Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction

TL;DR

This paper introduces Multi-node Lookahead Prediction (MnLP), a training strategy that enhances neural routing policies by enabling multi-step decision prediction, thereby improving long-term planning and generalization in vehicle routing problems.

Contribution

The paper proposes MnLP, a novel training method that predicts multiple future nodes simultaneously, improving neural policy planning without increasing inference complexity.

Findings

MnLP improves generalization across various problem sizes and distributions.

MnLP outperforms existing training methods in vehicle routing benchmarks.

MnLP can be integrated into diverse neural architectures seamlessly.

Abstract

Neural policies have shown promise in solving vehicle routing problems due to their reduced reliance on handcrafted heuristics. However, current training paradigms suffer from a fundamental limitation: they primarily focus on next-node prediction for solution construction, resulting in myopic decision-making that undermines long-horizon planning capacity. To this end, we introduce Multi-node Lookahead Prediction (MnLP), a novel training strategy that extends the supervised learning paradigm to predict multiple future nodes simultaneously. We incorporate causal and discardable MnLP modules that operate exclusively during training, facilitating models to anticipate multi-step decisions while preserving inference-time efficiency. By incorporating multi-depth auxiliary supervision into the loss function, MnLP equips neural policies with the ability of long-range contextual understanding. Experimentally, MnLP outperforms existing training methods, improving the generalization capability of neural policies across various problem sizes, distributions, and real-world benchmarks. Moreover, MnLP can be seamlessly integrated into diverse neural architectures without introducing additional inference overhead.