A Fast Hybrid Primal Heuristic for Multiband Robust Capacitated Network Design with Multiple Time Periods

TL;DR

This paper introduces a hybrid primal heuristic for the Robust Multiperiod Network Design Problem, effectively handling traffic uncertainty and multiple time periods, achieving high-quality solutions efficiently.

Contribution

It presents a novel hybrid heuristic combining randomized fixing and large neighborhood search for a complex robust network design problem.

Findings

The heuristic produces solutions with low optimality gaps.

It runs efficiently on realistic instances from SNDlib.

The approach effectively manages traffic uncertainty and multiple periods.

Abstract

We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (B\"using and D'Andreagiovanni, 2012), a refinement of classical Gamma-Robustness by Bertsimas and Sim that uses a system of multiple deviation bands. Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization, which exploits information coming from linear relaxations of the problem, and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.