Scenario-based multiobjective optimization approach for dealing with deep uncertainty in environmental problems

This paper considers optimization under deep uncertainty and proposes a scenario-based multiobjective optimization approach. In this approach, the performances of solutions in terms of all objectives in all selected scenarios are evaluated in one optimization problem. Therefore, the generated solutions are not only feasible in all selected scenarios but also robust efficient. That is, the approach guarantees that there exists no other solution which is not worse in all selected scenarios and, is better in at least one scenario. None of the previously proposed methods developed to handle multiple objectives under deep uncertainty, such as many-objective robust decision making (MORDM) framework, can guarantee either robust efficiency or feasibility of the final set of solutions in all selected scenarios. To demonstrate the approach, we use the classic shallow lake problem which is very often used to demonstrate and benchmark methodologic development in decision making under deep uncertainty. Results are also compared to different variants of the MORDM framework.