DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems

TL;DR

This paper introduces DPN, a novel RL-based approach that decouples customer partitioning and navigation in min-max VRPs, leading to superior routing solutions by learning distinct embeddings and leveraging symmetry.

Contribution

It proposes a new attention-based encoder and an agent-permutation-symmetric loss to improve learning effectiveness in min-max VRPs.

Findings

DPN outperforms existing methods in single-depot VRPs.

DPN achieves better route length minimization in multi-depot scenarios.

The decoupling approach enhances learning efficiency and solution quality.

Abstract

The min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have exhibited advantages in solving efficiency and optimality. However, these methods fail to exploit the problem-specific properties in learning representations, resulting in less effective features for decoding optimal routes. This paper considers the sequential planning process of min-max VRPs as two coupled optimization tasks: customer partition for different routes and customer navigation in each route (i.e., partition and navigation). To effectively process min-max VRP instances, we present a novel attention-based Partition-and-Navigation encoder (P&N Encoder) that learns distinct embeddings for partition and navigation. Furthermore, we utilize an inherent symmetry in decoding routes and develop an effective agent-permutation-symmetric (APS) loss function. Experimental results demonstrate that the proposed Decoupling-Partition-Navigation (DPN) method significantly surpasses existing learning-based methods in both single-depot and multi-depot min-max VRPs. Our code is available at