Multi-parametric programming based algorithms for the global solution of bi-level mixed-integer linear and quadratic programming problems

Abstract

Abstract Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Bi-level programming problems are very challenging to solve, even in the linear case. For classes of problems where the lower level problem also involves discrete variables, this complexity is further increased, typically requiring global optimization methods for its solution. In this work, we present a novel algorithm for the exact, global and parametric solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer quadratic programming problems (B-MIQP) containing both integer and continuous variables at both optimization levels. Computational implementation and computational performance of the algorithm are also discussed.