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This work deals with a class of problems under interval data uncertainty, namely interval robusthard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-ofthe-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.

In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some insight about the complexity of this problem. We introduce an L‐shaped decomposition approach for the polynomial formulation, thus allowing the optimal solution of large scale instances with up to 90 nodes. Finally, we propose a Kruskal based variable neighborhood search (VNS) metaheuristic to compute near optimal solutions with significantly less computational effort. Our numerical results show that the VNS approach provides tight near optimal solutions with a gap less than 1% for most of the instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 289–305 2015

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