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When modeling real-world challenges as optimization problems, we often encounter uncertainty in problem parameters; as well as the coexistence of multiple goals which are difficult to trade-off against each other. Robust optimization is an approach that addresses the challenge of parameter uncertainty, aiming to find a solution that is feasible under all scenarios (parameter realizations ) and best in the worst-case. Multi-objective optimization addresses the challenge of multiple objective functions by introducing the concept of efficiency (or Pareto optimality), which says that a solution x is worth to look at, if there is no other solution which is at least as good as x with respect to all considered goals, and better in at least one of them.

Several ideas have been proposed to combine these two concepts into the concept of robust efficiency, and we briefly illustrat these before we turn to solution approaches for robust multi-objective problems. There are (at least) two ways to design solution approaches for computing robust efficient solutions: we can try to generalize algorithms for (single-objective) robust optimization to the multi-objective case, or generalize algorithms for (deterministic) multi-objective optimization. Though most of these approaches are applicable for a wider class of problems, for the presentation we focus on biobjective combinatorial problems with bounded uncertainty in both objective functions using the concept of point-wise robust efficiency.