A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty

- A framework for multi-objective linear optimisation under uncertainty is proposed.
- The uncertainty and the multiple objectives are modelled as parameters.
- The optimal solution is expressed as explicit functions of the parameters.

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2) problem. Even though, some methods have been proposed for MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2 under uncertainty problem (MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles.