In response to the increasing complexity of military operations, the use of multiple heterogeneous unmanned aerial vehicles (UAVs) is essential for efficiently executing complex missions. This paper introduces an extended cooperative multi-task assignment problem (ECMTAP), which involves deploying heterogeneous UAVs from different base stations to accomplish specific missions, with a focus on minimizing overall mission completion time. ECMTAP categorizes targets into various types, each associated with unique task sets including {reconnaissance}, {attack, evaluation}, and {reconnaissance, attack, evaluation}. ECMTAP requires that attack tasks follow reconnaissance tasks, and evaluation tasks follow attack tasks, adding complexity due to specific timing constraints on each task. To tackle this problem, we propose a novel algorithm, the reinforcement search strategy-based adaptive large neighborhood search (RSALNS). To enhance the search capability, RASLNS utilizes two key destroy-repair operations: the intra-target tasks adjustment strategy and the evaluation tasks adjustment strategy. The former operation dismantles and reconstructs task sequences within a target, potentially resulting in suboptimal assignment of evaluation tasks, while the latter operation reassigns these tasks based on the first operation's output. Extensive experiments validate the effectiveness of the RSALNS algorithm in solving the ECMTAP, demonstrating its capability to generate high-quality solutions efficiently.
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