Solving nonlinear interval optimization problem using stochastic programming technique

In this paper a methodology is developed to solve a nonlinear interval optimization problem by transforming this to a general optimization problem which is free from interval uncertainty. To address the interval uncertainty, relation between an interval and a random variable is established according to the 3 sigma-rule. Using this relation an interval function is associated with a function of random variables and an interval inequality is associated with a chance constraint. The interval optimization problem is then transformed into a nonlinear stochastic programming problem. Further, the existence of a preferable solution of the original problem is established using Chance Constrained Programming technique.