{N+1}\sum _{i=0}^N{d}_{ij}{y}_{ij}^a\le D_a,\forall a=1,2,\dots ,M$$

(14)

where $d_{ij}$ represents the distance from task point i to task point j, indicating that the total distance flown by UAV a to execute tasks must not exceed its maximum flight range $D_a$.

(7)

Collaborative action constraint: To achieve coordinated and consistent actions, UAVs should arrive at the first task point simultaneously:

$${\displaystyle \frac{{\sum }_{j=1}^N{d}_{0j}{y}_{0j}^a}{v_a}}+t_a=t_{start},\forall a=1,2,\dots ,M$$

(15)

where ${\sum }_{j=1}^N{d}_{0j}{y}_{0j}^a$ represents the distance from the start point to the first task point, $t_a$ is the waiting time before UAV a takes off, and $t_{start}$ is the collaborative action start time. This constraint ensures that the takeoff time for each UAV is $t_{start}$, enabling all UAVs to reach the first task point simultaneously.

(8)

Flight time constraint: The total flight and task execution time for UAVs must not exceed their maximum flight time:

$$\sum _{j=1}^N\sum _{i=0}^N\left({\displaystyle \frac{d_{ij}}{v_a}}+t_{aj}\right)y_{ij}^a\le T_a,\forall a=1,2,\dots ,M$$

(16)

where $t_{aj}$ represents the time UAV a spends on task j, and $T_a$ denotes the maximum flight time of UAV a.

3.4. Mathematical Model of Task Assignment

In summary, the mathematical model for UAV task allocation established in this paper is described as follows:

$$\begin{array}{cc}\hfill & R=max{\displaystyle \frac{{{\displaystyle \sum _{a=1}^M}{\displaystyle \sum _{j=1}^N}\left({\lambda }_{aj}{\xi }_j{\tau }_j^{\frac{D_j^a}{v_a}+T_j^a}{x}_{aj}\right)}^2}{{\displaystyle \sum _{j=1}^N}{max}_a{\lambda }_{aj}{\xi }_j{\tau }_j^{\frac{D_{0j}^a}{v_a}+T_j^a}}}\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\left\{\begin{array}{cc}{x}_{aj}=\{0,1\},\hfill & j=1,2,\dots ,N,a=1,2,\dots ,M,\hfill \\ y_{ij}^a=\{0,1\},\hfill & i,j=1,2,\dots ,N,a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{a=1}^M}{\displaystyle \sum _{i=0}^N}{y}_{ij}^a=c_j,\hfill & \forall j=1,2,\dots ,N,\hfill \\ {\displaystyle \sum _{j=1}^N}{y}_{0j}^a=1,{\displaystyle \sum _{i=1}^N}{y}_{i(N+1)}^a=1,\hfill & \forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{j=0}^{N+1}}{y}_{ij}^a={\displaystyle \sum _{z=0}^{N+1}}{y}_{jz}^a,\hfill & \forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{i=1}^N}{y}_{ij}^a\le x_{aj},\hfill & \forall j=1,2,\dots ,N,\forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{j=1}^N}{\displaystyle \sum _{i=0}^N}{y}_{ij}^a\le L_a,\hfill & \forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{j=1}^{N+1}}{\displaystyle \sum _{i=0}^N}{d}_{ij}{y}_{ij}^a\le D_a,\hfill & \forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \frac{{\sum }_{j=1}^N{d}_{0j}{y}_{0j}^a}{v_a}}+t_a=t_{\mathrm{start}},\hfill & \forall a=1,2,\dots ,M,\hfill \\ {\displaystyle \sum _{j=1}^N}{\displaystyle \sum _{i=0}^N}\left({\displaystyle \frac{d_{ij}}{v_a}}+t_{aj}\right)y_{ij}^a\le T_a,\hfill & \forall a=1,2,\dots ,M.\hfill \end{array}\right.\hfill \end{array}$$

(17)

4. Algorithm and Analysis

This section introduces the Adaptive Sampling-Based Task Rationality Review Algorithm (ASTRRA). Section 4.1 provides an overview of the ASTRRA framework. Section 4.2 presents the adaptive sampling strategy, which reduces computational complexity while ensuring high-value tasks are sampled. Section 4.3 proposes a task review and classification method to address the coherence of UAV task paths, thereby improving overall task allocation revenue. Section 4.4 introduces a crossover path exchange strategy to minimize path intersections, further optimizing the allocation scheme.

4.1. Basic Idea and Framework

4.1.1. Introduction of LSTA

The baseline algorithm for our method is the lazy sample-based task allocation (LSTA) algorithm. To facilitate understanding, we first introduce the basic concept of the LSTA algorithm. LSTA, proposed by Zhang et al., [40] is an improved version of the CBBA, enhancing computational efficiency through a lazy strategy. The LSTA algorithm consists of two stages: the initialization stage and the task assignment auction stage.

• Initialization stage: In the first stage, each UAV randomly samples the task set with a pre-set probability to form its own task sample set, followed by initializing the initial task sample set.
• Task assignment auction stage: In the second stage, UAVs calculate and rank the marginal gains [41] for the initial task sample set formed in the first stage. Through negotiation, the task with the highest marginal value and its corresponding UAV are selected, followed by conflict detection. Finally, global consensus and update are performed, adding the task with the highest marginal value to the corresponding UAV’s task set while removing the same task from the sample sets of other UAVs involved in the conflict detection.

The overall process of the LSTA algorithm is shown in Figure 1.

4.1.2. Algorithm Overall Process

Our proposed ASTRRA makes three major improvements to the LSTA algorithm by introducing an adaptive sampling strategy, task review and classification method, and crossover path exchange strategy. The complete steps of the ASTRRA are as follows:

• Initialization stage: We propose an adaptive sampling strategy that dynamically adjusts the sampling probability. This strategy increases the sampling probability for high-value tasks and decreases it for low-value tasks, minimizing the risk of missing high-value tasks due to a low sampling probability and reducing the benefit loss caused by probability adjustment.
• Task assignment auction stage: This stage follows the same process as that of the LSTA algorithm. During each iteration, tasks are auctioned and allocated to the UAV with the highest bid, and the same tasks are removed from the task sample sets of other UAVs. This iterative process continues, completing the initial allocation through repeated auctions.
• Task review and classification stage: We propose a task review and classification method for tasks that are unreasonably allocated during the auction stage. After the first round of auctions for all tasks, tasks are reviewed for coherence using heading change angles and flight distances as indicators. Tasks identified as having coherence issues in the UAV task sequence and tasks assigned to UAVs with underutilized load capacities are classified into two categories, creating a coherence issue task pool and a load-balanced task pool. These two pools undergo a new round of auctions independently, improving the quality of task allocation.
• Crossover path exchange stage: After the task review and classification stage, we introduce a crossover path exchange strategy. This strategy is inspired by the lazy-based review consensus algorithm (LRCA) [42] proposed by Xu et al. for vehicle task allocation and the crossover step in genetic algorithms. The maximum consensus strategy assigns the best task in each iteration to the UAV with the highest bid, which may cause intersections between UAV task paths. By adding a crossover path exchange strategy, the allocation results can be further optimized.

The overall process of the ASTRRA is shown in Figure 2.

4.2. Adaptive Sampling Strategy

For small-scale scenarios, even if each UAV samples all task sets, the speed of LSTA can meet the real-time requirements of UAV task allocation. However, in large-scale task allocation problems, the increased number of tasks leads to a significant rise in computational load. In this context, partial sampling of the task sets can significantly reduce the computational burden, ensuring the speed of the algorithm.

To address large-scale task allocation, we must sample tasks from the task pool. Existing algorithms like LSTA and LRCA use fixed sampling strategies, where each UAV samples tasks from the pool with the same probability p, forming its initial task sample set. This method does not differentiate the importance of task samples. A uniform p value may result in key tasks being overlooked, causing unnecessary revenue loss.

Our proposed adaptive sampling strategy dynamically adjusts the sampling probability based on the characteristics of the tasks, considering their importance and fitness. For high-value tasks or tasks highly suitable for a specific UAV, the sampling probability p is increased, enhancing the chances of these tasks being prioritized. Conversely, for non-urgent or less suitable tasks, the sampling probability p is decreased to conserve resources, ensuring a balance between computational efficiency and task value maximization.

The detailed steps for calculating the dynamic sampling probability are as follows:

Step 1. Calculate the importance proportion s of the current task to be sampled in the task pool and the fitness proportion f of the current task to be sampled in the task pool:

$$s={\displaystyle \frac{{\xi }_j}{max\xi }},f={\displaystyle \frac{{\lambda }_{aj}}{max{\lambda }_a}}$$

(18)

where $\xi$ represents the set of task importance levels, $max\xi$ denotes the importance factor of the highest importance task in the task pool, ${\lambda }_a$ denotes the set of fitness levels of UAV a for the task samples in the task pool, and $max{\lambda }_a$ represents the fitness level of the task that matches UAV a the most.

Step 2. To ensure randomness in generating sampling probabilities, we introduce a random perturbation parameter $\delta$:

$$\delta ={\delta }_{0}e,\forall e\in [-1,1]$$

(19)

where e is a random number between $-1$ and 1, and ${\delta }_0$ is the perturbation scaling factor, empirically set to 0.1 in this study.

Step 3. Calculate the sampling probability p for UAV a for task j:

$$p=p_0(s\alpha +f\beta )\gamma +\delta =p_0\left({\displaystyle \frac{{\xi }_j}{max\xi }}\alpha +{\displaystyle \frac{{\lambda }_{aj}}{max{\lambda }_a}}\beta \right)\gamma +{\delta }_{0}e$$

(20)

where $p_0$ is the initial sampling probability. $\alpha$ and $\beta$ are adjustment coefficients with $\alpha +\beta =1$. By setting appropriate values for $\alpha$ and $\beta$, the weights of importance proportion s and fitness proportion f in the final sampling probability can be adjusted to ensure a more reasonable and balanced calculation. $\gamma$ is the sampling coefficient introduced to increase the overall sampling probability in response to potential decrease in probabilities caused by the introduction of s and f.

