# Distributed Task Allocation for Multiple UAVs Based on Swarm Benefit Optimization
## 1 Introduction
Among these auction-based methods, the Consensus-Based Bundle Algorithm (CBBA) [38] and the Performance Impact (PI) algorithm [39] are landmark approaches, upon which numerous subsequent algorithms have been developed [40; 41; 42; 43]. For instance, to ensure network connectivity, Literature [44] predicts network topology and identifies potential disconnection points, initializing CBBA with an empty set of allocation vectors, a relay list, and a prohibited task list. It leverages underutilized members as relays to enhance connectivity. In the context of replanning, Literature [40] achieves a balance between team convergence time and increased coordination within the CBBA framework, rapidly allocating new tasks by partially resetting previous allocations. Literature [41], on the other hand, enhances optimization performance through replanning based on PI methods, allowing multiple reallocations among agents by creating feasible time slots. Additionally, Literature [42] introduces two additional modules integrated with PI, supporting real-time dynamic online replanning and improving the algorithm's exploratory capabilities, respectively. It can be stated that CBBA introduces a task-level conflict resolution method, significantly reducing the network demands traditionally required to reach a consensus at the situational awareness level. On the other hand, PI proposes a performance optimization approach based on task cost, further minimizing the travel distance and completion time for tasks. However, CBBA's task allocation scheme does not update task scores, thus failing to reflect the true performance of tasks within the allocation scheme in real time. Meanwhile, PI only considers task cost based on distance, neglecting the task's value and its decay over time. To further enhance the performance of UAV swarms in executing time-sensitive tasks with varying values, this paper not only accounts for tasks' initial values and their decay over time but also updates the true performance of the task allocation scheme in real time. To enhance the optimization of task allocation, this paper undertakes the following innovative contributions:(1) Individual benefit variation is proposed to characterize the impact of tasks on UAV benefits, thereby enabling the optimization of swarm benefits directly through adjustments to individual benefit variations. (2) The proposed calculation of individual benefits not only takes into account the distance between tasks and UAVs but also considers the initial value of tasks and their decay over time. Additionally, the presented method updates the individual benefit variation values of tasks for UAVs in real-time, reflecting the most current state of task benefit changes within the swarm. (3) The effectiveness of the proposed method is validated through Monte Carlo simulation experiments. The results demonstrate that, compared to representative algorithms CBBA and PI, the proposed benefit variation (BV) method achieves average swarm benefit improvements of 0.60-1.95% and 0.91-4.02%, respectively. Furthermore, the advantages of the proposed method become more pronounced as the scale of UAVs and tasks increases. The remainder of this paper is organized as follows. Firstly, Section 2 presents the mathematical modeling of the task allocation problem for UAV swarms, formulating it as a constrained optimization model. Secondly, Section 3, which constitutes the core of this paper, introduces the fundamental ideas and detailed procedures for solving the optimization model. Lastly, the effectiveness of the proposed algorithm is validated through Monte Carlo simulation experiments in Section 4, and further discussion is present in Section 5. The paper concludes with Section 6, providing a summary of the work accomplished.