## 3 Algorithmic Framework
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fuel’s Temp.** & **w\({}_{1}\)/w\({}_{2}\)** & **Diesel\%** & **Biodiesel\%** & **TMFV** & **Cost** & **Density** \\ \hline \multirow{6}{*}{5 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.00\% & 25.00\% & \(-\)0.0771 & 1.6988 & 0.8340 \\  & w\({}_{1}\): 40\%, w\({}_{2}\): 60\% & 74.99\% & 25.01\% & \(-\)0.2267 & 1.6986 & 0.8355 \\  & w\({}_{1}\): 30\%, w\({}_{2}\): 70\% & 74.98\% & 25.02\% & \(-\)0.4167 & 1.6984 & 0.8358 \\  & w\({}_{1}\): 20\%, w\({}_{2}\): 80\% & 74.96\% & 25.04\% & \(-\)0.6378 & 1.6980 & 0.8366 \\  & w\({}_{1}\): 10\%, w\({}_{2}\): 90\% & 74.95\% & 25.05\% & \(-\)0.8451 & 1.6979 & 0.8379 \\ \hline \multirow{6}{*}{10 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.01\% & 24.99\% & \(-\)0.0727 & 1.7379 & 0.8349 \\  & w\({}_{1}\): 40\%, w\({}_{2}\): 60\% & 74.99\% & 25.01\% & \(-\)0.2588 & 1.7222 & 0.8357 \\  & w\({}_{1}\): 30\%, w\({}_{2}\): 70\% & 74.96\% & 25.04\% & \(-\)0.4506 & 1.7234 & 0.8364 \\  & w\({}_{1}\): 20\%, w\({}_{2}\): 80\% & 74.96\% & 25.04\% & \(-\)0.6428 & 1.7056 & 0.8378 \\  & w\({}_{1}\): 10\%, w\({}_{2}\): 90\% & 74.93\% & 25.07\% & \(-\)0.8322 & 1.6993 & 0.8381 \\ \hline \multirow{6}{*}{15 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.00\% & 25.00\% & \(-\)0.0715 & 1.7379 & 0.8356 \\  & w\({}_{1}\): 40\%, w\({}_{2}\): 60\% & 74.98\% & 25.02\% & \(-\)0.2684 & 1.7256 & 0.8361 \\  & w\({}_{1}\): 30\%, w\({}_{2}\): 70\% & 74.97\% & 25.03\% & \(-\)0.4754 & 1.7237 & 0.8369 \\  & w\({}_{1}\): 20\%, w\({}_{2}\): 80\% & 74.94\% & 25.06\% & \(-\)0.6682 & 1.7087 & 0.8380 \\  & w\({}_{1}\): 10\%, w\({}_{2}\): 90\% & 74.92\% & 25.08\% & \(-\)0.8481 & 1.7023 & 0.8384 \\ \hline \multirow{6}{*}{20 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.01\% & 24.99\% & \(-\)0.0704 & 1.7384 & 0.8367 \\  & w\({}_{1}\): 40\%, w\({}_{2}\): 60\% & 74.99\% & 25.01\% & \(-\)0.2791 & 1.7268 & 0.8373 \\ \cline{1-1}  & w\({}_{1}\): 30\%, w\({}_{2}\): 70\% & 74.96\% & 25.04\% & \(-\)0.4984 & 1.7245 & 0.8379 \\ \cline{1-1}  & w\({}_{1}\): 20\%, w\({}_{2}\): 80\% & 74.93\% & 25.07\% & \(-\)0.6709 & 1.7198 & 0.8386 \\ \cline{1-1}  & w\({}_{1}\): 10\%, w\({}_{2}\): 90\% & 74.91\% & 25.09\% & \(-\)0.8687 & 1.7067 & 0.8390 \\ \hline \multirow{6}{*}{25 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.02\% & 24.98\% & \(-\)0.0681 & 1.7386 & 0.8371 \\ \cline{1-1}  & w\({}_{1}\): 40\%, w\({}_{2}\): 60\% & 75.00\% & 25.00\% & \(-\)0.2981 & 1.7269 & 0.8375 \\ \cline{1-1}  & w\({}_{1}\): 30\%, w\({}_{2}\): 70\% & 74.96\% & 25.04\% & \(-\)0.5603 & 1.7258 & 0.8382 \\ \cline{1-1}  & w\({}_{1}\): 20\%, w\({}_{2}\): 80\% & 74.92\% & 25.08\% & \(-\)0.6991 & 1.7212 & 0.8389 \\ \cline{1-1}  & w\({}_{1}\): 10\%, w\({}_{2}\): 90\% & 74.88\% & 25.12\% & \(-\)0.8852 & 1.7112 & 0.8397 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Set 2 experiments for temperatures 5 \({}^{\circ}\)C–25 \({}^{\circ}\)C, Emphasis on Mixtures Density, \(w_{2}\geq 50\%\). