The Robust Set Covering Problem with interval data

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

“…Later on, Pereira and Averbakh [11] introduced the interval data min-max regret set covering problem. The authors proposed a mathematical formulation for the problem that is similar to 4 the one proposed by [5] for the interval data min-max regret traveling salesman problem.…”

“…The algorithm detailed above is applied to obtain optimal solutions for the interval robust-hard problems considered in this work, and their corresponding bounds are used to evaluate the quality of the solutions produced by the heuristic proposed in the next section. We highlight that other exact algorithms can be adapted and used for this purpose, such as the branch-and-cut algorithm proposed by Pereira and Averbakh [11] for the interval data min-max regret set covering problem.…”

“…An optimal solution for the model solved by our heuristic is not necessarily optimal for the original robust optimization problem. However, computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem [11] 3 showed that the heuristic is able to find optimal or near-optimal solutions, and that it improves the upper bounds obtained by both a state-of-the-art exact algorithm and a 2-approximation procedure for interval min-max regret problems.…”

Networks, uncertainty, applications and a crusade for optimality

“…The second enhancement to the BBD corresponds to an idea originally proposed by [Fischetti et al, 2010] and later used in [Pereira and Averbakh, 2011b] also in the context of MMR. Roughly speaking, the idea is the following: each of the incumbent solutionsX t found while solving (MP.1)-(MP.4) is used to generate a Benders cut (induced by the correspondingŶ t solution) that will be added to the model in the next iteration.…”

“…Only for few problems, the corresponding MMR counterpart is polynomially solvable [see Candia-Véjar et al, 2011]. Several exact and heuristic approaches have been proposed for different MMR problems including MMR-ST [Yaman et al, 2001, Montemmani and Gambardella, 2005, Montemmani, 2006, Nikulin, 2008, Kasperski, 2008, Kasperski et al, 2012, MMR-P [Karasan et al, 2004, Kasperski, 2008, MMR-A [Pereira and Averbakh, 2011a], MMR Set Covering [Pereira and Averbakh, 2011b], MMR-TSP [Montemmani et al, 2007].…”