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 are conducted for algorithmic performance validation. More experiments and analyses including the significance test, stability analysis, complexity analysis, sensitivity analysis, and ablation experiments are also conducted for comprehensive algorithmic evaluation. Experimental results show that our proposed DEA-DYPN ranks first according to the Friedman test, and outperforms the competitor algorithms at most 69%.

Solving Orienteering Problems by Hybridizing Evolutionary Algorithm and Deep Reinforcement Learning