  This work deals with a class of problems under interval data uncertainty,
namely interval robust-hard 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-of-the-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.
