Radius of Robust Feasibility for Mixed-Integer Problems

For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines value for maximal size uncertainty set such that MIP can be guaranteed. The approaches RRF in literature are restricted to continuous optimization problems. We first analyze relations between and its (LP) relaxation. In particular, we derive conditions under which LP relaxation have same RRF. Afterward, extend notion it applied large variety problems sets. contrast setting commonly used literature, consider every constraint potentially different is not necessarily full-dimensional. Thus, generalize MIPs include safe variables constraints; is, where uncertainties do affect certain or constraints. extended setting, again present methods computing LPs Finally, show new methodologies successfully instances MIPLIB 2017 Summary Contribution: Robust an important field operations research due capability protecting from data usually defined via so-called Intensive has been conducted developing algorithmically tractable reformulations semi-infinite However, applications also construct appropriate sets (i.e., prohibiting too conservative, intractable, even infeasible choice set). doing so, useful know “size” given feasible solution still exists. this paper, study one “size”: (RRF). contribute on theoretical side by generalizing as well “safe” constraints constraints). This allows apply many since exist most applications. provide