Matteo Fischetti

Bio: Matteo Fischetti is an academic researcher from University of Padua. The author has contributed to research in topics: Integer programming & Linear programming. The author has an hindex of 56, co-authored 170 publications receiving 9746 citations. Previous affiliations of Matteo Fischetti include University of Bologna & University of L'Aquila.

Modeling and Solving the Train Timetabling Problem

Abstract: The train timetabling problem aims at determining a periodic timetable for a set of trains that does not violate track capacities and satisfies some operational constraints. In particular, we concentrate on the problem of a single, one-way track linking two major stations, with a number of intermediate stations in between. Each train connects two given stations along the track (possibly different from the two major stations) and may have to stop for a minimum time in some of the intermediate stations. Trains can overtake each other only in correspondence of an intermediate station, and a minimum time interval between two consecutive departures and arrivals of trains in each station is specified.In this paper, we propose a graph theoretic formulation for the problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant. This formulation is used to derive an integer linear programming model that is relaxed in a Lagrangian way. A novel feature of our model is that the variables in the relaxed constraints are associated only with nodes (as opposed to arcs) of the aforementioned graph. This allows a considerable speed-up in the solution of the relaxation. The relaxation is embedded within a heuristic algorithm which makes extensive use of the dual information associated with the Lagrangian multipliers. We report extensive computational results on real-world instances provided from Ferrovie dello Stato SpA, the Italian railway company, and from Ansaldo Segnalamento Ferroviario SpA.

A Heuristic Method for the Set Covering Problem

Abstract: We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows an...

Algorithms for the Set Covering Problem

Abstract: The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and mass-transit companies. In this survey, we focus our attention on the most recent and effective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental comparison on the test-bed instances of Beasley's OR Library.

A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem

Abstract: We consider a variant of the classical symmetric Traveling Salesman Problem in which the nodes are partitioned into clusters and the salesman has to visit at least one node for each cluster This NP-hard problem is known in the literature as the symmetric Generalized Traveling Salesman Problem (GTSP), and finds practical applications in routing, scheduling and location-routing In a companion paper (Fischetti et al [Fischetti, M, J J Salazar, P Toth 1995 The symmetric generalized traveling salesman polytope Networks 26 113–123]) we modeled GTSP as an integer linear program, and studied the facial structure of two polytopes associated with the problem Here we propose exact and heuristic separation procedures for some classes of facet-defining inequalities, which are used within a branch-and-cut algorithm for the exact solution of GTSP Heuristic procedures are also described Extensive computational results for instances taken from the literature and involving up to 442 nodes are reported

The feasibility pump

Abstract: In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem of the form min{cTx:Ax≥b,xj integer ∀j ∈ **}. Trivially, a feasible solution can be defined as a point x* ∈ P:={x:Ax≥b} that is equal to its rounding **, where the rounded point ** is defined by ** := x*j if j ∈ ** and ** := x*j otherwise, and [·] represents scalar rounding to the nearest integer. Replacing “equal” with “as close as possible” relative to a suitable distance function Δ(x*, **), suggests the following Feasibility Pump (FP) heuristic for finding a feasible solution of a given MIP.We start from any x* ∈ P, and define its rounding **. At each FP iteration we look for a point x* ∈ P that is as close as possible to the current ** by solving the problem min {Δ(x, **): x ∈ P}. Assuming Δ(x, **) is chosen appropriately, this is an easily solvable LP problem. If Δ(x*, **)=0, then x* is a feasible MIP solution and we are done. Otherwise, we replace ** by the rounding of x*, and repeat.We report computational results on a set of 83 difficult 0-1 MIPs, using the commercial software ILOG-Cplex 8.1 as a benchmark. The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered. Interestingly, ILOG-Cplex could not find any feasible solution at the root node for 19 problems in our test-bed, whereas FP was unsuccessful in just 3 cases.

Ant system: optimization by a colony of cooperating agents

Abstract: An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call ant system (AS). We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical traveling salesman problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the ant system (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics-global data structure revision, distributed communication and probabilistic transitions of the AS.

Greedy Randomized Adaptive Search Procedures

Abstract: Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

Learning and optimization using the clonal selection principle

Abstract: The clonal selection principle is used to explain the basic features of an adaptive immune response to an antigenic stimulus. It establishes the idea that only those cells that recognize the antigens (Ag's) are selected to proliferate. The selected cells are subject to an affinity maturation process, which improves their affinity to the selective Ag's. This paper proposes a computational implementation of the clonal selection principle that explicitly takes into account the affinity maturation of the immune response. The general algorithm, named CLONALG, is derived primarily to perform machine learning and pattern recognition tasks, and then it is adapted to solve optimization problems, emphasizing multimodal and combinatorial optimization. Two versions of the algorithm are derived, their computational cost per iteration is presented, and a sensitivity analysis in relation to the user-defined parameters is given. CLONALG is also contrasted with evolutionary algorithms. Several benchmark problems are considered to evaluate the performance of CLONALG and it is also compared to a niching method for multimodal function optimization.