Outer Approximation

Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in North-western Italy.

The ability to determine in real-time the geographic location of client nodes is an important tool in wireless networks, allowing instantaneous mobile tracking, implementation of location-aware services and also efficient channel and power allocation planning. Among existing classical cooperative localization techniques for wireless networks, the maximum likelihood estimator (MLE) is theoretically the best. However, the gradient-based algorithms that are commonly used for maximum likelihood estimation are quite sensitive to the initial values and cannot achieve the theoretical optimal performance. In this paper, we propose a new iterative positioning algorithm based on received signal strength information that employs a location ordering strategy and a numerical nonlinear optimization method. The algorithm performance is evaluated through simulation for different network scenarios. A real wireless network scenario is also implemented in order to demonstrate the algorithm effectiveness. The proposed algorithm, while presenting a simplified implementation, can achieve better positioning estimates than the classical MLE approach based on the conjugated gradient.

This paper considers an outer approximation projection method for variational inequalities, in which the projections are not performed on the original set that appears in the variational inequality, but on a polyhedral convex set defined by the linearized constraints. It shows that the method converges linearly, when the starting point is sufficiently close to the solution and the step lengths are sufficiently small.

This paper considers an outer approximation projection method for variational inequalities, in which the projections are not performed on the original set that appears in the variational inequality, but on a polyhedral convex set defined by the linearized constraints. It shows that the method converges linearly, when the starting point is sufficiently close to the solution and the step lengths are sufficiently small.

This paper considers an outer approximation projection method for variational inequalities, in which the projections are not performed on the original set that appears in the variational inequality, but on a polyhedral convex set defined by the linearized constraints. It shows that the method converges linearly, when the starting point is sufficiently close to the solution and the step lengths are sufficiently small.

Many optimization problems involve integer and continuous variables that can be modeled as mixed integer nonlinear programming (MINLP) problems. This has led to a wide range of applications, in particular in some engineering areas. Here, we provide a brief overview on MINLP, and present a simple idea for a future nonconvex MINLP solution technique.

Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in Northwestern Italy.

The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. In this article, we propose an outer approximation algorithm for maximizing a function h(x) = ϕ(f (x)) over the efficient set X E of the bi-criteria convex programming problem Vmin{f (x) = (f 1 (x), f 2 (x)) T |x ∈ X}, where ϕ is an increasing function on f (X). The convergence of the algorithm is established. To illustrate the new algorithm, we apply it to the solution of the sample problem. Preliminary computational results with the proposed algorithm are reported.

The ability to determine in real-time the geographic location of client nodes is an important tool in wireless networks, allowing instantaneous mobile tracking, implementation of location-aware services and also efficient channel and power allocation planning. Among existing classical cooperative localization techniques for wireless networks, the maximum likelihood estimator (MLE) is theoretically the best. However, the gradient-based algorithms that are commonly used for maximum likelihood estimation are quite sensitive to the initial values and cannot achieve the theoretical optimal performance. In this paper, we propose a new iterative positioning algorithm based on received signal strength information that employs a location ordering strategy and a numerical nonlinear optimization method. The algorithm performance is evaluated through simulation for different network scenarios. A real wireless network scenario is also implemented in order to demonstrate the algorithm effectiveness. The proposed algorithm, while presenting a simplified implementation, can achieve better positioning estimates than the classical MLE approach based on the conjugated gradient.

This paper considers localization of a source or a sensor from distance measurements. We argue that linear algorithms proposed for this purpose are susceptible to poor noise performance. Instead given a set of sensors/anchors of known positions and measured distances of the source/sensor to be localized from them we propose a potentially nonconvex weighted cost function whose global minimum estimates the location of the source/sensor one seeks. The contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors/anchors of known positions, such that if the object to be localized is in this region, localization occurs by globally exponentially convergent gradient descent in the noise free case. Exponential convergence in the noise free case represents practical convergence as it ensures graceful performance degradation in the presence of noise. These results guide the deployment of sensors/anchors so that small subsets can be made responsible for practical localization in geographical areas determined by our approach.

