Multi-objective efficient global optimization of expensive simulation-based problem in presence of simulation failures

The multi-objective efficient global optimization (MOEGO), an extension of the single-objective efficient global optimization algorithm with the intention to handle multiple objectives, is one of the most frequently studied surrogate model-based optimization algorithms. However, the evaluation of the infill point obtained in each MOEGO update iteration using simulation tool may fail. Such evaluation failures are critical to the sequential MOEGO method as it leads to a premature halt of the optimization process due to the impossibility of updating the Kriging models approximating objectives. In this paper, a novel strategy to prevent the premature halt of the sequential MOEGO method is proposed. The key point is to introduce an additional Kriging model to predict the success possibility of the simulation at an unvisited point. Multi-objective expected improvement-based criteria incorporating the success possibility of the simulation are proposed. Experiments are performed on a set of six analytic problems, five low-fidelity airfoil shape optimization problems, and a high-fidelity axial flow compressor tandem cascade optimization problem. Results suggest that the proposed MOEGO-Kriging method is the only method that consistently performs well on analytic and practical problems. The methods using the least-square support vector machine (LSSVM) or weighted LSSVM as the predictor of success possibility perform competitively or worse compared with MOEGO-Kriging. The penalty-based method, assigning high objective values to the failed evaluations in minimization problem, yields the worst performance.