Test-Time Search in Neural Graph Coarsening for the Capacitated Vehicle Routing Problem

Yoonju Sim, Changhyun Kwon, Hyeonah Kim

Keywords: Cutting Plane Method, Test-time Search, Capacitated Vehicle Routing Problem

TL;DR: A training-free approach to enhancing learned cut separators for the CVRP by using test-time search: RCI cuts are further identified, and FCI cuts are newly discovered.

Abstract:

The identification of valid inequalities, such as Rounded capacity inequalities (RCIs), is a key component of cutting plane methods for the Capacitated Vehicle Routing Problem (CVRP).
While a neural separation method can learn to find high-quality cuts, improving the learned model further often requires costly retraining with diminishing returns.
This paper proposes an alternative approach: enhancing the performance of a trained model at inference time through two test-time search techniques.
First, we introduce stochastic edge selection into the graph coarsening procedure, replacing the previously proposed greedy approach.
Second, we propose the Graph Coarsening History-based Partitioning (GraphCHiP) algorithm, which leverages coarsening history to identify not only RCIs but also, for the first time, the Framed capacity inequalities (FCIs).
Experiments on randomly generated CVRP instances demonstrate the effectiveness of our approach in reducing the dual gap compared to the existing neural separation method.
Additionally, our method discovers effective FCIs on a specific instance, despite the challenging nature of identifying such cuts.

Submission Number: 41