A Global Optimization Algorithm for the Solution of Tri-Level Mixed-Integer Quadratic Programming Problems

Abstract

A novel algorithm for the global solution of a class of tri-level mixed-integer quadratic optimization problems containing both integer and continuous variables at all three optimization levels is presented. The class of problems we consider assumes that the quadratic terms in the objective function of the second level optimization problem do not contain any third level variables. To our knowledge, no other solution algorithm can tackle the class of problems considered in this work. Based on multi-parametric theory and our earlier results for tri-level linear programming problems, the main idea of the presented algorithm is to recast the lower levels of the tri-level optimization problem as multi-parametric programming problems, in which the optimization variables (continuous and integer) of all the upper level problems, are considered as parameters at the lower levels. The resulting parametric solutions are then substituted into the corresponding higher-level problems sequentially. Computational studies are presented to asses the efficiency and performance of the presented algorithm.