A Stochastic Optimization Method Using Weighted Empirical Distribution Function

Abstract

This paper provides a new approach to solve a Chance Constrained Problem (CCP). The CCP is formulated via Cumulative Distribution Function (CDF). Hence, instead of the primitive Monte Carlo simulation, an approximation of CDF can be used to evaluate the solution of the CCP. In order to approximate CDF, two kinds of techniques, Empirical CDF (ECDF) and Weighted Empirical CDF (W_ECDF), are presented. Furthermore, for solving the CCP efficiently, a new Differential Evolution (DE) based optimization method combined with either ECDF or W_ECDF is proposed. The results of numerical experiments show that DE with W_ECDF outperforms DE with ECDF.