An Attention-LSTM Hybrid Model for the Coordinated Routing of Multiple Vehicles
Reinforcement learning has recently shown promise in learning quality solutions in a number of combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drones (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination. In TSP-D, two different types of vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose an attention encoder-LSTM decoder hybrid model, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for coordinated routing of multiple vehicles than the attention-based model.
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