Network Design with Service Requirements: Scaling-up the Size of Solvable Problems

TL;DR

This paper introduces a new formulation and efficient algorithms for the Network Design with Service Requirements problem, enabling the solution of larger and more complex instances than previously possible.

Contribution

It proposes a path-based formulation and a fast enumeration algorithm, along with a column generation scheme embedded in a branch-and-cut-and-price framework, advancing the state-of-the-art.

Findings

The approach effectively solves larger problem instances.

The column generation scheme improves computational efficiency.

Results outperform existing methods on benchmark instances.

Abstract

Network design, a cornerstone of mathematical optimization, is about defining the main characteristics of a network satisfying requirements on connectivity, capacity, and level-of-service. It finds applications in logistics and transportation, telecommunications, data sharing, energy distribution, and distributed computing. In multi-commodity network design, one is required to design a network minimizing the installation cost of its arcs and the operational cost to serve a set of point-to-point connections. The definition of this prototypical problem was recently enriched by additional constraints imposing that each origin-destination of a connection is served by a single path satisfying one or more level-of-service requirements, thus defining the Network Design with Service Requirements [Balakrishnan, Li, and Mirchandani. Operations Research, 2017]. These constraints are crucial, e.g., in telecommunications and computer networks, in order to ensure reliable and low-latency communication. In this paper we provide a new formulation for the problem, where variables are associated with paths satisfying the end-to-end service requirements. We present a fast algorithm for enumerating all the exponentially-many feasible paths and, when this is not viable, we provide a column generation scheme that is embedded into a branch-and-cut-and-price algorithm. Extensive computational experiments on a large set of instances show that our approach is able to move a step further in the solution of the Network Design with Service Requirements, compared with the current state-of-the-art.