Multi-objective optimization problems under uncertainty (MOPs-U) have received considerable and increasing interest these recent years in the field of discrete and continuous multi-objective optimization. MOPs-U arise in many important decision making problems in various sciences and industries and pose challenges for both engineers and researchers. The sources of uncertainty in MOPs-U are due to many factors such as environment parameters, decision variables and objectives functions. In this talk, we consider both random and epistemic models of uncertainty in the design od multi-objective evolutionary algorithms