A novel multi-stage multi-scenario multi-objective optimisation framework for adaptive robust decision-making under deep uncertainty

Many real-world decision-making problems involve multiple decision-making stages and various objectives. Besides, most decisions need to be made before having complete knowledge about all aspects of the problem, leaving some sort of uncertainty. Deep uncertainty happens when the degree of uncertainty is so high that the probability distributions are not confidently knowable. In this situation, using wrong probability distributions leads to failure. Scenarios, instead, should be used to evaluate the consequences of any decisions in different plausible futures and find a robust solution. In this study, we proposed a novel multi-stage multi-scenario multi-objective optimisation framework for adaptive/dynamic robust decision-making under deep uncertainty using a more flexible definition of robustness by incorporating the risk attitude of the decision-makers. In this definition, a robust decision is one that performs relatively well (acceptable) in a broad range of scenarios. Two approaches, named multi-stage multi-scenario multi-objective and two-stage moving horizon, have been proposed and compared. Finally, the proposed approaches are applied in a case study of sequential portfolio selection under deep uncertainty, and the robustness of their solutions is discussed. • Propose a novel adaptive multi-stage robust multi-objective optimisation framework. • Expand the min–max robustness definition, incorporating the planner’s risk attitudes. • The proposed framework generates less-conservative, adaptable, robust decisions. • Propose a moving horizon approach for optimisation-based monitoring and adaptation. • A sequential portfolio selection case study under deep uncertainty is considered.