Algorithm 1 describes the adaptive sampling process for each UAV. First, calculate the importance proportion s and fitness proportion f, and generate the random perturbation parameter $\delta$ (lines 3–5). Then, calculate the sampling probability p for UAV a for task j according to the Equation (20) (line 6). If task j meets the sampling probability, it is added to the task sample set of UAV a (lines 7–9).

Algorithm 1 Adaptive sampling strategy of the ASTRRA

Input:  a, $p_0$, T, ${\delta }_0$, $\alpha$, $\beta$, $\gamma$ Output:  $N_a$  1: $N_a\leftarrow \varnothing$  2: for each task j in all task T do  3:    $s\leftarrow {\xi }_j/max\xi$  4:    $f\leftarrow {\lambda }_{aj}/max{\lambda }_a$  5:    $\delta \leftarrow {\delta }_0·\mathrm{random}(-1,1)$  6:    $p\leftarrow p_0(s\alpha +f\beta )\gamma +\delta$  7:    if probability is p then  8:      $N_a\leftarrow N_a\cup \left\{j\right\}$  9:    end if 10: end for 11: return $N_a$

4.3. Task Review and Classification Method

In the task auction stage, allocating the best current task to the highest-bidding UAV using the maximum consensus strategy can only guarantee a local optimum for that iteration, making it difficult to ensure a near-global optimal solution. Therefore, after the auction stage, a review of the rationality of the task allocation is necessary.

To further enhance the global optimality of task allocation, we propose a task review and classification method. This method aims to address potential coherence issues and the underutilization of resources in the initial task allocation, thereby optimizing the overall task allocation scheme. By reviewing the rationality of the assigned tasks, identifying tasks that need reassignment, and categorizing them based on the review results, tasks are directed into separate secondary auction stages, ensuring a more reasonable allocation for each task category. This process is repeated until the total revenue from task allocation no longer increases.

The specific steps for implementing the task review and classification method are as follows:

Step 1: Identify tasks with coherence issues in the UAV task sequence based on changes in the UAV’s heading angle and flight distance, specifically tasks with significant geographical spans between consecutive tasks. These tasks are added to the coherence issue task pool. The specific meanings of the two indicators are explained next.

Heading change angle: For the UAV task path set $P^a$, define the heading change angle to quantify the directional change at each task point in the path. For any task point $P_m^a$ (except the final task), the UAV will enter and exit at certain angles. Two vectors are drawn from task point $P_m^a$ to its preceding task point $P_{m-1}^a$ and succeeding task point $P_{m+1}^a$, respectively. The angle formed by these two vectors is the heading change angle, denoted as ${\theta }_m^a$. The calculation method for ${\theta }_m^a$ is as follows:

$${\theta }_m^a=arccos\left({\displaystyle \frac{\left(P_{m-1}^a-P_m^a\right)·\left(P_{m+1}^a-P_m^a\right)}{\parallel P_{m-1}^a-P_m^a\parallel \parallel P_{m+1}^a-P_m^a\parallel }}\right)$$

(21)

Flight distance: For any task point $P_m^a$ in the UAV task path, define the Euclidean distance to the next task point $P_{m+1}^a$ as the flight distance. The calculation formula for the flight distance $d_m^a$ is:

$$d_m^a=\parallel P_{m+1}^a-P_m^a\parallel$$

(22)

The heading change angle ${\theta }_m^a$ reflects the UAV’s turning angle at task point $P_m^a$ and can be understood as the UAV’s turning angle along the task path. The flight distance $d_m^a$ reflects the distance between task point $P_m^a$ and the next task point $P_{m+1}^a$.

Generally, the closer the UAV’s heading change angle is to 180°, the more reasonable the allocation result, and the higher the total revenue. For instance, in Figure 3, UAV4’s task path $T5\to T9\to T3$ has a small heading change angle, which indicates a potential coherence issue. If the heading change angle for the mth task of UAV a is very small and the flight distance to the next task point is very large, it is determined that the ($m+1$)th task has a coherence issue. Thus, the ($m+1$)th task of UAV a is added to the coherence issue task pool $T{P}_1$, and the remaining tasks of that UAV are added to the load-balanced task pool $T{P}_2$. For example, task $T4$ in Figure 3 not only has a small heading change angle but also a large flight distance, indicating a coherence issue. 

Step 2: Identify UAVs with load redundancy and their associated tasks. Load redundancy means the total number of tasks in the UAV task path is less than its maximum carrying capacity, potentially indicating the underutilization of resources. Therefore, tasks undertaken by UAVs with load redundancy are added to the load-balanced task pool $T{P}_2$.

