## 2 Methodology
### Stage 2--Optimization Stage  
After the technology suitable for the required hydrographic survey area has been selected and visually substantiated by the decision tree, multi-criterion optimization is applied. Multicriteria decision making (MCDM) is a procedure that combines the performance of decision alternatives across several contradicting, qualitative, and/or quantitative criteria and yields in a compromise solution [53; 54]. Relevant methods are frequently applicable, implacable, or explicable, in numerous real-life problems. They are widely used where sets of decision alternatives are evaluated against conflicting criteria [54; 55]. The most commonly used multicriteria decision method approach is the weighted sum method (WSM) [56; 57; 58]. Figure 4 shows MCDM and WSM procedures. Figure 4: Working process of multicriteria decision and weighted sum methods. From Figure 4, it can be observed there are three major steps. The first step starts with the construction of a pair-wise comparison matrix \(C=\left(c_{ij}\right)\), type \(\left(\mathrm{nxn}\right)\), between sets of criteria as is shown by Equation (10) [59]:  
\[C=\left[ \begin{array}{cccc}1&c_{12}&\cdots&c_{1n}\\ \frac{1}{c_{12}}&1&\cdots&c_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ \frac{1}{c_{1n}}&\frac{1}{c_{2n}}&\cdots&1\end{array} \right] \tag{10}\]  
where is \(c_{ij}=\frac{1}{c_{ji}},\ i\
eq j\) criteria of positive reciprocal matrix \(C\). Further, the pair-wise comparison matrix between criteria is obtained using [PERSON]'s scale from Table 2, [60; 61; 62]. For quantifying qualitative data, [PERSON] suggested a scale of relative importance, as shown in Table 2. The scale has five degrees of intensity (1, 3, 5, 7, and 9) and four intermediate levels (2, 4, 6, and 8). Thus, a value judgment corresponds to how many times one criterion is more important than another to each of them. Hence, the values used for any given pair of criteria vary from one (1) where they have equal importance to nine (9) where one is enormously more important than the other. Once a comparison matrix has been made, it is necessary to sum the values in each column of the pair-wise matrix, compute each element of the matrix by its column total, and calculate the weight vector by finding the row average as in Equation (11) [60; 63]:  
\[W=\left[ \begin{array}{c}w_{1}\\ w_{2}\\ \vdots\\ w_{n}\end{array} \right]=\left[ \begin{array}{c}\frac{\sum_{j=1}^{n}\frac{c_{ ij}}{\sum_{j=1}^{n}c_{ij}}}{n}\\ \frac{\sum_{j=1}^{n}\frac{c_{2j}}{\sum_{j=1}^{n}c_{2j}}}{n}\\ \vdots\\ \frac{\sum_{j=1}^{n}\frac{c_{nj}}{\sum_{j=1}^{n}c_{nj}}}{n}\end{array} \right] \tag{11}\]  
The weighted sum matrix is found by multiplying the pair-wise comparison matrix and the weight vector. Then, dividing all the elements of the weighted sum matrix by their respective priority vector element, a consistency vector (\(CV\)) is obtained as by Equation (12), [60; 61; 62; 63]:  
\[CV=\left[ \begin{array}{c}\frac{\sum_{j=1}^{n}c_{ij}-\overline{c_{ij}}}{w_{1 }}\\ \frac{\sum_{j=1}^{n}c_{2j}-\overline{c_{2j}}}{w_{2}}\\ \vdots\\ \frac{\sum_{j=1}^{n}c_{nj}+\overline{c_{nj}}}{w_{j}}\end{array} \right] \tag{12}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Intensity of Importance** & **Technology** \\ \hline
1 & Same importance \\
2 & Intermediate values \\
3 & Relatively more important \\
4 & Intermediate values \\
5 & Some more important \\
6 & Intermediate values \\
7 & Very more important \\
8 & Intermediate values \\
9 & Enormously important \\ \hline \hline \end{tabular}
\end{table} 
Table 2: [PERSON]’s scale of relative importance. Step 1 ends with performing the consistency index (\(CI\)) and consistency ration (\(CR\)). CI measures the degree of inconsistency, as is shown by Equation (13) [60; 61; 62; 63]:  
\[CI=\frac{\lambda_{max}-n}{n-1} \tag{13}\]  
where \(n\) is matrix size and \(\lambda_{max}\) is the largest principal eigenvalue of the positive reciprocal pair-wise comparison matrix.