## 3 Algorithmic Framework
### Experimental Results  
Initially, the suggested GA approach was applied to Set 1, involving 25,000 individual simulations per temperature (ranging between 5 and 25 \({}^{\circ}\)C) and weight combinations (w\({}_{1}\) and w\({}_{2}\)). This process spanned a duration of 3925.80 s (equivalent to approximately 65.43 min or approximately 1.09 h). Table 4 presents these experimental results from temperatures 5 \({}^{\circ}\)C to 25 \({}^{\circ}\)C, with columns information: w\({}_{1}\) and w\({}_{2}\) weights combination, diesel ingredient percentage in the mixture, biodiesel ingredient percentage in the mixture, evaluation function value of mixture, mixture cost, and mixture density. Weights w\({}_{1}\) and w\({}_{2}\) always sum up to 100% and w\({}_{1}\geq\) 50% due to the Emphasis on Cost criterion. Diesel ingredient percentage ranges between 74.89% and 75.02%, while biodiesel ingredient percentage amounts to 24.98-25.11%. Evaluation Function values stand from \(-\)0.0771 to 0.7007. A positive evaluation function value provides more influence on the cost criterion than the density criterion. On the other hand, a negative evaluation function value emphasizes the density criterion than the cost criterion. The Evaluation Function values in all groups are positive, except for w\({}_{1}\) = 50% and w\({}_{2}\) = 50%, which is negative but close to 0 value, which, as a result, provides a neutral criterion assessment. All the other groups offer clear priority to the cost criterion. Regarding cost criterion values, the new fuel mixtures cost between 1.6976 EUR/L and 1.7386 EUR/L. The last information concerns density criterion values that range from 0.8340 g/mL-0.8395 g/mL, satisfying the ASTM D1298-99 limits: 0.8200 g/mL-0.8450 g/mL. Each row in Table 4 provides details regarding the best mixture determined from 1000 independent simulations (totaling 25 optimal mixtures). The evaluation is centered around the minimum Total Mixture Function Value (TMFV). As the weight of w\({}_{1}\) increases, the TMFV value increases as well, signifying a greater emphasis on the cost criterion over the density criterion. There are slight variations in the percentages of ingredients, cost, and density among the optimal mixtures, as mentioned previously. Each experiment suggests an optimal solution--a biodiesel mixture (determined by temperature along with w\({}_{1}\) and w\({}_{2}\)). The lowest TMFV value was achieved in Set 1 at a temperature of 5 \({}^{\circ}\)C with w\({}_{1}\) = 50% and w\({}_{2}\) = 50%. A statistical analysis of the optimal solution in Set 1 follows. Set 1 (temperature 5 \({}^{\circ}\)C, w\({}_{1}\) = 90%, w\({}_{2}\) = 10%) Optimal Mixture:  
* Diesel percentage: 74.95% \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fuel’s Temperature** & **Min\%** & **Max\%** & **Cost EUR/L** & **Density g/mL** \\ \hline Diesel 5 \({}^{\circ}\)C & 1 & 99 & 2.0000 & 0.8191 \\ \hline Biodiesel 5 \({}^{\circ}\)C & 1 & 30 & 0.8091 & 0.8915 \\ \hline Diesel 10 \({}^{\circ}\)C & 1 & 99 & 2.0000 & 0.8206 \\ \hline Biodiesel 10 \({}^{\circ}\)C & 1 & 30 & 0.8091 & 0.8848 \\ \hline Diesel 15 \({}^{\circ}\)C & 1 & 99 & 2.0000 & 0.8220 \\ \hline Biodiesel 15 \({}^{\circ}\)C & 1 & 30 & 0.8091 & 0.8823 \\ \hline Diesel 20 \({}^{\circ}\)C & 1 & 99 & 2.0000 & 0.8234 \\ \hline Biodiesel 20 \({}^{\circ}\)C & 1 & 30 & 0.8091 & 0.8819 \\ \hline Diesel 25 \({}^{\circ}\)C & 1 & 99 & 2.0000 & 0.8249 \\ \hline Biodiesel 25 \({}^{\circ}\)C & 1 & 30 & 0.8091 & 0.8808 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Min and Max relative mixture composition (%), ingredient Cost and Density. In a series of 1000 separate trials, the lowest Total Mixture Function Value (TMFV) recorded was 0.6322, while the highest TMFV reached was 0.6587. The difference between the minimum and maximum TMFV values is 0.0265. Meanwhile, the average TMFV across all trials stands at 0.6432, with a standard deviation of 0.0051 (refer to Figure 3a).