We propose a manager-worker framework based on deep reinforcement learning to tackle a hard yet nontrivial variant of Travelling Salesman Problem (TSP), \ie~multiple-vehicle TSP with time window and rejections (mTSPTWR), where customers who cannot be served before the deadline are subject to rejections. Particularly, in the proposed framework, a manager agent learns to divide mTSPTWR into sub-routing tasks by assigning customers to each vehicle via a Graph Isomorphism Network (GIN) based policy network. A worker agent learns to solve sub-routing tasks by minimizing the cost in terms of both tour length and rejection rate for each vehicle, the maximum of which is then fed back to the manager agent to learn better assignments. Experimental results demonstrate that the proposed framework outperforms strong baselines in terms of higher solution quality and shorter computation time. More importantly, the trained agents also achieve competitive performance for solving unseen larger instances.
翻译:我们提议了一个基于深层强化学习的管理者-工人框架,以解决具有时窗和拒绝(mTSPTWR)的“旅行销售商问题”(TSP)的硬性但非边际变式,即“多车TSP”和“时间窗口和拒绝(mTSPTWR)”,在这种变式中,无法在最后期限之前提供服务的客户会遭到拒绝。特别是,在拟议的框架中,管理者代理人学会将MTSPPWER分成分路任务,通过基于“图形地貌网络”的政策网络(GIN)向每辆车辆分配客户。 工人代理人学会通过尽量减少每辆车辆的旅游时间长度和拒绝率(mTSPTPWR)解决分道任务。 实验结果显示,拟议的框架在更高的解决方案质量和较短的计算时间方面超越了强有力的基线。 更重要的是,受过培训的代理人在解决看不见的大案例方面也取得了竞争性业绩。