# Interpretable Optimization: Why and How We Should Explain Optimization Models
## 3 Problem Reduction and Surrogate Model Building
### Experimental Design and Factor Reduction
Sequential analysis [66] structures experiments sequentially to avoid sampling where more information is not required. This is extremely useful when experiments are expensive, as it allows for the flexible introduction of new information as more problem features are discovered. Complementarily, if the problem structure is known, optimal design [67] allows parameters to be estimated without bias and with minimum variance. A non-optimal design requires more experimental runs, leading to higher computational costs. Table 2 shows a comparison among the methods described in this subsection, highlighting their main strengths and weaknesses, as well as pointing out problems where they are particularly well suited. The [PERSON] method, Taguchi method, sequential analysis, and optimal design represent distinct strategies within experimental design and analysis, each tailored to different goals and contexts. The Morris method is a GSA technique ideal for computational models with many input variables, primarily used for early-stage screening to identify influential factors. In contrast, the Taguchi method focuses on improving process robustness and reducing variation by using orthogonal arrays and maximizing signal-to-noise ratios, mak \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Morris Method** & **Taguchi Method** & **Sequential Analysis** & **Optimal Design** \\ \hline \multirow{4}{*}{**Strengths**} & Simple to implement and computationally efficient [68; 69] & Robust to noise factors and requires a reduced number of experiments [70] & It is an adaptive method where experiments are based on previous results and it uses resources [67; 66] \\  & Mostly qualitative and results may be unstable if there are strong nonlinearities [56; 57] & Less suited for complex iterations [72; 73] & It requires ongoing analyses and it is sensitive to initial sampling biases [74] & It requires accurate model hypotheses [75] \\  & Identification of key variables at an early stage & Problems where robustness is important & Reduce number of experiments when problem features are unclear & Reduce number of experiments when problems are clear \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of [PERSON] method, [PERSON] method, sequential analysis and optimal design. ing it well suited for quality engineering in industrial settings. Sequential analysis differs fundamentally as it enables data-driven decisions during experimentation, allowing trials to be stopped early based on accumulated evidence--an approach particularly valuable in clinical trials. Finally, optimal design methods, such as D-optimal or A-optimal designs, aim to maximize the statistical efficiency of parameter estimation by strategically selecting design points based on model structure. While all four methods serve experimental purposes, they vary significantly in statistical rigor, adaptability, and application domains--from qualitative screening and robust quality control to dynamic decision-making and precision modeling. While these techniques have been widely adopted in statistical modeling, their application to mathematical optimization remains underexplored. The challenge is to adapt these principles to identify decision-relevant variables and constraints, ensuring that the simplified model remains faithful to the original problem's structure. To address these challenges, there is a need for simplification and surrogate model methods that explicitly preserve decision-relevant structures rather than solely focusing on computational efficiency.