# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 1 Introduction: Interpretability in Machine Learning and Optimization
### Interpretability in Optimization  
In contrast to IML, the paradigm of interpretability has not yet permeated mathematical optimization. The decision-making process remains a black box; once an optimization model is defined and executed, the only output is the optimal solution, sometimes accompanied by sensitivity analyses or dual values. These techniques provide limited insight into the reasoning behind a decision, making it difficult for practitioners to understand the model's logic and assess its reliability [11]. The reality of optimization in practice is somehow deceiving with respect to transparency, as the optimization model itself is transparent; its elements, such as parameters, variables, and equations, are humanly understandable because a human indeed designed them. However, the link between these elements and the solution is not transparent. For example, in planning power transmission networks, we might have an excellent understanding of all the power system dynamics introduced in the model. Still, the resulting plan is entirely detached from its determining factors, i.e., which reinforcements are due to alleviating congestion, which ones support the integration of new renewable generation, or which ones serve to increase robustness. This is crucial information for discussing different solution alternatives. Still, this information is not available from the straightforward resolution of the optimization problem and, as of now, can only be elicited with effort through specific, tailor-made analyses and a significant deal of expert knowledge. The growing complexity of real-world optimization problems exacerbates this challenge. Modern decision-making involves large-scale datasets, uncertain parameters, and evolving constraints, requiring models that are not only computationally robust but also increasingly interpretable. However, this need remains largely unanswered. This means the existing body of work is still relatively small in this context, although it is growing rapidly. We would argue that the realization that the importance of interpretability in the context of optimization is already happening, and this field would greatly benefit from a coherent perspective like the one we present in this paper. Most existing approaches are data-driven [12; 13], leveraging historical data and model outputs to provide insights into the decision-making process. Another key strategy is using counterfactual explanations, which aim to clarify why a particular decision was made by comparing it to alternative scenarios [14; 15]. Most research in this field remains problem-specific, tackling distinct applications rather than providing a broad methodological strategy. Some examples include the study of optimal stopping decisions [16] or project scheduling [17]. Recently, [PERSON] and [PERSON] [18] recognized the issue of missing interpretability as a cause for the low acceptance of optimization results among decision-makers. Theirsolution was to apply the developments of IML by building surrogate models that follow optimization solutions as closely as possible, using the easily interpretable rules of a univariate decision tree. In [19], our own team developed a similar application to a unit commitment problem (an optimization problem in power systems that determines the optimal schedule of generating units over a given time horizon to meet electricity demand at minimal cost, while satisfying operational and system constraints) by building a linear regression tree (see Figure 1) that provided the solution not only in terms of generating power but also by illustrating how additional demand should be distributed among the generators in the case of a marginal increase. Other highly interpretable models applied include optimal policy trees [20] and optimal prescriptive trees [21], which map optimization instances to predefined treatment options, offering a more intuitive representation of decision-making rules.