## 4 Methods
### Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA) Method  
MOORA is a strategy employed for the optimization of two or more conflicting qualities (objectives) at the same time, based on certain constraints. Multi-objective optimization challenges include maximizing profit while limiting product cost, optimizing vehicle performance while minimizing fuel consumption, and reducing weight thereby increasing a certain technical component strength [44]. The MOORA technique, proposed by [PERSON] [44], offers a multi-objective optimization methodology that is used to handle a variety of complicated decision-making challenges related to manufacturing. While ranking or selecting alternatives from a set of available options, the MOORA technique analyses both beneficial and non-beneficial criteria. The MOORA technique starts with the development of a decision matrix that compares the efficiency of several options in terms of numerous attributes (objectives). As a result, the MOORA approach can be efficiently used as a tool for rating and selecting alternatives from a large number of available options. **Step 1. ** Create a decision-making matrix including all of the available information related to the attributes. A Matrix \(A_{m\times n}\) is used to represent the given data, as illustrated in the equation below. \[A=\left[a_{ij}\right]_{m\times n}=\left[ \begin{array}{cccc}a_{11}&a_{12}& \ldots&a_{1n}\\ a_{21}&a_{22}&\ldots&a_{2n}\\ \ddots&\ddots&\ddots&\ddots\\ a_{m1}&a_{m2}&\ldots&a_{mm}\end{array} \right] \tag{20}\]  
Here, \(a_{ij}\) indicates the performance or effectiveness of the \(i\)th option associated with the \(j\)th attribute, m represents the count of alternatives present, and \(n\) represents the count of attributes. The performance of each option on an attribute is then matched with a numerator that reflects all of the alternatives in regard to that attribute, resulting in a ratio system. **Step 2. ** Normalize the decision matrix  
According to [PERSON] et al. [45], the square root of the sum of the squares of each alternative per attribute would be the best option for this denominator. It is expressed as follows:  
\[a_{ij}^{*}=\frac{a_{ij}}{\sqrt{\left[\sum\limits_{i=1}^{m}x_{ij}^{2}\right]}}j =1,2,...,n \tag{21}\]  
where \(a_{ij}^{*}\) refers to the normalized performance of the \(i\)th alternative based on the \(j\)th attribute. Here, \(a_{ij}^{*}\) is a dimensionless number lying in the range [0, 1]. **Step 3. ** Optimize the attributes and find the normalized assessment value  
These normalized performances are summed up during maximization for the beneficial attributes and subtracted during minimization in multi-objective optimization for the non-beneficial attributes. As a result, the normalized assessment value (\(NA_{i}\)) is determined as follows:  
\[NA_{i}=\sum\limits_{j=1}^{h}a_{ij}^{*}-\sum\limits_{j=h+1}^{n}a_{ij}^{*} \tag{22}\]  
Here, \(h\) represents the attributes to be maximized, (\(n\)-\(h\)) denotes the attributes that are to be minimized, and \(NA_{i}\) indicates the normalized assessment value that is related to the \(i\)th alternative across the attributes. In numerous situations, it is quite common to find that some attributes seem to be more important than others. The weight of an attribute (significance coefficient) is multiplied by its corresponding weight (significance coefficient)to give it additional prominence [46]. When the weights of these attributes are considered, the equation looks like this:  
\[NA_{i}=\sum_{j=1}^{h}w_{j}a_{ij}^{*}-\sum_{j=h+1}^{n}w_{j}a_{ij}^{*} \tag{23}\]  
where, \(w_{j}\) is the \(j\)th attribute's weight, which is calculated by applying the AHP or the entropy approach. **Step 4. ** Rank the alternatives, depending on normalized assessment values  
The \(NA_{i}\) value might be positive or negative, based on the sum of the decision matrix's maxima that includes the beneficial attributes and the minimum value including the non-beneficial attributes. The final preference is shown by an ordinal ranking of \(NA_{i}\).