The set covering problem is a well-known NP-hard combinatorial optimization problem with wide practical applications. This paper introduces a novel heuristic for the uni-cost set covering problem. An iterated approximation algorithm (ITEG) based on this heuristic is developed: in the rst iteration a cover is constructed, and in the next iterations a new cover is built by starting with part of t...

The unicost set covering problem is a NP-hard and it has many applications. In this paper we propose a new algorithm based on local search for solving the unicost set covering problem. A fitness function is proposed for this problem and different neighborhood relations are considered for the exploration of the neighborhood of the current solution. A new approach is introduced for effective expl...

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 and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the Italian Operational Research Society, org...

In this paper we present a study of several Ant Colony Optimization (ACO) algorithms for the Set Covering Problem. In our computational study we emphasize the influence of different ways of defining the heuristic information on the performance of the ACO algorithms. Finally, we show that the best performing ACO algorithms we implemented, when combined with a fine-tuned local search procedure, r...

Biogeography-Based Optimization Algorithm (BBOA) is a kind of new global optimization algorithm inspired by biogeography. It mimics the migration behavior of animals in nature to solve optimization and engineering problems. In this paper, BBOA for the Set Covering Problem (SCP) is proposed. SCP is a classic combinatorial problem from NP-hard list problems. It consist to find a set of solutions ...

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements...

A clutter (V;E) packs if the smallest number of vertices needed to intersect all the edges (i.e. a transversal) is equal to the maximum number of pairwise disjoint edges (i.e. a matching). This terminology is due to Seymour 1977. A clutter is minimally nonpacking if it does not pack but all its minors pack. A 0,1 matrix is minimally nonpacking if it is the edge-vertex incidence matrix of a mini...

In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial problem to a simple set covering problem. The nature of the complexity bounds provided is tightly connected with Shannon effect and semi-effect for this classes.

We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of adversarial noise. Certain noisy query learning problems are a special case of our problem. Crucial to ...