This study investigates the scheduling problem of return communication tasks for unmanned aerial vehicle (UAV) swarms, where disaster relief environmental global positioning is hampered. To characterize the utility of these tasks and optimize scheduling decisions, we developed a time window-constrained scheduling model that operates under constraints, including communication base station time windows, battery levels, and task uniqueness. To solve the above model, we propose an enhanced algorithm through integrating Dueling Deep Q-Network (Dueling DQN) into adaptive large neighborhood search (ALNS), referred to as Dueling DQN-ALNS. The Dueling DQN component develops a method to update strategy weights, while the action space defines the destruction and selection strategies for the ALNS scheduling solution across different time windows. Meanwhile, we design a two-stage algorithm framework consisting of centralized offline training and decentralized online scheduling. Compared to traditionally optimized search algorithms, the proposed algorithm could continuously and dynamically interact with the environment to acquire state information about the scheduling solution. The solution ability of Dueling DQN is 3.75% higher than that of the Ant Colony Optimization (ACO) algorithm, 5.9% higher than that of the basic ALNS algorithm, and 9.37% higher than that of the differential evolution algorithm (DE). This verified its efficiency and advantages in the scheduling problem of return communication tasks for UAVs.