On the acceleration of global optimization algorithms by coupling cutting plane decomposition algorithms with machine learning and advanced data analytics

Data-driven technologies have demonstrated their potential on various scientific and industrial applications. Their use in the development of generic optimization algorithms is relatively unexplored. The paper presents such an application to design a global optimization algorithm that is generic and suitable to address quadratic box constraint problems. The new method reformulates cutting plane decomposition methods substituting the solution of the master problem by a data-driven selection of cutting planes. The paper presents the theoretical background, data technologies used and computational results that compare the new against state-of-the-art methods. Computational experiments include 100 quadratic programming (QP) problems featuring a wide range of density (25-75%), size (40-100 variables), and complexity. Results are particularly encouraging and demonstrate significant reductions in the duality gap, as high as 40-60% scope on average. Largest improvements are traced in larger formulations (over 100 variables, 75% density). The research is based solely on data produced at a particular iteration. Future work is intended to extend the analysis comparing and considering data patterns across different iterations, also to apply the methodology in other classes of optimization problems