Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions

• Published in: Journal of global optimization Vol. 91; no. 4; pp. 897 - 922
• Main Authors: Kleijnen, Jack P. C., Angün, Ebru, van Nieuwenhuyse, Inneke, van Beers, Wim C. M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2025; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Constraints; Engineering; Gaussian process; Global optimization; Kuhn-Tucker method; Literature reviews; Machine learning; Mathematical programming; Mathematics; Mathematics and Statistics; Methods; Operations Research/Decision Theory; Optimization; Real Functions; Simulation; Efficient global optimization; Gaussian process; Karush-Kuhn-Tucker conditions; Bayesian optimization; Kriging; Machine learning
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-024-01448-3

We develop a novel methodology for solving constrained optimization problems in deterministic simulation. In these problems, the goal (or objective) output is to be minimized, subject to one or more constraints for the other outputs and for the inputs. Our methododology combines the“Karush-Kuhn-Tucker”(KKT) conditions with“efficient global optimization”(EGO).These KKT conditions are well-known first-order necessary optimality conditions in white-box mathematical optimization, but our method is the first EGO method that uses these conditions. EGO is a popular type of algorithm that is closely related to“Bayesian optimization” and“active machine learning”, as they all use Gaussian processes or Kriging to approximate the input/output behavior of black-box models. We numerically compare the performance of our KKT-EGO algorithm and two alternative EGO algorithms, in several popular examples. In some examples our algorithm converges faster to the true optimum, so our algorithm may provide a suitable alternative.