An Enhancement of the NSGA-II Reliability Optimization Using Extended Kalman Filter Based Initialization

Abstract

The real-life design and engineering problems are multi-objective and nonlinear problems that also contain high level uncertainty. Finding the optimal solution for uncertain problems is a huge challenge, because of the uncertainty. These uncertain variables can be satisfied with reliable boundary conditions. In literature, there are several reliability-based optimization methods using moments methods which are mainly approximated approaches using the first-order Taylor expansion in the limit state function. These methods are easy to integrate with the performance measurement (objective) functions to determine reliable and optimal solutions. In this study, a novel reliability-based design optimization approach is proposed using FORM and SORM based reliability methods for a real-life engineering and safety problem (car side impact and deflection problem) and other benchmark functions. The optimization engine is a Kalman filter based enhanced evolutionary optimization algorithm (NSGA-II). Since the basic Kalman filter is suitable to minimize the noise in linear type problems, they are efficient solutions for nonlinear problems. In this study, an extended Kalman filter-based approach is utilized with evolutionary algorithm to obtain a better solution set at the initialization stage. The performances of the proposed algorithms are assessed using hypervolume indicator approach for the basic NSGA-II, FORM and SORM based reliability added NSGA-II, basic NSGA-II with extended Kalman filter (EKF); and FORM and SORM based reliability added NSGA-II with EKF. According to the hypervolume indicator results, EKF filter performed better with reliability-based NSGA-II.