Chebyshev inequality based approach to chance constrained optimization problems using differential evolution

Abstract

A new approach to solve Chance Constrained Optimization Problem (CCOP) without using the Monte Carlo simulation is proposed. Specifically, the prediction interval based on Chebyshev inequality is used to estimate a stochastic function value included in CCOP from a set of samples. By using the prediction interval, CCOP is transformed into Upper-bound Constrained Optimization Problem (UCOP). The feasible solution of UCOP is proved to be feasible for CCOP. In order to solve UCOP efficiently, a modified Differential Evolution (DE) combined with three sample-saving techniques is also proposed. Through the numerical experiments, the usefulness of the proposed approach is demonstrated.