## 4 Case Study  
The described methodology is applied to two projects with different context and purpose. Project 1: Mountain road in a nature park in the province of Madrid (Spain) and Project 2: New highway under construction in Andalusia (Spain). Validity will be verified by the behavior in the solution to be adopted when there are variations in the weight of criteria, the changes in the compromise solution will be determined using the VIKOR method. And lastly, the results will be compared to the obtained results using the TOPSIS method. A small set of criteria and typologies have been taken into account to show the methodology simply. As alternatives are considered, four typologies included in Table 2: a reinforced concrete wall built in situ, garden wall, green wall reinforced with geotextiles, and riprap wall. These typologies have been selected given that they represent a bigger variety of retaining walls. In the decision-making process, we choose as determining criteria the following: construction cost in \(\text{\text{\text  
Selection criteria are independent. To evaluate the different alternatives concerning the selection criteria, firstly the cost and performance of construction has been determined based on the advice of suppliers, Spanish Ministry of Development [1,44], as well as the advice of designers and contractors who were consulted for this purpose. Next, for the quantitative evaluation of the different alternatives for the qualitative criteria: technical culture and customs and preservation and maintenance necessities, paired comparisons according to the Saaty scale of the AHP method [18,35] are used to determine such a quantitative assessment. In this way, the quantitative assessment of each alternative for each qualitative criterion varies between 0 and 1, with 0 being the lowest value and 1 the highest value for each criterion. The results obtained for each alternative respect to each selection criterion have been included in Table 3. If these results are analyzed, it can be seen that, for example, the alternative of reinforced concrete retaining wall is the one which obtains the lowest valuation concerning the criterion of landscape integration, is the one that is built most frequently and, on the contrary, is the alternative which requires the least conservation and maintenance actions throughout the life cycle. Once the assessment of the alternatives has been determined, the values \(f_{i}\)* and \(f_{i}\)-, being the best and worst values of each criteria function, are calculated according to the VIKOR method. The results are included in Table 4.  
It is important to highlight that the importance of each criterion depends on the location where the retaining wall is going to be constructed. Thus, for each project, and before using the VIKOR and TOPSIS methods, the weight vector is determined, by paired comparisons, and by applying the AHP. So, for project 1, given the environmental factors, when using the AHP method for obtaining the weight vector by paired comparisons, the weight vector is obtained, \(w\) = (0.03; 0.08; 0.54; 0.21; 0.13). It is important to remember that the consistency of the comparison matrix must be identified. After determining the consistency following equation (1), the consistency ratio = 0.094697, which is under 0.1, is obtained. Therefore, the assessments made can be considered as consistent. Then, Equations (2)-(4) are applied to calculate the S\({}_{j}\), \(R_{j}\) and \(Q_{j}\) values. The alternatives classification list will be established according to the values of S, R and Q, to establish the solution or the ensemble of compromise solutions. To carry out the simulation and application of the VIKOR and TOPSIS methods, an algorithm has been developed in the