Multiparametric robust solutions for combinatorial problems with parameterized locally budgeted uncertainty

In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The algorithm consists of applying a multiparametric algorithm to obtain a near optimal multiparametric solution relative to the objective function for a combinatorial problem defined to find a robust solution for parameters fixed. As far as we know this is the first algorithm presented to do that task. Computational experience is presented to shortest path and $p$-medians problems