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Many real-world vehicle routing problems involve rich sets of constraintswith respect to the capacities of the vehicles, time windows for customers etc.While in recent years first machine learning models have been developed tosolve basic vehicle routing problems faster than optimization heuristics,complex constraints rarely are taken into consideration. Due to their generalprocedure to construct solutions sequentially route by route, these methodsgeneralize unfavorably to such problems. In this paper, we develop a policymodel that is able to start and extend multiple routes concurrently by usingattention on the joint action space of several tours. In that way the model isable to select routes and customers and thus learns to make difficulttrade-offs between routes. In comprehensive experiments on three variants ofthe vehicle routing problem with time windows we show that our model calledJAMPR works well for different problem sizes and outperforms the existingstate-of-the-art constructive model. For two of the three variants it alsocreates significantly better solutions than a comparable meta-heuristic solver.

Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention