# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 7 Conclusions: The Road Ahead  
Interpretable optimization is an emerging field that addresses a crucial gap between mathematical optimization and real-world decision-making. While interpretability has gained significant attention in machine learning, optimization models often remain completely opaque, limiting their adoption and trustworthiness. The ability to understand and justify optimization decisions is essential, particularly in high-stakes applications such as energy planning, healthcare, and resource allocation. Without transparency, stakeholders may struggle to assess the reliability of model outputs, leading to resistance to implementation or unintended biases in decision-making. Ensuring that optimization-driven decisions align with ethical and legal standards is key. Unlike black-box machine learning models, classical optimization inherently possesses a degree of transparency due to its explicit mathematical formulation. However, the link between a model's structure and its final solution is often unclear, necessitating enhancements in interpretability. This paper introduces a framework for interpretable optimization that builds upon the following three key pillars: simplification and surrogate modeling to retain decision-relevant structures, near-optimal solution analysis to provide competitive alternatives, and rationale generation to ensure that solutions are explainable and actionable. Each of these elements contributes to making optimization models not only computationally efficient but also accessible to decision-makers. The first pillar of the framework is simplification and surrogate modeling. One of the major challenges in optimization lies in its complexity. Large-scale problems often require reduction techniques, such as presolving and decomposition, to improve computational feasibility and efficiency. However, these methods can sometimes obscure the original problem structure, reducing interpretability. For example, presolve techniques can distinguish between directly eliminating constraints whose removal does not affect the feasible region of the optimization problem--such as eliminating duplicated constraints--and other techniques that may affect the interpretability of the solutions, such as aggregating several constraints into a single one. Presolve and decomposition techniques can serve as a starting point to derive specific interpretation-driven methods that simplify the problem in a meaningful manner. For instance, the recourse function defined as a function of key variables in Benders' decomposition, the dual multipliers in Lagrangean relaxation, or the subproblems in ADMM all present very interesting potentials that could be exploited in methods tailored for this purpose. In addition, techniques such as sensitivity analysis, the Morris method, and Design of Experiments in general can help prioritize relevant factors, improving the clarity of optimization models while maintaining their decision-making utility. This can also be used as a stepping stone in the development of interpretable surrogates focused on factors that are not only relevant in terms of their impact but also closely linked to the most intuitive variables and parameters of the problem. The second pillar of the framework is near-optimal solution analysis. Techniques such as MGA and MAA provide ways to systematically identify diverse yet effective solutions. Evolutionary and heuristic approaches, as well as landscape fitness analysis, enhance this process by explicitly exploring subobjectives or providing a description of the entire solution space. However, there is a challenge in making these methods scalable for large problems, as well as in defining meaningful diversity among alternatives, ensuring that solutions are not only mathematically distinct but also practically relevant [109]. Future work should focus on integrating near-optimal analysis into standard optimization frameworks to improve usability in real-world decision-making.