A Neural Separation Algorithm for the Rounded Capacity Inequalities

TL;DR

This paper introduces a learning-based separation heuristic using graph neural networks to efficiently generate rounded capacity inequalities, improving lower bounds in large-scale vehicle routing problems.

Contribution

The paper presents a novel GNN-based heuristic for the separation problem in VRPs, enabling faster and more effective cut generation for large instances.

Findings

Outperforms CVRPSEP on large problems with over 400 customers

Provides better lower bounds for capacitated VRPs with up to 1,000 customers

Demonstrates the effectiveness of graph coarsening in learning-based separation methods

Abstract

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity inequalities (RCIs) are the most fundamental. To generate RCIs, we need to solve the separation problem, whose exact solution takes a long time to obtain; therefore, heuristic methods are widely used. We design a learning-based separation heuristic algorithm with graph coarsening that learns the solutions of the exact separation problem with a graph neural network (GNN), which is trained with small instances of 50 to 100 customers. We embed our separation algorithm within the cutting plane method to find a lower bound for the capacitated VRP (CVRP) with up to 1,000 customers. We compare the performance of our approach with CVRPSEP, a popular separation software package for various cuts used in solving VRPs. Our computational results show that our approach finds better lower bounds than CVRPSEP for large-scale problems with 400 or more customers, while CVRPSEP shows strong competency for problems with less than 400 customers.