Step 3: Reassign UAVs for the coherence issue task pool and the load-balanced task pool. Tasks with coherence issues typically reduce overall task execution efficiency and yield lower revenue for UAVs. Hence, more UAVs need to be allocated to the coherence issue task pool. Conversely, tasks in the load-balanced task pool are usually less difficult to execute and closer in distance, requiring fewer UAVs. The UAVs reallocated for task pools $T{P}_1$ and $T{P}_2$ are denoted as $A_1^{*}$ and $A_2^{*}$, respectively. The number of UAVs $M_1^{*}$ and $M_2^{*}$ reallocated to $T{P}_1$ and $T{P}_2$ are calculated as: 

$$\begin{array}{cc}\hfill M_1^{*}& =⌈{\displaystyle \frac{N_1}{L}}⌉+\epsilon \hfill \\ \hfill M_2^{*}& =M_1+M_2-M_1^{*}\hfill \end{array}$$

(23)

where $M_1$ denotes the number of UAVs with coherence issues, $M_2$ denotes the number of UAVs with load redundancy, $M_1^{*}$ and $M_2^{*}$ denote the number of UAVs reallocated to task pools $T{P}_1$ and $T{P}_2$, $N_1$ denotes the total number of tasks in the coherence issue task pool, L is the maximum load capacity of a UAV, and $\epsilon$ is the additional number of UAVs allocated to the coherence issue task pool based on practical considerations. In this paper, $\epsilon$ is set to 1.

Step 4: Re-enter the task assignment auction stage for the two task pools $T{P}_1$ and $T{P}_2$. Conduct separate auctions for these task pools, repeating the process until revenue no longer increases.

According to the review rules, task $T4$ undertaken by UAV3 in Figure 3 has a coherence issue, while UAV 1 and UAV 2 have load redundancy. Figure 4 shows the reassignment results after reassigning the tasks, where task $T4$ is assigned to UAV 2, and task $T6$ is added to UAV 1’s task path, significantly improving the allocation results.

Algorithm 2 details the implementation of the task review and classification method. During the task assignment auction stage, UAVs achieve initial task allocation using the maximum consensus strategy, and the assigned task paths are stored in $path$, with the task path of UAV a denoted as $pat{h}_a$. First, tasks of UAVs with no more than one actual task are added to the load-balanced task pool $T{P}_2$, recording the corresponding UAV identifiers (lines 5–8). Then, for UAVs with more than one actual task, we calculate the heading change angle $\theta$ of the mth task and the flight distance d to the $(m+1)$th task using vectors $vectorA$ and $vectorB$ (lines 8–11). If the heading change angle is small and the flight distance is long, it is determined that the task has a coherence issue, and subsequent tasks from the mth task in the UAV task path are added to the coherence issue task pool $T{P}_1$, while previous tasks are added to the load-balanced task pool $T{P}_2$, recording the UAV identifiers (lines 12–15). The different threshold combinations $({\theta }_1,l_1)$ and $({\theta }_2,l_2)$ are used for this judgment. If the UAV has no coherence issue but the number of tasks it undertakes has not reached its maximum carrying capacity, all tasks undertaken by that UAV are added to the load-balanced task pool, recording the UAV identifiers (lines 16–19). Finally, after all tasks have been reviewed and classified (lines 1–21), we reallocate UAVs to the two task pools accordingly (lines 22–25).

Algorithm 2 Task review and classification method of the ASTRRA

Input:  $path$ Output:  $T{P}_1$, $T{P}_2$, ${\mathcal{A}}_1^{*}$, ${\mathcal{A}}_2^{*}$  1: $T{P}_1,T{P}_2,{\mathcal{A}}_1,{\mathcal{A}}_2,{\mathcal{A}}^{*},{\mathcal{A}}_1^{*},{\mathcal{A}}_2^{*}\leftarrow \varnothing$, $M_1,M_2,M_1^{*}\leftarrow 0$  2: for each UAV’s $pat{h}_a$ in all $path$ do  3:    if len($pat{h}_a$) $\le 1$ then  4:      $T{P}_2\leftarrow T{P}_2\cup \left\{pat{h}_a\right\}$  5:      ${\mathcal{A}}_2\leftarrow {\mathcal{A}}_2\cup \left\{a\right\}$  6:    end if  7:    for each task m in $pat{h}_a$ do  8:      $vectorA\leftarrow pat{h}_a[m-1]-pat{h}_a\left[m\right]$  9:      $vectorB\leftarrow pat{h}_a[m+1]-pat{h}_a\left[m\right]$ 10:      $\theta \leftarrow$ the angle between $vectorA$ and $vectorB$ 11:      $d\leftarrow$ the length of $vectorB$ 12:      if $(\theta <{\theta }_1$ and $d>l_1\left)\mathbf{or}\right(\theta <{\theta }_2$ and $d>l_2)$ or other combination conditions then 13:         $T{P}_1\leftarrow T{P}_1\cup \left\{pat{h}_a[m+1:]\right\}$ 14:         $T{P}_2\leftarrow T{P}_2\cup \left\{pat{h}_a[:m+1]\right\}$ 15:         ${\mathcal{A}}_1\leftarrow {\mathcal{A}}_1\cup \left\{a\right\}$ 16:         else if len($pat{h}_a$) < L then 17:         $T{P}_2\leftarrow T{P}_2\cup \left\{pat{h}_a\right\}$ 18:         ${\mathcal{A}}_2\leftarrow {\mathcal{A}}_2\cup \left\{a\right\}$ 19:      end if 20:    end for 21: end for 22: ${\mathcal{A}}^{*}\leftarrow {\mathcal{A}}_1\cup {\mathcal{A}}_2$ 23: $M_1^{*}\leftarrow \mathrm{len}(N_1/L)+ϵ$ 24: ${\mathcal{A}}_1^{*}\leftarrow {\mathcal{A}}^{*}[:M_1^{*}]$ 25: ${\mathcal{A}}_2^{*}\leftarrow {\mathcal{A}}^{*}[M_1^{*}:]$ 26: return  $T{P}_1,T{P}_2,{\mathcal{A}}_1^{*},{\mathcal{A}}_2^{*}$

