Set covering problem is the model for many important industrial applications. In this paper, we solve some benchmarks of this problem with ant colony optimization algorithms using a new transition rule. A look-ahead mechanism was incorporated to check constraint consistency in ant computing. Computational results are presented showing the advantages to use this additional mechanism to ant syste...

This work introduces a robust formulation of the uncertain set covering problem combining the concepts of robust and probabilistic optimization and defines ’Γ-robust α-covers’. It is shown that the proposed robust uncertain set covering problem can be stated as a compact mixed-integer linear programming model which can be solved with modern computer software. This model is a natural extension o...

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We define an NP-hard clustered variant of the Set Covering Problem where subsets are partitioned into K clusters and a fixed cost is paid for selecting at least one subset in a given cluster. We show that the problem is approximable within ratio (1+ ǫ)(e/e− 1)H(q), where q is the maximum number of elements covered by a cluster and H(q) = ∑q i=1 1 i . Key-words: Integer Programming, Set Covering...

This paper deals with the Set Covering with Pairs Problem (SCPP). This problem is a generalization of the Set Covering Problem (SCP), which is known to be NP-hard. The difference between both problems is that, in the SCPP, one element of the universe is admitted to be covered if there are at least two specific objects chosen to cover it. In this context, three constructive heuristics, one local...

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b-matching problem. In general, we may use a polynomial-time greedy heuristic similar to the one for the classical weighted set covering problem ...