In this work, we consider a scenario in which we have to monitor some locations of interest in a geographical area by means of a wireless sensor network. Our aim is to keep the network operational for as long as possible, while preventing certain sensors from being active simultaneously, since they would interfere with one another causing data loss, need for retransmissions and overall affecting the throughput and efficiency of the network. We propose an exact approach based on column generation, as well as a heuristic algorithm to solve its separation problem. Computational tests prove our approach to be effective, and that the introduction of our heuristic in the Column Generation framework allows significant gains in terms of required computational effort.

We consider a scenario in which certain target locations are monitored through sensors, which are scattered all over a considered area. A quality-of-service threshold imposes that, at any given time, a predefined percentage of the overall number of targets must be monitored. Furthermore, the activated sensors must be able to transmit the sensed information to a central base station, and the different roles assumed by the sensors (sensing, relay or idle) lead to different energy consumptions. We propose an exact algorithm to solve the problem of maximizing the operational time in this scenario, and test it on a set of benchmark instances.

In this paper we face the problem of maximizing the amount of time over which a set of target points, located in a given geographic region, can be monitored by means of a wireless sensor network. The problem is well known in the literature as Maximum Network Lifetime Problem (MLP). In the last few years the problem and a number of variants have been tackled with success by means of different resolution approaches, including exact approaches based on column generation techniques. In this work we propose an exact approach which combines a column generation approach with a genetic algorithm aimed at solving efficiently its separation problem. The genetic algorithm is specifically aimed at the Maximum Network ?-Lifetime Problem (?-MLP), a variant of MLP in which a given fraction of targets is allowed to be left uncovered at all times; however, since ?-MLP is a generalization of MLP, it can be used to solve the classical problem as well. The computational results, obtained on the benchmark instances, show that our approach overcomes the algorithms, available in the literature, to solve both MLP and ?-MLP.

Wireless sensor networks are generally composed of a large number of hardware devices of the same type, deployed over a region of interest in order to perform a monitoring activity on a set of target points. Nowadays, several different types of sensor devices exist, which are able to monitor different aspects of the region of interest (including sound, vibrations, proximity, chemical contaminants, among others) and may be deployed together in a heterogeneous network. In this work, we face the problem of maximizing the amount of time during which such a network can remain operational, while maintaining at all times a minimum coverage guarantee for all the different sensor types. Some global regularity conditions in order to guarantee a fair level of coverage for each sensor type to each target are also taken into account in a second variant of the proposed problem. For both problem variants we developed an exact approach, which is based on a column generation algorithm whose subproblem is either solved heuristically by means of a genetic algorithm or optimally by an appropriate ILP formulation. In our computational tests the proposed genetic algorithm is shown to be able to dramatically speed up the procedure, enabling the resolution of large-scale instances within reasonable computational times.

In this article, we face the problem of ensuring reliability of a wireless sensor network which is monitoring a given set of points of interest while maximizing its lifetime (i.e., the amount of time over which the monitoring activity can be performed). The two objectives are contrasting. Indeed, the traditional approach to achieve reliability involves providing redundant coverage, which, however, drastically reduces the network lifetime. We propose an alternative strategy where sensors adapt their sensing radii in response to failures to restore feasibility only when needed. We provide Column Generation exact algorithms for both the traditional approach and our variant, as well as a heuristic procedure for the coverage restoration phase. The advantages of our approach are shown by means of computational tests on a set of instances and failure simulations.

In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant problem in this field and show its relations with the Minimum Branch Vertices and the Minimum Degree Sum Problems. We present a unified memetic algorithm for the three problems and show its effectiveness on a wide range of test instances. © 2013 Elsevier B.V. All rights reserved.

In the k-labeled Spanning Forest Problem (kLSF), given a graph G with a label (color) assigned to each edge, and an integer positive value kmax we look for the minimum number of connected components that can be obtained by using at most kmax different labels. The problem is strictly related to the Minimum Labelling Spanning Tree Problem (MLST), since a spanning tree of the graph (i.e. a single connected component) would obviously be an optimal solution for the kLSF, if it can be obtained without violating the bound on kmax. In this work we present heuristic and exact approaches to solve this new problem.

An important problem in the context of wireless sensor networks is the Maximum Network Lifetime Problem (MLP): find a collection of subset of sensors (cover) each covering the whole set of targets and assign them an activation time so that network lifetime is maximized. In this paper we consider a variant of MLP, where we allow each cover to neglect a certain fraction (1 - ?) of the targets. We analyze the problem and show that the total network lifetime can be hugely improved by neglecting a very small portion of the targets. An exact approach, based on a Column Generation scheme, is presented and a heuristic solution algorithm is also provided to initialize the approach. The proposed approaches are tested on a wide set of instances. The experimentation shows the effectiveness of both the proposed problems and solution algorithms in extending network lifetime and improving target coverage time when some regularity conditions are taken into account. © 2011 Springer-Verlag.

