A Global Optimization Algorithm for the Solution of Mixed-Integer Quadratic Adjustable Robust Optimization Problems under Endogenous Uncertainty

This work proposes an algorithm for the solution of the two-stage mixed-integer quadratic adjustable robust optimization (ARO) problem under endogenous uncertainty. This class of ARO problems is often used in Chemical Engineering application such as scheduling and control problems, but there are only a handful of approaches attempting to solve them. For our developed approach, the two-stage ARO problem is firstly reformulated as a tri-level mixed-integer quadratic programming problem, and the exact and global solution is obtained using multi-parametric programming. The proposed algorithm was verified and compared with other approaches such as the affine decision rules, the column-and-constraint generation algorithm, and full enumeration of extreme points. We showed that our algorithm has the ability to solve ARO problems that, to our knowledge, cannot be solved by any other algorithm. To assess the efficiency and the performance of the proposed algorithm, a computational study was performed.