The robust decision-making framework (RDM) has been extended to consider multiple objective functions and scenarios. However, the practical applications of these extensions are mostly limited to academic case studies. The main reasons are: (i) substantial cognitive load in tracking all the trade-offs across scenarios and the interplay between uncertainties and trade-offs, (ii) lack of decision-makers’ involvement in solution generation and confidence. To address these problems, this study proposes a novel interactive framework involving decision-makers in searching for the most preferred robust solutions utilizing interactive multiobjective optimization methods. The proposed interactive framework provides a learning phase for decision-makers to discover the problem characteristics, the feasibility of their preferences, and how uncertainty may affect the outcomes of a decision. This involvement and learning allow them to control and direct the multiobjective search during the solution generation process, boosting their confidence and assurance in implementing the identified robust solutions in practice.

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.