Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach

Consider a multiobjective decision problem with uncertainty in the objective functions, given as set of scenarios. In single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and good quality for all possible A well-known alternative method single-objective case is compare decisions under optimal benefit hindsight, i.e. minimize (possibly scaled) regret not having chosen decision. this contribution, we extend concept from setting introduce proper definition multivariate (robust) (relative) regret. contrast few existing ideas that mix scalarization optimization, clearly separate modelling its numerical solution. Moreover, our approach limited finite or interval furthermore, computations at least approximations tractable several important special cases. We illustrate approaches based on biobjective shortest path uncertainty.