Efficient global design optimization incorporating expected functions estimation criteria

Abstract

Global optimization methods are used widely because the methods can provide a global optimum when the problem includes many local minima. However, the computational cost of global optimization can be very high because all design spaces are searched in order to obtain the global optimum. Also, the computational cost is increased when the optimization of an engineering problem is performed through an expensive computational analysis tool such as CFD (Computational Fluid Dynamics) or RCS (Radar Cross Section). Therefore, surrogate modeling can be used in design optimization of systems in order to reduce the computational cost. EGO (Efficient Global Optimization) is one of the representative global design optimization methods using the surrogate model. EGO was proposed by Jones et al. [1], it obtains an optimum solution with a surrogate model. The surrogate model is updated with new sample obtaining the maximum EI (Expected Improvement). The EI is defined as the expectation value that the prediction value can be smaller than the present minimum value at new sample point. Ahn et al. [2] proposed feasibility and activity estimation criteria then applied these criteria to EGO in order to improve the computational efficiency. The function of the criteria is to identify whether the surrogate model of the constraint function has to be updated or not at every iteration during optimization. In this study, two tasks are performed in order to improve the computational efficiency of the method pro-posed by Ahn et al. [2]. First, the feasibility estimation criterion proposed by Ahn et al. [2] is modified by mod-ifying EV (Expected Violation) and considering the feasibility tolerance. The efficiency of EGO incorporating the modified feasibility estimation criterion was demonstrated by the test functions. It is found that the EGO incorporating the modified criterion can be applied efficiently to practical engineering problems. Second, the selective EI concept is proposed in ord...