Francesco Carrabs - Academia.edu (original) (raw)

Papers by Francesco Carrabs

The aim of the Connected Maximum Lifetime Problem is to define a schedule for the activation inte... more The aim of the Connected Maximum Lifetime Problem is to define a schedule for the activation intervals of the sensors deployed inside a region of interest, such that at all times the activated sensors can monitor a set of interesting target locations and route the collected information to a central base station, while maximizing the total amount of time over which the sensor network can be operational. Complete or partial coverage of the targets are taken into account. To optimally solve the problem, we propose a column generation approach which makes use of an appropriately designed genetic algorithm to overcome the difficulty of solving the subproblem to optimality in each iteration. Moreover, we also devise a heuristic by stopping the column generation procedure as soon as the columns found by the genetic algorithm do not improve the incumbent solution. Comparisons with previous approaches proposed in the literature show our algorithms to be highly competitive, both in terms of solution quality and computational time.

Journal of Network and Computer Applications, 2015

In this paper we face the problem of maximizing the amount of time over which a set of target poi... more 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 α-Lifetime Problem (α-MLP), a variant of MLP in which a given fraction of targets is allowed to be left uncovered at all times; however, since α-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 literature, to solve both MLP and α-MLP.

Journal of Optimization Theory and Applications

Computers & Operations Research, 2015

Wireless sensor networks are generally composed of a large number of hardware devices of the same... more 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.

2014 17th International Conference on Network-Based Information Systems, 2014

ABSTRACT This paper concerns the problem to place N non overlapping circles in a circular contain... more ABSTRACT This paper concerns the problem to place N non overlapping circles in a circular container with minimum radius. This is a well known and widely studied problem with applications in manufacturing and logistics and, in particular, to problems related to cutting and packing. In this paper we propose an algorithm that by applying a strength along a selected direction on each circle, simulates the shifting of circles on the plane and tries to reduce the radius of the circular container during this movements. The algorithm is based on a multistart technique where the starting solutions are produced by a tabu search heuristic that uses also the current best solution. The algorithm takes part in a public international contest in order to find optimal solutions to a special case in circle packing. The contest saw the participation of 155 teams and our algorithm achieved the tenth position.

Procedia - Social and Behavioral Sciences, 2014

This paper addresses a variant of the classical clique problem in which the edges of the graph ar... more This paper addresses a variant of the classical clique problem in which the edges of the graph are labeled. The problem consists of finding a clique as large as possible whose edge set contains at most b ∈ Z + different labels. Moreover, in case of more feasible cliques of the same maximum size, we look for the one with the minimum number of labels. We study the time complexity of the problem, also in special cases, and we propose a mathematical programming approach for its solution by introducing two different formulations: the basic and the enforced. We experimentally evaluate the performance of the proposed approach on a set of benchmark instances (DIMACS) suitably adapted to the problem.

Given a vertex weighted graph G, a minimum Weighted Feedback Vertex Set (MWFVS) is a subset F ⊆ V... more Given a vertex weighted graph G, a minimum Weighted Feedback Vertex Set (MWFVS) is a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F . The MWFVS on general graph is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve MWFVS on it. We will discuss, moreover, how this result could be used to effectively improve the approximated solution of any known heuristic to solve MWFVS on a general graph.

Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) cons... more Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F . The WFVP on general graphs is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve WFVP on it.

Given an undirected and vertex weighted graph G = (V, E, w), the Weighted Feedback Vertex Problem... more Given an undirected and vertex weighted graph G = (V, E, w), the Weighted Feedback Vertex Problem (WFVP) consists of finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard and to be polynomially solvable on some special classes of graphs (e.g., interval graphs, co-comparability graphs, diamond graphs). In this paper we introduce an extension of diamond graphs, namely the k-diamond graphs, and give a dynamic programming algorithm to solve WFVP in linear time on this class of graphs. Other than solving an open question, this algorithm allows an efficient exploration of a neighborhood structure that can be defined by using such a class of graphs. We used this neighborhood structure inside our Iterated Tabu Search heuristic. Our extensive experimental show the effectiveness of this heuristic in improving the solution provided by a 2-approximate algorithm for the WFVPon general graphs.

Networks, 2013

This article studies the double traveling salesman problem with two stacks. A number of requests ... more This article studies the double traveling salesman problem with two stacks. A number of requests have to be served where each request consists in the pickup and delivery of an item. All the pickup operations have to be performed before any delivery can take place. A single vehicle is available that starts from a depot, performs all the pickup operations and returns to the depot. Then, it performs all the delivery operations and returns to the depot. The items are loaded in two stacks, each served independently from the other with a last-in-first-out policy. The objective is the minimization of the total cost of the pickup and delivery tours. We propose a branchand-bound approach to solve the problem. The algorithm uses properties of the problem both to tighten the lower bounds and to avoid the exploration of redundant subtrees. Computational results performed on benchmark instances reveal that the algorithm outperforms the other exact approaches for this problem.

INFORMS Journal on Computing, 2007

This paper addresses a variation of the traveling salesman problem with pickup and delivery in wh... more This paper addresses a variation of the traveling salesman problem with pickup and delivery in which loading and unloading operations have to be executed in a LIFO (Last-in-First-Out) order. We introduce three new local search operators for this problem which are then embedded within a variable neighborhood search heuristic. We evaluate the performance of the heuristic on data adapted from TSPLIB instances.

INFOR: Information Systems and Operational Research, 2007

This paper introduces an additive branch-and-bound algorithm for two variants of the pickup and d... more This paper introduces an additive branch-and-bound algorithm for two variants of the pickup and delivery traveling salesman problem in which loading and unloading operations have to be performed either in a Last-In-First-Out (LIFO) or in a First-In-First-Out (FIFO) order. Two relaxations are used within the additive approach: the assignment problem and the shortest spanning r-arborescence problem. The quality of the lower bounds is further improved by a set of elimination rules applied at each node of the search tree to remove from the problem arcs that cannot belong to feasible solutions because of precedence relationships.

Electronic Notes in Discrete Mathematics, 2004

Computers & Operations Research, 2009

Given a graph G where a label is associated with each edge, we address the problem of looking for... more Given a graph G where a label is associated with each edge, we address the problem of looking for a maximum matching of G using the minimum number of different labels, namely the Labeled Maximum Matching Problem. It is a relatively new problem whose application is related to the timetabling problem . We prove it is NP-complete and present four different mathematical formulations. Moreover, we propose an exact algorithm based on a branchand-bound approach to solve it. We evaluate the performance of our algorithm on a wide set of instances and compare our computational times with the ones required by CPLEX to solve the proposed mathematical formulations. Test results show the effectiveness of our procedure, that hugely outperforms the solver.

Computational Optimization and Applications, 2013

We study a variant of the spanning tree problem where we require that, for a given connected grap... more We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and compare different relaxations of them, namely lagrangian relaxation, continuous relaxation, mixed integer-continuous relaxation. We approach the solution of the Lagrangian dual both by means of a standard subgradient method and an ad-hoc finite ascent algorithm based on updating one multiplier at the time. We provide numerical result comparison of all the considered relaxations on a wide set of benchmark instances. A useful follow-up of tackling the Lagrangian dual is the possibility of getting a feasible solution for the original problem with no extra costs. We evaluate the quality of the resulting upper bound by comparison either with the optimal solution, whenever available, or with the feasible solution provided by some existing heuristic algorithms.