Jingwen Li

Yining Ma, Jingwen Li, Zhiguang Cao et al.

We present an efficient Neural Neighborhood Search (N2S) approach for pickup and delivery problems (PDPs). In specific, we design a powerful Synthesis Attention that allows the vanilla self-attention to synthesize various types of features regarding a route solution. We also exploit two customized decoders that automatically learn to perform removal and reinsertion of a pickup-delivery node pair to tackle the precedence constraint. Additionally, a diversity enhancement scheme is leveraged to further ameliorate the performance. Our N2S is generic, and extensive experiments on two canonical PDP variants show that it can produce state-of-the-art results among existing neural methods. Moreover, it even outstrips the well-known LKH3 solver on the more constrained PDP variant. Our implementation for N2S is available online.

Jingwen Li, Liang Xin, Zhiguang Cao et al.

Recently, there is an emerging trend to apply deep reinforcement learning to solve the vehicle routing problem (VRP), where a learnt policy governs the selection of next node for visiting. However, existing methods could not handle well the pairing and precedence relationships in the pickup and delivery problem (PDP), which is a representative variant of VRP. To address this challenging issue, we leverage a novel neural network integrated with a heterogeneous attention mechanism to empower the policy in deep reinforcement learning to automatically select the nodes. In particular, the heterogeneous attention mechanism specifically prescribes attentions for each role of the nodes while taking into account the precedence constraint, i.e., the pickup node must precede the pairing delivery node. Further integrated with a masking scheme, the learnt policy is expected to find higher-quality solutions for solving PDP. Extensive experimental results show that our method outperforms the state-of-the-art heuristic and deep learning model, respectively, and generalizes well to different distributions and problem sizes.

Jingwen Li, Yining Ma, Ruize Gao et al.

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence, their key to construct a solution solely lies in the selection of the next node (customer) to visit excluding the selection of vehicle. However, vehicles in real-world scenarios are likely to be heterogeneous with different characteristics that affect their capacity (or travel speed), rendering existing DRL methods less effective. In this paper, we tackle heterogeneous CVRP (HCVRP), where vehicles are mainly characterized by different capacities. We consider both min-max and min-sum objectives for HCVRP, which aim to minimize the longest or total travel time of the vehicle(s) in the fleet. To solve those problems, we propose a DRL method based on the attention mechanism with a vehicle selection decoder accounting for the heterogeneous fleet constraint and a node selection decoder accounting for the route construction, which learns to construct a solution by automatically selecting both a vehicle and a node for this vehicle at each step. Experimental results based on randomly generated instances show that, with desirable generalization to various problem sizes, our method outperforms the state-of-the-art DRL method and most of the conventional heuristics, and also delivers competitive performance against the state-of-the-art heuristic method, i.e., SISR. Additionally, the results of extended experiments demonstrate that our method is also able to solve CVRPLib instances with satisfactory performance.

Yining Ma, Jingwen Li, Zhiguang Cao et al.

Recently, Transformer has become a prevailing deep architecture for solving vehicle routing problems (VRPs). However, it is less effective in learning improvement models for VRP because its positional encoding (PE) method is not suitable in representing VRP solutions. This paper presents a novel Dual-Aspect Collaborative Transformer (DACT) to learn embeddings for the node and positional features separately, instead of fusing them together as done in existing ones, so as to avoid potential noises and incompatible correlations. Moreover, the positional features are embedded through a novel cyclic positional encoding (CPE) method to allow Transformer to effectively capture the circularity and symmetry of VRP solutions (i.e., cyclic sequences). We train DACT using Proximal Policy Optimization and design a curriculum learning strategy for better sample efficiency. We apply DACT to solve the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP). Results show that our DACT outperforms existing Transformer based improvement models, and exhibits much better generalization performance across different problem sizes on synthetic and benchmark instances, respectively.