4.4. Crossover Path Exchange Strategy

The task assignment auction stage ensures that the highest-bidding UAV gets assigned the optimal task at each auction round. However, this approach cannot avoid crossover issues between UAV task paths post-assignment. Typically, intersecting paths are not the most efficient allocation. To address this, we propose the crossover path exchange strategy to resolve path crossover issues between UAVs. While the LRCA also handles path crossovers, it primarily focuses on local optimization, which may inadvertently reduce overall benefits. In contrast, our method improves the total benefits of task allocation while maintaining the original benefits, ensuring global optimization.

The implementation steps of the crossover path exchange strategy are as follows:

Step 1. Calculate the directional relationship of path segments. For UAV a, consider the path segment formed by task point $P_m^a$ (not the final task) and its subsequent task point $P_{m+1}^a$. For UAV b, consider the path segment formed by task point $P_n^b$ and its subsequent task point $P_{n+1}^b$. The four directional relationships $o_1$, $o_2$, $o_3$, and $o_4$ are calculated using the cross product of vectors:

$$\begin{array}{cc}\hfill o_1& =(P_{m+1}^a-P_m^a)\times (P_n^b-P_m^a)\hfill \\ \hfill o_2& =(P_{m+1}^a-P_m^a)\times (P_{n+1}^b-P_m^a)\hfill \\ \hfill o_3& =(P_{n+1}^b-P_n^b)\times (P_m^a-P_n^b)\hfill \\ \hfill o_4& =(P_{n+1}^b-P_n^b)\times (P_{m+1}^a-P_n^b)\hfill \end{array}$$

(24)

where $o_1$ and $o_2$ determine the relationship of points $P_n^b$ and $P_{n+1}^b$ relative to segment $P_m^a{P}_{m+1}^a$, while $o_3$ and $o_4$ determine the relationship of points $P_m^a$ and $P_{m+1}^a$ relative to segment $P_n^b{P}_{n+1}^b$.

Step 2. Determine the crossover between UAV paths. Using the directional relationships, determine if the path $P_m^a{P}_{m+1}^a$ of UAV a and the path $P_n^b{P}_{n+1}^b$ of UAV b intersect. If $o_1$ and $o_2$ have opposite directions and $o_3$ and $o_4$ have opposite directions, the segments intersect. Additionally, if any of $o_1$, $o_2$, $o_3$, or $o_4$ is zero and the corresponding point lies on the other segment, the segments intersect as well.

Step 3. Exchange task paths and calculate post-exchange benefits. Swap the paths following task m for UAV a with those following task n for UAV b. If the UAVs still meet load constraints after the swap, calculate the benefits of the new paths.

Step 4. Update UAV paths. Evaluate the benefits before and after the path exchange. If the total benefit increases post-exchange, update the paths for UAV a and UAV b to the new paths.

In Figure 5, the path segment $T4–T1$ for UAV 1 intersects with the path segment $T8–T11$ for UAV 2. After applying the crossover path exchange strategy, the updated paths of the UAVs are shown in Figure 6, where $T1–T5$ of UAV 1 has been exchanged with $T11–T6$ of UAV 2, resulting in a further increase in the total benefit of task assignment.

Algorithm 3 details the crossover path exchange strategy process. It traverses through the task paths of two UAVs (lines 2–9), swapping paths $p_1{p}_2$ of UAV a and $q_1{q}_2$ of UAV b when they intersect (lines 10–12). If the load constraints are satisfied post-swap, the algorithm calculates the benefits (lines 13–15) and updates the UAV paths (lines 16–19).

Algorithm 3 Cross-path exchange strategy of the ASTRRA.

Input:  $path$ Output:  $path$  1: $pat{h}_{a\_new}\leftarrow \varnothing$, $pat{h}_{b\_new}\leftarrow \varnothing$,$rewar{d}_{old}\leftarrow 0$, $rewar{d}_{new}\leftarrow 0$,  2: for each UAV’s $pat{h}_a$ in all $path$ do  3:    for each task m in $pat{h}_a$ do  4:      $p_1\leftarrow pat{h}_a\left[m\right]$  5:      $p_2\leftarrow pat{h}_a[m+1]$  6:      for each UAV’s $pat{h}_b$ in $path[a:]$ do  7:         for each task n in $pat{h}_b$ do  8:           $q_1\leftarrow pat{h}_b\left[n\right]$  9:           $q_2\leftarrow pat{h}_b[n+1]$ 10:           if segment $p_1{p}_2$ intersects segment $q_1{q}_2$ then 11:              $pat{h}_{a\_new}\leftarrow pat{h}_a[:m+1]+pat{h}_b[m+1:]$ 12:              $pat{h}_{b\_new}\leftarrow pat{h}_b[:m+1]+pat{h}_a[m+1:]$ 13:              if the swapped paths do not exceed the maximum UAV’s payload then 14:                $rewar{d}_{old}\leftarrow f(pat{h}_a\cup pat{h}_b)$ 15:                $rewar{d}_{new}\leftarrow f(pat{h}_{a\_new}\cup pat{h}_{b\_new})$ 16:                if $rewar{d}_{new}\ge rewar{d}_{old}$ then 17:                   $pat{h}_a\leftarrow pat{h}_{a\_new}$ 18:                   $pat{h}_b\leftarrow pat{h}_{b\_new}$ 19:                end if 20:              end if 21:           end if 22:         end for 23:      end for 24:    end for 25: end for 26: return  $path$

5. Experiments and Analysis

In this section, numerical simulations are conducted to verify the effectiveness and real-time performance of the ASTRRA for UAV task allocation in real-world environments. First, we analyze the improvement effect of the ASTRRA. Then, its performance is comprehensively evaluated through comparison with the most representative algorithms. Finally, simulations of secondary allocation after UAV damage are conducted to demonstrate that the proposed algorithm meets the real-time requirements of actual mission execution.

All experiments were conducted on a laptop running Windows 10 Home Chinese Edition. The computer was equipped with an Intel(R) Core(TM) i5-9300H CPU @ 2.40GHz and 16 GB of DDR4 2666 MHz memory (Lenovo, Beijing, China), and the simulations were performed using Python 3.10.

5.1. Validation of Effectiveness

To analyze the effectiveness of the ASTRRA, all experiments were conducted in a 5000 × 5000-m two-dimensional area. Each UAV could perform multiple tasks, but each task only needed to be performed once. UAVs started from the same point, and tasks were randomly distributed in the two-dimensional area, with a task sampling probability set to one. The threshold combinations $(\theta ,l)$ were defined in four groups: $(90,2000)$, $(100,2200)$, $(110,2400)$, and $(120,2500)$. The specific experimental parameter settings are shown in

Table 2. Parameter settings for validation experiments.

Object	Attribute	Description
Map	Area Size	5000 m × 5000 m
UAV	Number of UAVs	20
	UAV base location	(2200, 2500)
	Maximum load capacity	3
	Speed	60 km/h
Task	Number of Tasks	50
	Task location	Randomly distributed within the map area
	Time discount factor	0.90
	Importance factor	0.85
	Suitability factor	0.75
	Task execution time	6 s

, and the specific coordinates of the tasks are shown in

Table 3. Task IDs and their corresponding coordinates.

ID	Coord (m)	ID	Coord (m)	ID	Coord (m)	ID	Coord (m)	ID	Coord (m)
0	5274, 3402	10	2930, 4886	20	1707, 2359	30	4257, 113	40	2478, 3845
1	3072, 240	11	3646, 1478	21	1270, 3716	31	499, 1735	41	5164, 266
2	4234, 2197	12	2432, 3229	22	1070, 4432	32	1382, 1421	42	2880, 537
3	3520, 3547	13	1383, 2171	23	3044, 4136	33	4713, 3274	43	948, 1178
4	1999, 2817	14	5124, 3083	24	2775, 991	34	5288, 4769	44	5129, 1601
5	3348, 3544	15	479, 1466	25	646, 3411	35	1106, 2078	45	526, 723
6	4970, 2472	16	1862, 1582	26	4229, 4725	36	3338, 1022	46	3197, 3681
7	3646, 2356	17	2461, 4327	27	5276, 2948	37	1854, 1722	47	3077, 1873
8	1835, 2032	18	4246, 2951	28	1709, 1278	38	4713, 4293	48	2306, 3394
9	4385, 3389	19	3345, 4883	29	1671, 2965	39	4081, 3251	49	3489, 4175

, where the “ID” column represents the task numbers, and the “Coord (m)” column lists the (x-coordinate, y-coordinate) of the tasks.

The scenario parameters were input into both the LSTA algorithm and the ASTRRA, and the task allocation results are shown in Figure 7. In these figures, the blue Y-shaped symbols represent UAV starting points, the red star-shaped symbols represent target task points, the numbers next to the red star-shaped symbols represent target the task point numbers, the green circular symbols represent UAV final task points, and the dashed lines represent UAV task paths. Figure 7a shows the original LSTA algorithm results, which indicate relatively satisfactory allocations, but some UAV task paths have significant heading change angles and flying distances, indicating coherence problems where the geographical span between tasks for the same UAV is too large. Additionally, some task paths exhibit crossover issues. Examples of paths with coherence or crossover issues include {37, 30, 41}, {28, 14, 27}, {40, 10, 34}, and {3, 39, 18}, leading to a decrease in total task allocation benefit and hindering UAV flight efficiency. Figure 7b shows the results of the newly proposed ASTRRA, which, through the task review and classification method and crossover path exchange strategy, minimizes coherence issues in UAV task paths and reduces crossovers between UAV paths, resulting in a more reasonable task allocation compared to the original LSTA algorithm.

