Rigorous analysis of Pareto fronts in sustainability studies based on bilevel optimization: Application to the redesign of the UK electricity mix
Abstract Multi objective optimization (MOO) is at present widely used in the design and planning of sustainable systems where economic, environmental and social aspects must be considered simultaneously. The solution of a multi objective model is given by a set of Pareto optimal points that feature the property that they cannot be improved in one objective without necessarily worsening at least another one. Identifying the best Pareto solution from this set is challenging, particularly when many objectives and decision makers are involved in the analysis. In this work, we propose the first rigorous method (to the authors' knowledge) based on bilevel optimization to explore Pareto points that allows to: (i) identify in a systematic manner non dominated solutions which are particularly appealing for decision makers; (ii) quantify the distance between any (suboptimal) feasible point of a MOO model and its Pareto front (i.e. project suboptimal points onto the Pareto frontier) and (iii) establish improvement targets for suboptimal solutions of a MOO (through projection onto the Pareto front) that if attained would make them optimal. Overall, our method allows analysing Pareto fronts and selecting a final Pareto point to be implemented in practice without the need to define subjective weights in an explicit manner. We illustrate the capabilities of our approach through its application to the optimization of the UK electricity mix according to several economic, environmental and social indicators.