In this work, an acoustic sensor network for a relative localization system is analyzed by reporting the accuracy achieved in the position estimation. The proposed system has been designed for those applications where objects are not restricted to a particular environment and thus one cannot depend on any external infrastructure to compute their positions. The objects are capable of computing spatial relations among themselves using only acoustic emissions as a ranging mechanism. The object positions are computed by a multidimensional scaling (MDS) technique and, afterwards, a least-square algorithm, based on the Levenberg-Marquardt algorithm (LMA), is applied to refine results. Regarding the position estimation, all the parameters involved in the computation of the temporary relations with the proposed ranging mechanism have been considered. The obtained results show that a fine-grained localization can be achieved considering a Gaussian distribution error in the proposed ranging mechanism. Furthermore, since acoustic sensors require a line-of-sight to properly work, the system has been tested by modeling the lost of this line-of-sight as a non-Gaussian error. A suitable position estimation has been achieved even if it is considered a bias of up to 25 of the line-of-sight measurements among a set of nodes.

The performance of several existing and partly new algorithms for positioning of sensor node based on distance estimate is compared when the distance estimates are obtained from a measurement campaign. The distance estimates are based on time-of-arrival measurements done by ultrawideband devices in an indoor office environment. Two different positioning techniques are compared: statistical and geometrical. In statistical category, distributed weighted-multidimensional scaling (dwMDS), least squares, and sum ...

This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes are positively biased, e.g., in non-line-of-sight conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the worst-case position error can be defined as the maximum distance between the estimate and any point in the feasible set (the first bound).

The problem of positioning targets based on distance estimates is studied for cooperative wireless sensor networks when there is limited a priori information about measurements noise. To solve this problem, two different methods of positioning are considered: statistical and geometrical. Based on a geometric interpretation, we show that the positioning problem can be rendered as finding the intersection of a number of convex sets. To find this intersection, we propose two different methods based on projection onto convex sets and outer-approximation. In the statistical approach, a partly novel two-step linear estimator is proposed which can be expressed in a closed-form solution. We also propose a new constrained non-linear least squares algorithm based on constraints derived in the outerapproximation approach. Simulation results show that the geometrical methods are more robust against non-line-of-sight measurements than the statistical approaches while in dense networks with lineof-sight measurements statistical approaches outperform geometrical methods.

The performance of several existing and partly new algorithms for positioning of sensor node based on distance estimate is compared when the distance estimates are obtained from a measurement campaign. The distance estimates are based on time-of-arrival measurements done by ultrawideband devices in an indoor office environment. Two different positioning techniques are compared: statistical and geometrical. In statistical category, distributed

Localization of an isotropic acoustic source using energy measurements from distributed sensors is considered. While most acoustic source localization algorithms require that distance estimates between the sensors and the source of interest are available, we propose a linear least squares criterion that does not make such an assumption. The new criterion can yield the location of the source and its transmit power in closed form. A weighted least squares cost function is also considered, and distributed implementation of the proposed estimators is studied. Numerical results indicate significant performance improvement as compared to a linear least squares based approach that utilizes energy ratios, and comparable performance to other estimators of higher computational complexity.

Abstract The problem of positioning targets based on distance estimates is studied for cooperative wireless sensor networks when there is limited a priori information about measurements noise. To solve this problem, two different methods of positioning are considered: statistical and geometrical. Based on a geometric interpretation, we show that the positioning problem can be rendered as finding the intersection of a number of convex sets.

In this semi-tutorial paper, the positioning problem is formulated as a convex feasibility problem (CFP). To solve the CFP for non-cooperative networks, we con- sider the well-known projection onto convex sets (POCS) technique, and study its properties for positioning. We also study outer-approximation (OA) methods to solve CFP problems. We then show how the POCS estimate can be upper bounded by solving a non-convex optimization problem. Moreover, we introduce two tech- niques based on OA and POCS to solve the CFP for cooperative networks and obtain two new distributed algorithms. Simulation results show that the proposed algorithms are robust against non-line-of-sight conditions.