Integer and mixed-integer bi-level

Integer and mixed-integer bi-level problems have been seldom considered due to their extreme complexity. Nonetheless, among the works that can be found in the literature, three main categories emerged. The first one relies on a decomposition mechanism while the second one is based on a modified Branch and Bound . The last one takes advantage of the existing parametric programming approaches to solve the lower-level . Exact approaches are not suitable for real applications due to the complexity induced by a second level. To tackle this problem, researchers turned towards metaheuristics. Designed to cope with N P-hard problems, metaheuristics have been widely employed with success and have bi-level equivalents. Since convex bi-level problems are N P-hard contrary to their single-level convex counterparts, the scope of metaheuristics has been extended. We extended the taxonomy proposed by Talbi in [34] and the recent advances, five main categories can be observed in the literature and are illustrated in Fig. 2.