On the use of data engineering and machine learning in global optimization applications with cutting plane approximations
V. Deligianni, A. Marousi, A. Chalkis, A. Kokossis,
Computer Aided Chemical Engineering,Volume 51, pp. 1297-1302, 2022
global optimization; cutting planes; cut selection; data analytics
This work explores data analytics in the development of optimization methodology for global optimization, as applied through decomposition methods and cutting plane algorithms. Cutting planes are treated as data populations, generated at each iteration, population elements are renewed based on the incumbent solution. The current contribution explores qualitative aspects studied in the previous, essentially attempting to expand the affinity norm to temporal sets of data in full and low dimensional spaces. The separation problem is examined using clustering techniques and is tested against a library of quadratic and box constrained optimization problems, that feature varying sparsity and density patterns. The affinity metric was formed, to efficiently evaluate overlapping cutting planes, noting significant improvement in performance. In continuation of these results, normal vector clustering examines the direction of the hyperplanes, by utilizing the cosine similarity of the normal vectors. Temporal data approach aims to prevent repetitions of chosen sub spaces within rounds. Temporal data outperformed the affinity metric approach on the largest problem tested, for tight elimination criteria. Normal vector clustering accelerated the algorithm beyond previous work, in the first round, but failed to further close the duality gap. Overall, analytics are found to dramatically improve the duality gap and the quality of the solution, consistently in all the problems tested. In conclusion, the geometrical interpretation of the dual space holds the most promising lines for future work.