Mixed-Integer Approaches to Constrained Optimum Communication Spanning Tree Problem

TL;DR

This paper introduces new mixed-integer linear and bilinear formulations for the constrained optimum communication spanning tree problem, demonstrating their computational advantages over traditional models through extensive experiments.

Contribution

The paper proposes novel distance-based mixed-integer formulations using Bellman-type conditions and matrix equations, improving solution efficiency for the problem.

Findings

Distance-based formulations outperform multicommodity flow models.

Linear formulations show superior computational performance.

Real-world data validates the effectiveness of the proposed methods.

Abstract

Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or binary variables, and interconnection between distance variables is established using the recursive Bellman-type conditions or using matrix equations from algebraic graph theory. These non-linear relations are used either directly giving rise to the bilinear formulations, or, through the big-M reformulation, resulting in the linear programs. A branch-and-bound framework of Gurobi 9.0 optimization software is employed to compare performance of the novel formulations on the example of an optimum requirement spanning tree problem with additional vertex degree constraints. Several real-world requirements matrices from transportation industry are used to generate a number of examples of different size, and computational experiments show the superiority of the two novel linear distance-based formulations over the the traditional multicommodity flow model.