## 3 Methodology
### Decision Making Using TOPSIS  
Following the generation of the Pareto-optimal solution set via NSGA-II, a systematic decision-making procedure was required to select a representative configuration for practical implementation. While the Pareto front offers a spectrum of trade-offs between total cost and CO\({}_{2}\) emissions, it does not inherently prioritize one solution over another [53]. To address this, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed as a scalar ranking method. TOPSIS is a well-established multi-criteria decision-making (MCDM) algorithm that ranks alternatives based on their geometric proximity to an ideal solution and remoteness from an anti-ideal solution, thereby offering an objective framework for alternative evaluation when multiple performance indicators are present [54]. A decision matrix was constructed using the total unit cost and CO\({}_{2}\)-equivalent emission values of the Pareto-optimal alternatives. These values were normalized using vector normalization, as shown in Equation (19) [32]. \[\tau_{ij}=\frac{x_{ij}}{\sqrt{\sum_{i=1}^{n}x_{ij}^{2}}} \tag{19}\]  
where \(\tau_{ij}\) is the normalized value for alternative iii and criterion j, and \(x_{ij}\) is the original objective value. Subsequently, each normalized objective was assigned an equal weight of 0.5, reflecting an a priori assumption of equal importance in the absence of stakeholder bias. The normalized and weighted matrix was then used to compute the Euclidean distance of each alternative to the ideal solution (Equation (20)), defined as the hypothetical point with the lowest cost and lowest CO\({}_{2}\) value among all Pareto solutions. Similarly, the distance to the anti-ideal solution, representing the highest values of both objectives, was also computed (Equation (21)) [32]. The closeness coefficient for each solution was calculated as the ratio of its distance to the anti-ideal point over the sum of its distances to the ideal and anti-ideal points. This coefficient, bounded between 0 and 1, quantifies how close a solution is to the optimal target configuration, with higher values indicating better performance. \[D_{i}^{+}=\sqrt{\sum_{j=1}^{m}w_{j}^{2}\left(r_{ij}-A_{j}^{+}\right)^{2}} \tag{20}\]  
\[D_{i}^{-}=\sqrt{\sum_{j=1}^{m}w_{j}^{2}\left(r_{ij}-A_{j}^{-}\right)^{2}} \tag{21}\]  
where  
\(D_{i}^{+}\): Distance of alternative i to the ideal solution (lower cost and emission),  
\(D_{i}^{-}\): Distance of alternative i to the anti-ideal solution (higher cost and emission),  
\(w_{j}\): Weight assigned to criterion j,  
\(\tau_{ij}\): Normalized value of criterion j for alternative i,  
\(A_{j}^{+}\): Ideal (best) value for criterion j,  
\(A_{j}^{-}\): Anti-ideal (worst) value for criterion j,  
m: Total number of criteria (here, m = 2; cost and emission). Once the distances are calculated, the closeness coefficient (CC) for each alternative \(i\) is computed as Equation (22) [32]. \[\text{CC}_{\text{i}}=\frac{\text{D}_{\text{i}}^{-}}{\text{D}_{\text{i}}^{+}+\text {D}_{\text{i}}^{-}} \tag{22}\]  
where \(\text{CC}_{\text{i}}\) is the closeness coefficient for alternative i, representing the relative proximity of the alternative to the ideal solution in the normalized objective space. The solution exhibiting the highest closeness coefficient was selected as the recommended operating configuration, as it provided the most balanced compromise between cost efficiency and environmental impact within the feasible design space. In addition to identifying a single optimal point, the ranked list of alternatives generated by TOPSIS was retained to support flexible decision making. This is particularly valuable in infrastructure planning contexts, where external constraints--such as carbon pricing policies, transport accessibility, or regional emission targets--may shift the relative desirability of different trade-offs [55; 56].