Paolo Nobili

Minimum power multicasting problem in wireless networks

In this paper we deal with the minimum power multicasting (MPM) problem in wireless ad-hoc networks. By using an appropriate choice of the decision variables and by exploiting the topological properties of the problem, we are able to define an original formulation based on a Set Covering model. Moreover, we propose for its solution two exact procedures that include a preprocessing technique that reduces the huge number of the model’s constraints. We also report some experimental results carried out on a set of randomly generated test problems.

Optimal routing and resource allocation in multi-hop wireless networks

This paper addresses the problem of simultaneously optimizing power consumption and routing in multi-hop wireless networks while forcing the satisfaction of the required transmission demands between given origin–destination pairs. We devise a linear programming model for the selection of optimal routes and transmission schemes where both the power and link capacity levels are suitably discretized. Since the constraint matrix of such a model contains a huge number of columns, we propose an exact algorithm for its solution based on a column-generation approach. The associated column-generation procedure is based on the solution of linear integer programming models. We report some computational results on networks with up to 65 nodes, showing the feasibility of our solution approach.

Some Valid Inequalities for the Probabilistic Minimum Power Multicasting Problem

Abstract In this paper we describe some results on the linear integer programming formulation of the Probabilistic Minimum Power Multicast (PMPM) problem for wireless networks. The PMPM problem consists in optimally assigning transmission powers to the nodes of a given network in order to establish a multihop connection between a source node and a set of destination nodes. The nodes are subject to failure with some probability, however the assignment should be made so that the reliability of the connection is above a given threshold level. This model reflects the necessity of taking into account the uncertainty of hosts availability in a telecommunication network.

Minimum power multicasting in wireless networks under probabilistic node failures

In this paper we deal with a probabilistic extension of the minimum power multicast (MPM) problem for wireless networks. The deterministic MPM problem consists in assigning transmission powers to the nodes, so that a multihop connection can be established between a source and a given set of destination nodes and the total power required is minimized. We present an extension to the basic problem, where node failure probabilities for the transmission are explicitly considered. This model reflects the necessity of taking uncertainty into account in the availability of the hosts. The novelty of the probabilistic minimum power multicast (PMPM) problem treated in this paper consists in the minimization of the assigned transmission powers, imposing at the same time a global reliability level to the solution network. An integer linear programming formulation for the PMPM problem is presented. Furthermore, an exact algorithm based on an iterative row and column generation procedure, as well as a heuristic method are proposed. Computational experiments are finally presented.

Energy consumption minimization in railway planning

The estimation of running times is essential for the railway timetable definition. The trains travel duration must respect some constraints, which depend on the railway network. Usually, the running times minimize the trains travel duration on the railway network. They are typically calculated without considering the energy consumption. The green transportation has recently gained significant importance. In this paper, the energy consumption in the running times estimation is taken into account by defining an optimization problem to calculate the running times for the railway timetable definition. This optimization problem finds the running times which minimize the energy consumption. Precisely, an algorithm to handle the optimization problem with the integration platform for multi-objective and multi-disciplinary optimization modeFRONTIER is defined. The algorithm is tested on a case study and the results are validated with the OpenTrack Railway Simulation Tool.

A MILP Algorithm for the Minimization of Train Delay and Energy Consumption

A new timetable must be calculated in real-time when train operations are perturbed. The energy consumption is becoming a central issue both from the environmental and economic perspective but it is usually neglected in the timetable recalculation. In this paper, we formalize the real-time Energy Consumption Minimization Problem (rtECMP). The rtECMP is the real-time optimization problem of finding the driving regime combination for each train that minimizes the energy consumption, respecting given routing and precedences between trains. We model the trade-off between minimizing the energy consumption and the total delay by considering as objective their weighted sum. We propose an algorithm to solve the rtECMP, based on the solution of a mixed-integer linear programming (MILP) model. We test this algorithm on the Pierrefitte-Gonesse control area, which is a critical area in France with dense mixed traffic. In particular, we consider a one-hour traffic perturbation. In this situation, we take into account different routing and precedence possibilities and we solve the corresponding rtECMP. This experimental analysis shows the influence on the solution of the weights associated with energy consumption and delay in the objective function. The results show that the problem is too difficult to be solved to optimality in real time, but is indeed tractable.

Routing and scheduling in wireless ad hoc networks

Computing capacity bounds of ad hoc networks, as well as optimizing radio resource allocation in order to approach those bounds is a hard task that have recently attracted the interest of the research community. In this paper we address the problem of jointly optimizing the routing of flows, the transmission scheduling over wireless links along the path, and the emitted power for bandwidth guaranteed traffic demands. We propose a mixed integer linear programming model which considers the signal to interference and noise ratio at receiver and accounts for the effect of adaptive transmission rate through a set of discrete link capacity and power values. To find the optimal solution of the proposed problem we provide an algorithm based on column generation. Reported numerical results on networks with up to 50 nodes and 170 links show the effectiveness of the proposed approach even with quite bit problem instances.