Statistical surrogate model based sampling criterion for stochastic global optimization of problems with constraints

Sequential surrogate model-based global optimization algorithms, such as super-EGO, have been developed to increase the efficiency of commonly used global optimization technique as well as to ensure the accuracy of optimization. However, earlier studies have drawbacks because there are three phases in the optimization loop and empirical parameters. We propose a united sampling criterion to simplify the algorithm and to achieve the global optimum of problems with constraints without any empirical parameters. It is able to select the points located in a feasible region with high model uncertainty as well as the points along the boundary of constraint at the lowest objective value. The mean squared error determines which criterion is more dominant among the infill sampling criterion and boundary sampling criterion. Also, the method guarantees the accuracy of the surrogate model because the sample points are not located within extremely small regions like super-EGO. The performance of the proposed method, such as the solvability of a problem, convergence properties, and efficiency, are validated through nonlinear numerical examples with disconnected feasible regions.