Fabio D'Andreagiovanni

Christina Büsing, Fabio D'Andreagiovanni

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. The critical aim of our work is to close the knowledge gap about the adoption of a multi-band uncertainty set in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, which have been interested in getting a better modeling of arbitrary distributions, built on historical data of the uncertainty affecting the considered real-world problems. In this paper, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.

Christina Büsing, Fabio D'Andreagiovanni

The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling resolution by partitioning the band into multiple sub-bands is advisable. The critical aim of our work is to close the knowledge gap on the adoption of multi-band uncertainty in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, interested in getting a better modeling of arbitrary shaped distributions, built on historical data about the uncertainty affecting the considered real-world problems.

Fabio D'Andreagiovanni, Jonatan Krolikowski, Jonad Pulaj

We investigate the Robust Multiperiod Network Design Problem, a generalization of the classical Capacitated Network Design Problem that additionally considers multiple design periods and provides solutions protected against traffic uncertainty. Given the intrinsic difficulty of the problem, which proves challenging even for state-of-the art commercial solvers, we propose a hybrid primal heuristic based on the combination of ant colony optimization and an exact large neighborhood search. Computational experiments on a set of realistic instances from the SNDlib show that our heuristic can find solutions of extremely good quality with low optimality gap.

Fabio D'Andreagiovanni

Base station cooperation (BSC) has recently arisen as a promising way to increase the capacity of a wireless network. Implementing BSC adds a new design dimension to the classical wireless network design problem: how to define the subset of base stations (clusters) that coordinate to serve a user. Though the problem of forming clusters has been extensively discussed from a technical point of view, there is still a lack of effective optimization models for its representation and algorithms for its solution. In this work, we make a further step towards filling such gap: 1) we generalize the classical network design problem by adding cooperation as an additional decision dimension; 2) we develop a strong formulation for the resulting problem; 3) we define a new hybrid solution algorithm that combines exact large neighborhood search and ant colony optimization. Finally, we assess the performance of our new model and algorithm on a set of realistic instances of a WiMAX network.

Fabio D'Andreagiovanni

Over the last decade, wireless networks have experienced an impressive growth and now play a main role in many telecommunications systems. As a consequence, scarce radio resources, such as frequencies, became congested and the need for effective and efficient assignment methods arose. In this work, we present a Genetic Algorithm for solving large instances of the Power, Frequency and Modulation Assignment Problem, arising in the design of wireless networks. To our best knowledge, this is the first Genetic Algorithm that is proposed for such problem. Compared to previous works, our approach allows a wider exploration of the set of power solutions, while eliminating sources of numerical problems. The performance of the algorithm is assessed by tests over a set of large realistic instances of a Fixed WiMAX Network.

Fabio D'Andreagiovanni, Antonella Nardin, Enrico Natalizio

We consider the problem of optimally designing a body wireless sensor network, while taking into account the uncertainty of data generation of biosensors. Since the related min-max robustness Integer Linear Programming (ILP) problem can be difficult to solve even for state-of-the-art commercial optimization solvers, we propose an original heuristic for its solution. The heuristic combines deterministic and probabilistic variable fixing strategies, guided by the information coming from strengthened linear relaxations of the ILP robust model, and includes a very large neighborhood search for reparation and improvement of generated solutions, formulated as an ILP problem solved exactly. Computational tests on realistic instances show that our heuristic finds solutions of much higher quality than a state-of-the-art solver and than an effective benchmark heuristic.

Fabio D'Andreagiovanni, Fabian Mett, Jonad Pulaj

We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage. Since the problem can prove challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic which combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.

Fabio D'Andreagiovanni, Jonatan Krolikowski, Jonad Pulaj

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 (Büsing 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.