Global Robust Optimisation for Non-Convex Quadratic Programs: Application to Pooling Problems

Robust optimisation is a powerful approach for addressing uncertainty ensuring constraint satisfaction for all uncertain parameter realisations. While convex robust optimisation problems are effectively tackled using robust reformulations and cutting plane methods, extending these techniques to non-convex problems remains largely unexplored. In this work we propose a method that is based on a parallel robustness and optimality search. We introduce a novel spatial Branch-and-Bound algorithm integrated with robust cutting-planes for solving non-convex robust optimisation problems. The algorithm systematically incorporates global and robust optimisation techniques, leveraging McCormick relaxations. The proposed algorithm is evaluated on benchmark pooling problems with uncertain feed quality, demonstrating algorithm stability and solution robustness. The computational time for the examined case studies is within the same order of magnitude as state-of-the-art. The findings of this work highlight the potential of the proposed algorithm in tackling quadratic non-convex robust optimisation problems, particularly in chemical engineering applications.