In the colourful travelling salesman problem (CTSP), given a graph G with a (not necessarily distinct) label (colour) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types. We propose two new heuristics based on the deconstruction of a Hamiltonian tour into subpaths and their reconstruction into a new tour, as well as an adaptation of an existing approach. Extensive experimentation shows the effectiveness of the proposed approaches.

The aim of this chapter is to present an overview of the main results for a well-known optimization problem and an emerging optimization area, as well as introducing a new problem which is related to both of them. The first part of the chapter presents an overview of the main existing results for the classical maximum flow problem. The maximum flow problem is one of the most studied optimization problems in the last decades. Besides its many practical applications, it also arises as a subproblem of several other complex problems (e.g., min cost flow, matching, covering on bipartite graphs). Subsequently, the chapter introduces some problems defined on edge-labeled graphs by reviewing the most relevant results in this field. Edge-labeled graphs are used to model situations where it is crucial to represent qualitative differences (instead of quantitative ones) among different regions of the graph itself. Finally, the maximum flow problem with the minimum number of labels (MF-ML) problem is presented and discussed. The aim is to maximize the network flow as well as the homogeneity of the solution on a capacitated network with logic attributes.

Wireless sensor networks involve many different real-world contexts, such as monitoring and control tasks for traffic, surveillance, military and environmental applications, among others. Usually, these applications consider the use of a large number of low-cost sensing devices to monitor the activities occurring in a certain set of target locations. We want to individuate a set of covers (that is, subsets of sensors that can cover the whole set of targets) and appropriate activation times for each of them in order to maximize the total amount of time in which the monitoring activity can be performed (network lifetime), under the constraint given by the limited power of the battery contained in each sensor. A variant of this problem considers that each sensor can be activated in a certain number of alternative power levels, which determine different sensing ranges and power consumptions. We present some heuristic approaches and an exact approach based on the column generation technique. An extensive experimental phase proves the advantage in terms of solution quality of using adjustable sensing ranges with respect to the classical single range scheme. © 2012 Elsevier B.V. All rights reserved.

Wireless sensor networks involve a large area of real-world contexts, such as national security, military and environmental control applications, traffic monitoring, among others. These applications generally consider the use of a large number of low-cost sensing devices to monitor the activities occurring in a certain set of target locations. One of the most important issue that is considered in this context is maximizing network lifetime, that is the amount of time in which this monitoring activity can be performed by opportunely switching the sensors from active to sleep mode. Indeed, the lifetime of the network can be maximized by individuating subset of sensors (i.e., covers) and switching among them. Two important aspects need to be taken into account among others: (i) coverage: each determined cover has to cover the entire set of targets, and (ii) connectivity: each cover should provide satisfactory network connectivity so that sensors can communicate for data gathering or data fusion (connected covers). In this paper we consider the problem of determining the maximum network lifetime to monitor all the targets by means of connected covers. We analyze the problem and propose an exact approach based on column generation and two heuristic approaches, namely a greedy algorithm and a GRASP algorithm, to solve it. We analyze the performance of the heuristic approaches by comparing the obtained solutions with those provided by the exact approach when available. Our preliminary experimental results show the proposed solution algorithms to be promising in terms of tradeoff between quality of solutions and computational effort. © 2011 Springer-Verlag.

The Push-Tree Problem is a recently addressed optimization problem, with the aim to minimize the total amount of traffic generated on information broadcasting networks by a compromise between the use of "push" and "pull" mechanisms. That is, the push-tree problem can be seen as a mixture of building multicast trees with respect to nodes receiving pieces of information while further nodes may obtain information from the closest node within the tree by means of shortest paths. In this sense we are accounting for tradeoffs of push and pull mechanisms in information distribution. The objective of this paper is to extend the literature on the problem by presenting four mathematical formulations and by defining and applying some metaheuristics for its resolution. © Springer Science+Business Media, LLC 2009.

Given a graph G with a label (color) assigned to each edge (not necessarily properly) we look for an hamiltonian cycle of G with the minimum number of different colors. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity or other properties by means of limited number of different connections. We analyze the complexity of the problem on special graph classes and propose, for the general case, heuristic resolution algorithms. Performances of the algorithms are experimentally evaluated on a set of instances and compared with the exact solution value provided by a solver. © 2006 Elsevier B.V. All rights reserved.