“…Graphically, one of these three positions would be the solution for the optimization problem in (9) under a certain criterion of variance given as V crit . Another two ways to obtain variance: Taylor series expanded based method and Monte Carlo Simulation are employed to calculate the response variances centered at positions (1, 1), (1,3) and (3,2), and the results are compared with Sobol'-based method in Table 1. It can be seen that results from Sobol'-based method are close to those from MCS, which are considered accurate with a relatively large sample size (i.e., 100,000).…”