Determination of suboptimal importance sampling functions by genetic algorithms

Abstract

Based on the notion of variance reduction, the term suboptimal Importance Sampling Function (ISF) is introduced and defined in this paper. A suboptimal ISF is an importance sampling Probability Density Function (PDF) that minimizes the variance of probability estimate. This paper presents a numerical procedure of determining a suboptimal ISF from a variance-minimization problem. The suboptimal ISF is specifically defined in terms of a parametric PDF. Genetic Algorithms (GAs) are applied as a tool for determining the variance-minimizing ISF parameters and thus obtaining the corresponding suboptimal ISF. It is found in the formulation of the objective function that a pre-sampling around the Point of Maximum Likelihood (PML) in the domain of interest, i.e., event/failure domain, will significantly enhance the efficiency and the effectiveness of the determination procedure. Numerical examples show that the numeric-based operations in GAs enable the algorithms to support objective functions with high degree of complexity. The proposed methodology is useful for the risk and reliability analysis of rare events involving complex systems, in which analytical solutions are generally not available and the analysis must resort to numerical methods of solution. © 2007 Taylor & Francis Group.