Due to the normalization of the objective function in Section 3, the total benefit value ranged between zero and one. The data in

Table 4. Task assignment results of LSTA and ASTRRA.

Algorithm	UAV Task Path	Reward Value	Runtime (s)
LSTA	{4, 22}, {20, 15}, {8, 43}, {29, 25}, {12, 23, 19},	0.947711	0.027328
	{37, 30, 41}, {13, 31}, {48, 17, 38}, {16, 44}, {47, 11, 36},
	{35, 27}, {28, 14}, {32, 45}, {40, 10, 34}, {7, 2, 6},
	{21, 0}, {46, 49, 26}, {5, 9, 33}, {24, 42, 1}, {3, 39, 18}
ASTRRA	{8, 32, 45}, {29, 25}, {37, 43}, {13, 35, 31}, {12, 23, 26},	0.969324	0.047354
	{14, 0}, {48, 17}, {44, 41, 30}, {39, 18}, {47, 11, 36},
	{27}, {4, 21, 22}, {16, 28}, {40, 10, 19}, {7, 2, 6},
	{20, 15}, {46, 49, 34}, {5, 38}, {24, 42, 1}, {3, 9, 33}

show the results of 100 repeated simulations for the above scenario. The results indicate that the benefit of the LSTA algorithm was 0.947711, while the ASTRRA achieved a benefit of 0.969324. Clearly, the ASTRRA not only effectively resolved unreasonable task path allocation issues but also significantly increased the total task allocation benefit. Although the addition of multiple review strategies in the ASTRRA increased the runtime from the original 0.027328 s to 0.047354 s, the calculation speed remained within the millisecond range, fully meeting real-time task allocation requirements.

5.2. Comparative Analysis

To evaluate the performance of the proposed ASTRRA, comprehensive comparative experiments were conducted. In the comparative analysis, we selected the most representative algorithms: CBBA [31], DSTA [32], LSTA [40], and LRCA [42]. To verify the effectiveness of our algorithm at different scales of task allocation scenarios, we selected 20, 30, 40, and 50 UAVs with corresponding task numbers of 50, 80, 100, and 130, respectively. In each scenario, UAVs were set to the same initial starting point, and task points were randomly distributed in a 5000 × 5000 map to ensure that each algorithm was tested under identical conditions. To enhance the reliability of the results, 100 rounds of Monte Carlo simulations were performed for each algorithm in each scenario. The specific experimental parameter settings are shown in

Table 5. Parameter settings for comparative analysis experiments.

Object	Attribute	Scenario 1	Scenario 2	Scenario 3	Scenario 4
Map	Area Size	5000 m × 5000 m
UAV	Number of UAVs	20	30	40	50
	UAV base location	Randomly select a point within the map area
	Maximum load capacity	3
	Speed	60 km/h
Tasks	Number of Tasks	50	80	100	130
	Task location	Randomly distributed within the map area
	Time discount factor	0.8
	Task importance factor	Randomly distributed within [0.8–0.9]
	Suitability factor	Randomly distributed within [0.9–1]
	Task execution time	Randomly distributed within [6–30] s

.

In our study, the performance of the ASTRRA task allocation algorithm was evaluated using box plots. Figure 8 shows the box plots of the total benefit values for the five algorithms in different scenarios. Each box plot displays the total benefit values for different algorithms when allocating varying numbers of UAVs (20, 30, 40, and 50) and tasks (50, 80, 100, and 130). As shown in the figure, the ASTRRA consistently performed the best in all scenarios, with the median always positioned higher and the interquartile range narrower, indicating a more concentrated and stable distribution of rewards compared to the other four algorithms.

Table 6. Average rewards of five algorithms in different scenarios.

Scenarios	CBBA	DSTA	LSTA	LRCA	ASTRRA
20 UAVs—50 Tasks	0.739779	0.827821	0.827821	0.819542	0.853296
30 UAVs—80 Tasks	0.761244	0.863158	0.863158	0.848905	0.874448
40 UAVs—100 Tasks	0.764791	0.876372	0.876372	0.867653	0.886147
50 UAVs—130 Tasks	0.746481	0.866691	0.866691	0.854172	0.881346

summarizes the average benefit values for task allocation in different scenarios, clearly showing that the average benefit value of the ASTRRA is always higher than that of the other four algorithms, providing superior allocation results. Therefore, the proposed ASTRRA effectively enhances the total benefit value for task allocation and exhibits superior robustness and consistency in various scenarios compared to other algorithms.

Figure 9 shows the box plots of the runtime for the five algorithms in different scale scenarios. Due to the random generation of influencing factors in each round of simulation and the multiple review strategies added in the ASTRRA, the continuity problems and path crossings in UAV task paths vary. As a result, the box size is larger compared to that of the LSTA and LRCA algorithms, indicating slightly greater fluctuations in runtime for the ASTRRA.

