Variable-fidelity expected improvement based efficient global optimization of expensive problems in presence of simulation failures and its parallelization

Abstract

To further alleviate the computational cost of single-fidelity efficient global optimization (EGO) method, the variable-fidelity surrogate-based EGO method assisted by variable-fidelity expected improvement (VF-EI) criterion has emerged and demonstrated to be efficient. This method follows the EGO framework and inherits the sequential feature of EGO, which is, only one infill sample is obtained in each iteration to update the surrogate. Such sequential feature makes the method vulnerable in solving the engineering design optimization problems in which the simulator will possibly crash, especially in computational fluid dynamic involved geometry shape optimization problems. In this paper, a strategy to deal with the existence of simulation failures in variable-fidelity surrogate based sequential optimization method is proposed. By introducing additional Kriging model, which can be updated regardless of the simulation status of the newly selected infill point, to approximate the simulation success possibility, the iterative optimal search process of sequential method will not halt prematurely if a simulation failure of infill point happens. With the available simulation success possibility, new infill criteria based on VF-EI are developed to ensure the effectiveness and efficiency of the proposed method. Further, to accelerate the optimization process with the aid of parallel computation, the sequential method is parallelized by utilizing an influence function to prevent point clustering. Experiment results over analytic and engineering problems show that the proposed sequential method outperforms the method employing the penalty and imputation strategies to deal with simulation failures and the parallel method can accelerate the optimal search compared with the proposed sequential method.