# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 2 What Is Interpretable Optimization?
### The Pillars of Interpretability in Optimization  
Our approach goes beyond these metrics by proposing several pillars or dimensions where interpretability metrics can be subsequently applied. We have identified three such pillars, which are shown in Figure 2 and will be reviewed in the remaining sections of this article.  
The first pillar--simplification and surrogate model building--involves identifying the key variables, constraints, and relationships among them that define an optimization problem, while preserving its structural integrity. Traditional problem simplification techniques have aimed to improve computational efficiency by removing superfluous constraints and extraneous variables without explicitly considering interpretability. In contrast, interpretable optimization seeks to create simplifications that maintain decision-relevant information while making models easier to understand, even if some accuracy is lost in the process. These interpretable surrogates will serve as a complement to the initial problem rather than as a substitute, where the most important elements of the formulation, as well as their relationships, are extracted and presented. This means that, in the case of classical optimization, the formulation of the problem serves as the gold-standard definition of the decision, and every aspect highlighted in the surrogate model will be linked back to this original formulation.  
The second pillar--near-optimal solution analysis--focuses on mapping the landscape of acceptable solutions, providing decision-makers with alternatives that are almost as good as the optimal solution. Many real-world optimization problems exhibit degeneracy, meaning multiple solutions yield similar objective values but with different trade-offs. Traditional optimization frameworks often emphasize finding a single optimal solution, overlooking the broader decision space. Metaheuristics, on the other hand, have been more cautious about the issues surrounding near-optimal solutions and have often made a point of returning not only one but a set of attractive alternatives. By analyzing near-optimal  
Figure 2: The three pillars of interpretable optimization.  
alternatives, interpretable optimization enables decision-makers to choose solutions that align with contextual priorities, constraints, and stakeholder preferences. In addition, the analysis of near-optimal solutions involves creating a perspective on the fitness landscape of the problem, which will inevitably be linked to the structure of solutions.  
The third pillar--Rationale generation--addresses the fundamental challenge of explaining optimization outcomes. Instead of presenting an optimal decision as a purely mathematical result, interpretable optimization seeks to generate formal explanations for why a particular solution was selected. This involves linking decision variables to constraints and objectives, identifying causal relationships, and clearly articulating trade-offs. While methods such as dual variables and shadow prices provide limited insights on which resources are valuable and the general effect of constraints, interpretable optimization should aim to develop more comprehensive explanatory frameworks that improve trust and facilitate better decision-making, including generating rationales in natural language, which are easily understandable not only by modeling experts but also by stakeholders.  
The remainder of this paper is devoted to presenting the initial work that has emerged in these three pillars. Then, we discuss real-world applications and future research directions, demonstrating the potential impact of interpretable optimization across various domains.