A new methodology for solving multi-objective stochastic optimization problems with independent objective functions

For multi-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. However, the Pareto optimal set only pertains to deterministic results. Our research aims to introduce Pareto Uncertainty Index which reflects the stochastic nature of the problem in the results. The proposed method is applied to a simplified Generation Expansion Planning problem to test the Pareto Uncertainty Index idea.