Representability of forests via generalized subtour elimination constraints

TL;DR

This paper characterizes which forests can be represented by generalized subtour elimination constraints (GSECs), expanding their applicability to broader combinatorial problems like robust spanning trees.

Contribution

It provides the first characterization of forest families representable by GSECs, enabling new formulations for vehicle routing and network design problems.

Findings

Recovered vehicle routing formulations not previously obtainable.

Demonstrated GSECs can model robust capacitated minimum spanning trees.

Broadened the scope of GSEC-based formulations in combinatorial optimization.

Abstract

Generalized subtour elimination constraints (GSECs) are widely used in state-of-the-art exact algorithms for vehicle routing and network design problems, as their right-hand sides often capture problem-specific feasibility conditions of each solution component. In this work, we present the first characterization of the families of forests that can be represented as the integer points inside a polytope defined by GSECs. This result generalizes a recent framework developed for vehicle routing problems under uncertainty and broadens the applicability of GSEC-based formulations to a wider class of combinatorial problems. In particular, using our characterization, we recover vehicle routing formulations that could not be obtained with previous results. Additionally, we show that GSECs can naturally model a robust variant of the capacitated minimum spanning tree problem.