Bi-level problems are extremely cha

Bi-level problems are extremely challenging from a mathematical point of view. In fact, a bi-level feasible solution is necessarily lower-level optimal. Consequently, a N P-hard lower-level problem makes bi-level feasibility N P-hard as well. The bi-level feasible search space, named Inducible Region, is not known apriori even if both upper-level and lower-level search spaces are clearly defined. Indeed, in a singlelevel problem, the search space is defined by the bounds and constraints that linked decision variables. In a bi-level problem, an additional optimization problem is part of the constraints. It means that the search space can only be discovered if we are able to solve this problem to optimality..