## 3 Methodology
### MCDM Methods  
A methodology for resolving the problem has been set out, combining two multiple-criteria decision-making methods, the analytic hierarchy process (AHP) and the VIKOR methods. The obtained selection will be compared with the one resulting when applying the TOPSIS method in substitution of the VIKOR method. Both methods are focused on trying to find the solution that is closest to the optimal solution but with a different process of evaluation [21]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Criteria** & **Type of Criterion** & **Relevance** \\ \hline External requirements & Retaining wall dimensions & Quantitative & High \\ External requirements & Space available & Quantitative & High \\ External requirements & Traffic restrictions & Qualitative & Medium \\ External requirements & Influence on public services & Qualitative & High \\ External requirements & Space available in the base of the wall & Quantitative & Medium \\ External requirements & Permissible settlement & Quantitative & High \\ External requirements & On-site overloading & Quantitative & High \\ External requirements & Seismicity & Quantitative & High \\ External requirements & Permeability & Quantitative & Medium \\ External requirements & Aesthetic appearance & Qualitative & Low \\ External requirements & Technical culture and customs & Qualitative & Medium \\ Environmental & Noise and vibration during construction & Quantitative & Medium \\ Environmental & Construction and demolition residues & Quantitative & High \\ Environmental & Landscape integration & Qualitative & High \\ Environmental & Energy use and greenhouse gas emissions (life & Quantitative & High \\  & cycle) & Quantitative & High \\ Construction requirements & Construction performance & Quantitative & High \\ Construction requirements & Elements inside the ground: round stones, gravel, & Qualitative & Low \\ Construction requirements & Surface disturbances & Qualitative & Low \\ Construction requirements & Machinery and specialized equipment & Qualitative & High \\ Construction requirements & Spaces for material storage & Quantitative & Medium \\ Construction requirements & Material availability & Quantitative & Medium \\ Characteristics of the soil natural & Density of the retained material & Quantitative & Medium \\ Characteristics of the soil natural & Interstitial water pressure & Quantitative & Medium \\ Characteristics of the soil natural & Soil resistance (internal angle of friction) & Quantitative & High \\ Economic criteria & Construction cost & Quantitative & High \\ Economic criteria & Preservation and maintenance necessities & Quantitative/Qualitative & High \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selection criteria. Source: the authors’ own research. Figure 1: Steps or stages of the decision-making process. By the analytic hierarchy process (AHP), the weight eigenvector is calculated for the criteria that determine which is the most ideal solution, by making a paired comparison of them for each project [34]. It must be taken into account that the weight eigenvector is not the same for each project, since certain criteria may have bigger importance in comparison to the others, depending on the characteristics of the project. We must remember that AHP measures the global inconsistency of the views by the consistency ratio (CR), calculated by dividing the consistency index (\(CI\)) and the random index (RI), and it should be of less than 10%. The consistency index measures the consistency of the comparison matrix [18]. \[CI=\ \frac{\lambda_{max}-n}{n-1} \tag{1}\]  
where \(\lambda_{max}\) is the biggest value of the transposed matrix of the paired comparison matrix, and n is the matrix range. The RI is an index which measures the consistency of a random matrix [18; 35]. On the other hand, through paired comparisons we can establish the \"behavior\" of each alternative for each of the qualitative criteria that are part of the making-decision processes, to obtain a quantitative assessment for qualitative criteria.