Non-parametric stochastic subset optimization utilizing multivariate boundary kernels and adaptive stochastic sampling

The implementation of NP-SSO (non-parametric stochastic subset optimization) to general design under uncertainty problems and its enhancement through various soft computing techniques is discussed. NP-SSO relies on iterative simulation of samples of the design variables from an auxiliary probability density, and approximates the objective function through kernel density estimation (KDE) using these samples. To deal with boundary correction in complex domains, a multivariate boundary KDE based on local linear estimation is adopted in this work. Also, a non-parametric characterization of the search space at each iteration using a framework based on support vector machine is formulated. To further improve computational efficiency, an adaptive kernel sampling density formulation is integrated and an adaptive, iterative selection of the number of samples needed for the KDE implementation is established.