Multi-scenario multi-objective robust optimization under deep uncertainty: A posteriori approach. (October 2021) - Shavazipour, Babooshka; Kwakkel, Jan H.; Miettinen, Kaisa
Abstract: This paper proposes a novel optimization approach for multi-scenario multi-objective robust decision making, as well as an alternative way for scenario discovery and identifying vulnerable scenarios even before any solution generation. To demonstrate and test the novel approach, we use the classic shallow lake problem. We compare the results obtained with the novel approach to those obtained with previously used approaches. We show that the novel approach guarantees the feasibility and robust efficiency of the produced solutions under all selected scenarios, while decreasing computation cost, addresses the scenario-dependency issues, and enables the decision-makers to explore the trade-off between optimality/feasibility in any selected scenario and robustness across a broader range of scenarios. We also find that the lake problem is ill-suited for reflecting trade-offs in robust performance over the set of scenarios and Pareto optimality in any specific scenario, highlighting the need for novel benchmark problems to properly evaluate novel approaches. Highlights: A novel optimization approach for multi-scenario multi-objective robust decision making (MORDM) is proposed. The concept of scalarizing functions in the robust decision making framework is introduced. Decision makers can explore trade-offs between Pareto optimality in selected scenarios and robustness over scenarios. A novel approach for scenario discovery is proposed to determine vulnerable scenarios before generating any solution. The weakness of the lake problem in reflecting trade-offs between objectives in different scenarios is highlighted.