Benders decomposition for Network Design Covering Problems

TL;DR

This paper introduces Benders decomposition techniques for two network design covering problems, optimizing network coverage and costs with stabilization and cut-set methods, supported by computational experiments.

Contribution

It develops a Benders decomposition approach with stabilization and cut-set inequalities for covering network design problems, enhancing solution efficiency.

Findings

Benders decomposition effectively solves the network covering problems.

Stabilization methods improve convergence speed.

Adding initial solutions enhances computational performance.

Abstract

We consider two covering variants of the network design problem. We are given a set of origin/destination pairs, called O/D pairs, and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the Maximal Covering Network Design problem, one must determine a network that maximizes the total fulfilled demand of the covered O/D pairs subject to a budget constraint on the design costs of the network. In the second problem, called the Partial Covering Network Design problem, the design cost is minimized while a lower bound is set on the total demand covered. After presenting formulations, we develop a Benders decomposition approach to solve the problems. Further, we consider several stabilization methods to determine Benders cuts as well as the addition of cut-set inequalities to the master problem. We also consider the impact of adding an initial solution to our methods. Computational experiments show the efficiency of these different aspects.