Table 7. Average runtime of five algorithms under different scenarios.

Scenarios	CBBA (s)	DSTA (s)	LSTA (s)	LRCA (s)	ASTRRA (s)
20 UAVs—50 Tasks	2.927	0.261	0.029	0.051	0.046
30 UAVs—80 Tasks	13.425	0.930	0.068	0.137	0.123
40 UAVs—100 Tasks	35.747	1.973	0.116	0.252	0.203
50 UAVs—130 Tasks	89.874	3.998	0.203	0.474	0.372

summarizes the average runtime of the algorithms in different scenarios, showing that the average runtime of the ASTRRA is second only to the LSTA algorithm. Although the runtime of the ASTRRA increased, it remained in the millisecond range, fully meeting the real-time requirements for task allocation.

Figure 10 shows the average benefit value and average runtime of the ASTRRA in different scenarios. As the scale of UAVs and tasks increased, the total benefit value of task allocation showed an upward trend. The highest reward, 88.61%, was achieved when there were 40 UAVs and 100 tasks. Although the runtime of the algorithm also increased with the scale of the scenario, running the ASTRRA in a large-scale scenario with 50 UAVs and 130 tasks only took 0.3730 s, which is negligible for practical applications.

Figure 11 shows the average benefit and average runtime when allocating 130 tasks to 50 UAVs with a crossover path exchange strategy executed 15 times under different sampling probabilities. At lower sampling probabilities (e.g., 0.5), the runtime of the ASTRRA is relatively short, and the adaptive sampling strategy minimizes the impact on benefits. As the sampling probability increases, the runtime gradually increases, and the total benefit value also increases. When the sampling probability is one, the total benefit value is the highest. The ASTRRA adjusts the sampling probability to ensure high benefits while keeping the running time within an acceptable range, effectively balancing the benefits and running time, and is suitable for various task allocation scenarios.

5.3. Dynamic Reassignment after Damage

UAVs may encounter damage or failure while performing tasks. Figure 12 simulates the results of dynamic reallocation after UAV damage. When a UAV malfunctions, the system immediately performs secondary allocation. In this simulation, the gray line represents the originally assigned task path, the green line indicates the task path after the first reallocation following UAV damage, and the yellow and red lines represent the task paths after the second and third reallocations, respectively.

Table 8. Results of dynamic reassignment of UAV damage.

Round	Damaged UAV	Remaining Task Count	Task Path after Reassignment	Runtime (s)
1	UAV 3	35	{43}, {25}, {45}, {23, 19}, {9}, {17},	0.012919
			{6, 41}, {39, 33, 0}, {11, 36}, {18, 14, 27},
			{21, 22}, {30}, {10}, {2, 44}, {31, 15},
			{46, 49}, {5, 26}, {24, 42, 1}, {3, 38, 34}
2	UAV 18	26	{}, {}, {45, 1}, {23, 19}, {9, 0}, {}, {6, 41},	0.006938
			{39, 33, 30}, {36}, {18, 14, 27}, {22}, {42},
			{10}, {2, 44}, {31, 15}, {49}, {26}, {38, 34}
3	UAV 19	19	{}, {}, {45, 1}, {19}, {14, 27}, {},	0.004029
			{44, 41, 30}, {9, 34}, {36}, {33, 0},
			{22}, {42}, {10}, {6}, {}, {38}, {26}

provides information on the damaged UAVs and the related dynamic reallocation details. The results show that the runtime for task reallocation decreased as task completion progressed, meaning the higher the task completion rate, the lower the computational burden for reallocation. When UAVs were damaged during task execution, the ASTRRA could quickly perform secondary allocation, effectively handling unexpected situations during the mission.

6. Conclusions

This paper investigated the UAV task assignment problem under realistic constraints. Building upon conventional models, we introduced task path decision variables to mathematically describe UAV task paths and proposed collaborative action constraints to ensure effective collaboration among UAVs. To solve the task assignment problem, we developed the ASTRRA. Through an adaptive sampling strategy, high-value targets were sampled efficiently, maximizing the balance between efficiency and task value. To address coherence issues in UAV task paths, we proposed the task review and classification method. By identifying issues in the UAV mission paths, we categorized tasks with coherence problems and tasks for UAVs that had not reached their load limit and auctioned them independently. Additionally, to handle possible path crossovers between UAV task paths, we introduced the crossover path exchange strategy. This strategy reduced path crossovers and further optimized task assignment, enhancing the total benefit. Effectiveness experiment demonstrated the effectiveness of the ASTRRA in improving UAV task paths. Comparative experiments showed that ASTRRA performed well across various task scale scenarios, significantly increasing the total benefit of task assignment. Damage reassignment experiments indicated that the ASTRRA could quickly respond to changes in the task environment, ensuring the real-time nature of task assignment. Future work will focus on optimizing multi-UAV task assignment strategies, particularly considering the impact of obstacles and improving algorithm performance.