Effective Sampling, Modeling and Optimization of Constrained Black-box Problems

An effective strategy for the sampling, modeling, and optimization of black-box problems with constraints is proposed. Black-box systems are often approximated and solved using surrogate models. Motivated by the fact that the surrogate model needs to be accurate in the feasible region, we use feasible samples to train surrogate model and reduce the overall number of function evaluations. A new mathematical programming based approach is employed to obtain the desired number of feasible, unique and space-filling samples. We then approximate the black-box function by kriging function and apply trust region based e -exact method to converge to a local optimal solution. The overall framework comprising of mathematical programs to obtain feasible samples, modeling and optimization was tested on a suite of 16 problems from GlobalLib. Compared to case when both feasible and infeasible samples are used to train surrogate model, an average reduction of 25.69% was observed when only the feasible samples are selected a priori. The framework is also applied to optimize operating conditions of a tri-reformer to convert and utilize CO2 from power plants.