Multi-objective optimisation under deep uncertainty

This paper presents a scenario-based Multi-Objective structure to handle decision problems under deep uncertainty. Most of the decisions in real-life problems need to be made in the absence of complete knowledge about the consequences of the decision and/or are characterised by uncertainties about the future which is unpredictable. These uncertainties are almost impossible to reduce by gathering more information and are not statistical in nature. Therefore, classical probability-based approaches, such as stochastic programming, do not address these problems; as they require a correctly-defined complete sample space, strong assumptions (e.g. normality), or both. The proposed method extends the concept of two-stage stochastic programming with recourse to address the capability of dealing with deep uncertainty through the use of scenario planning rather than statistical expectation. In this research, scenarios are used as a dimension of preference to avoid problems relating to the assessment and use of probabilities under deep uncertainty. Such scenario-based thinking involved a multi-objective representation of performance under different future conditions as an alternative to expectation. To the best of our knowledge, this is the first attempt of performing a multi-criteria evaluation under deep uncertainty through a structured optimisation model. The proposed structure replacing probabilities (in dynamic systems with deep uncertainties) by aspirations within a goal programming structure. In fact, this paper also proposes an extension of the goal programming paradigm to deal with deep uncertainty. Furthermore, we will explain how this structure can be modelled, implemented, and solved by Goal Programming using some simple, but not trivial, examples. Further discussion and comparisons with some popular existing methods will also provided to highlight the superiorities of the proposed structure.