📝 SummarXiv

Abstract

Optimization models are fundamental tools for providing quantitative insights to decision-makers. However, models, objectives, and constraints do not capture all real-world factors accurately. Thus, instead of the single optimal solution, real-world stakeholders are often interested in the near-optimal space -- solutions that lie within a specified margin of the optimal objective value. Solutions in the near-optimal space can then be assessed regarding desirable non-modeled or qualitative aspects. The near-optimal space is usually explored by so-called Modelling to Generate Alternatives (MGA) methods. However, current MGA approaches mainly employ heuristics, which do not measure or guarantee convergence. We propose a method called ORACLE, which guarantees generation and exploration on the \emph{entire near-optimal} space by exploiting convexity. ORACLE iteratively approximates the near-optimal space by introducing a metric that both measures convergence and suggests exploration directions. Once the approximations are refined to a desired tolerance, any near-optimal designs can be generated with negligible computational effort. We compare our approach with existing methods on a sector-coupled energy system model of Switzerland. ORACLE is the only method able to guarantee convergence within a desired tolerance. Additionally, we show that heuristic MGA methods miss large areas of the near-optimal space, potentially skewing decision-making by leaving viable options for the energy transition off the table.