# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 4 Analysis of Near-Optimal Solutions
### A Need to Integrate Optimization  
Finding near-optimal solutions involves several significant challenges that must be carefully addressed to enhance their practical value in decision-making. One of the foremost difficulties lies in defining meaningful diversity [109]. Merely identifying different solutions is not enough; decision-makers require alternatives that vary significantly in terms of constraints, decision variables, and trade-offs. While techniques like MGA have been designed to enforce structural diversity, their integration into standard optimization frameworks--in a way that exploits problem structure rather than blindly solving multiple problem instances--remains an ongoing research endeavor [84].  
Another major hurdle is the effective visualization and interpretation of near-optimal solutions. Decision-makers often struggle to extract actionable insights from large sets of solutions, particularly when trade-offs are complex and multidimensional. To enhance interpretability, decision maps, heatmaps, and clustering-based categorization can provide more intuitive representations of alternative solutions [110]. However, despite their potential, these tools must be further refined to ensure usability across a broad range of applications.  
One particular issue is that the QOAs should be expressed in terms that experts would understand, which some authors have referred to as \"meta-solutions\" [18]. The automatic definition of these meta-solutions as a function of their features is a challenge, as it is usually assumed that it is only through experts that this definition can be found.  
The next section introduces the advances made in generating solution rationales, corresponding to the third pillar of the proposed framework, and builds on the previous developments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Strengths** & **Weaknesses** \\ \hline Sensitivity Analysis & It is available in most solvers, and therefore its application is straightforward [96; 97]. & It only evaluates the feasible region close to the optimal solution and offers limited performance if the problem is not linear [98]. \\ Revised Simplex Method (with perturbation) & It is computationally efficient [99]. & Its main usefulness relies on LP problems [100]. \\ Modeling to Generate Alternatives (MGA) & It maintains a balance between exploring the feasible region to generate near-optimal solutions and the computational burden [101]. & It may be computationally intense, and it does not guarantee a thorough exploration of each near-optimal zone of the feasible region [102; 103]. \\ K-optimal Solution Algorithms & It facilitates the decision-making process by providing solutions in a structured way [104]. & It may be difficult to apply to large-scale problems if the parameter k is very large because it requires executing the model k times [104]. \\  & It performs an exhaustive evaluation of the feasible region and is guaranteed to find all near-optimal solutions closer than a specified threshold [86]. & It is very computationally intense [86]. \\ Evolutionary Multi-Objective Optimization (EMO) & It is particularly well suited for multiobjective problems and can deal with nonlinearities [105; 106]. & It may need expert tuning of parameters, and there is no guarantee of optimality [107]. \\ Fitness Landscape Analysis (FLA) & It helps us understand features of complicated problems [108]. & It has seen minimal use in multiobjective problems so far [108]. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of near-optimal solutions analysis methods.