Weighted empirical distribution based approach to Chance Constrained Optimization Problems using Differential Evolution

Abstract

This paper proposes a new approach to solve Chance Constrained Optimization Problems (CCOPs). The stochastic objective and constraint values in CCOP are evaluated efficiently by using an approximation of Cumulative Distribution Function (CDF) instead of the primitive Monte Carlo simulation. In order to approximate CDF from samples, a technique of the computational statistics called Empirical CDF (ECDF) is widely known. In this paper, an improved version of ECDF named Weighted Empirical CDF (W ECDF) is used. Then, for solving CCOP, a modified Differential Evolution (DE) combined with W ECDF is proposed. The results of numerical experiments show that DE with W ECDF finds a feasible solution of CCOP and outperforms DE with ECDF in the accuracy of solution.