Multi-objective optimization with uncertainty: Probabilistic and fuzzy approaches

The study of multi-objective optimization has matured to a level where uncertainty is considered when comparing and evaluating solutions for any given problem. This paper reviews the current techniques that have been proposed to include uncertainty within a multi-objective framework. Probabilistic as well as fuzzy methods are reviewed. A new method to identify sample representative solutions from a set of Pareto-optimal solutions, that extends the concept of a median, has been proposed. A method to compare solutions when not all objective functions are equal, i.e. when a hierarchy of objectives exist, is also proposed.