Learning to Handle Complex Constraints for Vehicle Routing Problems

TL;DR

This paper introduces the PIP framework that improves neural methods for complex vehicle routing problems by proactively preventing infeasibility through constraint-aware masking, leading to better solutions and reduced infeasible solutions.

Contribution

The paper proposes the PIP framework with an auxiliary decoder and adaptive strategies to enhance neural VRP methods, especially for complex constraints, with reduced computational costs.

Findings

Significant reduction in infeasible solutions.

Improved solution quality on challenging VRPs.

PIP is a generic enhancement for neural VRP methods.

Abstract

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex constraints, especially when obtaining the masking itself is NP-hard. In this paper, we propose a novel Proactive Infeasibility Prevention (PIP) framework to advance the capabilities of neural methods towards more complex VRPs. Our PIP integrates the Lagrangian multiplier as a basis to enhance constraint awareness and introduces preventative infeasibility masking to proactively steer the solution construction process. Moreover, we present PIP-D, which employs an auxiliary decoder and two adaptive strategies to learn and predict these tailored masks, potentially enhancing performance while significantly reducing computational costs during training. To verify our PIP designs, we conduct extensive experiments on the highly challenging Traveling Salesman Problem with Time Window (TSPTW), and TSP with Draft Limit (TSPDL) variants under different constraint hardness levels. Notably, our PIP is generic to boost many neural methods, and exhibits both a significant reduction in infeasible rate and a substantial improvement in solution quality.