The OP has many real-life applications such as tourism route planning, home fuel delivery, unmanned aerial vehicle reconnaissance mission planning, and facility inspection. However, traditional exact algorithms, heuristics, and learning methods have difficulty balancing optimization efficiency and accuracy, especially for large-scale cases. This study proposes a problem decomposition-based double-layer optimization framework named DEA-DYPN to solve OPs. By combining the evolutionary algorithm and deep reinforcement learning method, we significantly reduce the difficulty of solving large-scale OPs. DEA-DYPN significantly outperforms the compared representative algorithms in experiments, especially in instances with more than 50 nodes. This hybrid optimization approach provides a new idea for solving traditional combinatorial optimization problems. The modularity design facilitates its expansion to other variants of the OP.

The orienteering problem (OP) is widely applied in real life. However, as the scale of real-world problem scenarios grows quickly, traditional exact, heuristics, and learning-based methods have difficulty balancing optimization accuracy and efficiency. This study proposes a problem decomposition-based double-layer optimization framework named DEA-DYPN to solve OPs. Using a diversity evolutionary algorithm (DEA) as the external optimizer and a dynamic pointer network (DYPN) as the inner optimizer, we significantly reduce the difficulty of solving large-scale OPs. Several targeted optimization operators are innovatively designed for stronger search ability, including a greedy population initialization heuristic, an elite strategy, a population restart mechanism, and a fitness-sharing selection strategy. Moreover, a dynamic embedding mechanism is introduced to DYPN to improve its characteristic learning ability. Extensive comparative experiments on OP instances with sizes from 20 to 500 a...