# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 1 Introduction: Interpretability in Machine Learning and Optimization
### Interpretability in Optimization
Another recent advancement was described by [PERSON] and [PERSON] [18]; their surrogate framework was extended to incorporate \"feature-based descriptions\" of both problem instances and solutions. Their concept of feature and meta-solution will be explored in depth when we address near-optimal solutions. Other methodological precedents of interpretable optimization--albeit indirect--will be discussed in detail in this article, including presolve methods in linear and mixed-integer programming, which identify the elements of a problem that do not impact the solution but focus on reducing computational burden rather than enhancing human understanding [22]. Another line of research that will be reviewed concerns scenario analysis and sensitivity studies, which provide insights into how solutions change under different conditions. Still, they do not explain why a specific decision is reached in the first place [23]. The motivation for this article is to propose a framework--drawing inspiration from all the techniques developed for IML--that advances the work towards increasing interpretability in mathematical optimization, a topic that has been overlooked until now. The lack of interpretability of results provided by traditional mathematical optimization models hinders their applicability in real-life problems, where the stakes are high and a clear understanding of the constraints and trade-offs among alternative solutions is needed. To bridge the gap that still exists when applying optimization to decision problems, this paper introduces the concept of interpretable optimization. Interpretable optimization is a framework that draws concepts from IML but advances its conceptualization in the following three different dimensions or pillars, which are necessary to deepen our understanding of solutions: (1) problem simplification and surrogate building; (2) near-optimal solution analysis and fitness landscape analysis; and (3) rationale generation. Instead  
Figure 1: Commitment variable explained as a function of the scenario; fragment taken from [19]. of treating optimization purely as a computational tool, this approach aims to make its outcomes more comprehensible and actionable for decision-makers. This paper presents a literature review that encompasses the most relevant methods and techniques related to interpretable optimization. While our review provides a broad view of these techniques classified under our proposed conceptualization, it is, by necessity, nonsystematic; interpretable optimization is not an established term but rather introduced by us, as are its dimensions. This also means that there is no specific term or keyword that the reviewed works satisfy, but rather an aim; therefore, we believe this effort, which highlights our experience with methods and techniques, can be extremely valuable for the reader. Hence, simply explained, there are two inclusion criteria. First, they should be relevant to the field of classical optimization. For instance, explainable machine learning techniques are excluded from our review for this reason. Secondly, they should have some potential in terms of improving the interpretability of optimization results. This implies that either they help simplify a problem, potentially leading to a simpler-to-interpret one, or they provide results to an optimization problem that can be interpreted, or they assist in interpreting the results that other methods provide. This paper is organized as follows: Section 2 introduces the concept of interpretable optimization, outlining its necessity and potential benefits. It defines interpretability in the optimization context and discusses its fundamental differences from explainability. Section 3 explores problem reduction and surrogate model building, detailing techniques such as constraint aggregation, presolving, decomposition, and factor reduction. These methods aim to simplify optimization problems while preserving decision-relevant structures, enhancing computational efficiency and human interpretability.