SCR, an efficient global optimization algorithm for constrained black-box problems

Abstract This paper proposes a surrogate based, global-search derivative free algorithm which is specifically designed for computationally expensive black-box (simulation-based) optimization problems with constraints. The algorithm, called SCR ( Surrogate - CMAES - RQLIF ), uses kriging to generate surrogate models of the black-box objective function and black-box constraints. These surrogate models are optimized using the global-search algorithm CMA-ES with the quadratic penalty approach for the constraints. The quality of the kriging surrogates is checked, and the surrogates are updated at each iteration by adding the point found by CMA-ES and additional training points. Once the region of the global optimum has been approximately defined, local search is performed using the hybrid direct-search/model based algorithm RQLIF . After each iteration the points sampled by RQLIF and some additional points found within the optimal region are used to update the surrogate model. Tests on 25 unconstrained and 21 constrained literature test problems show that SCR outperforms benchmark optimization algorithms. The outstanding performance of SCR is also confirmed on two real-world black-box problems arising in process engineering with computationally expensive simulations: the techno-economic optimization of a CO 2 Purification Unit (CPU) and a Vacuum Pressure Swing Adsorption Unit (VPSA).