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We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that 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.
The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads
to mixed-integer linear programs with constraint matrices containing tiny
coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the
standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known
and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear
and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.
The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.
This study investigates how to model and solve the problem of optimally designing FTTx telecommunications access networks integrating wired and wireless technologies, while taking into account the uncertainty of wireless signal propagation. We propose an original robust optimization model for the related robust 3-architecture Connected Facility Location problem, which includes additional variables and constraints to model wireless signal coverage represented through signal-to-interference ratios. Since the resulting robust problem can prove very challenging even for a modern state-of-the art optimization solver, we propose to solve it by an original primal heuristic that combines a probabilistic variable fixing procedure, guided by peculiar Linear Programming relaxations, with a Mixed Integer Programming heuristic, based on an exact very large neighborhood search. A numerical study carried out on a set of realistic instances show that our heuristic can find solutions of much higher quality than a state-of-the-art solver.
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.
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.
A central assumption in classical optimization is that all the input data of a
problem are exact. However, in many real-world problems, the input data are subject
to uncertainty. In such situations, neglecting uncertainty may lead to nominally optimal
solutions that are actually suboptimal or even infeasible. Robust optimization
offers a remedy for optimization under uncertainty by considering only the subset of
solutions protected against the data deviations. In this paper, we provide an overview
of the main theoretical results of multiband robustness, a new robust optimization
model that extends and refines the classical theory introduced by Bertsimas and Sim.
After introducing some new results for the special case of pure binary programs, we
focus on the harvest scheduling problem and show how multiband robustness can
be adopted to tackle the uncertainty affecting the volume of produced timber and
grant a reduction in the price of robustness.
We provide an overview of new theoretical results that we obtained while further investigating multiband robust optimization, a new model for robust optimization that we recently proposed to tackle uncertainty in mixed-integer linear programming. This new model extends and refines the classical Gamma-robustness model of Bertsimas and Sim and is particularly useful in the common case of arbitrary asymmetric distributions of the uncertainty. Here, we focus on uncertain 0-1 programs and we analyze their robust counterparts when the uncertainty is represented through a multiband set. Our investigations were inspired by the needs of our industrial partners in the research project ROBUKOM.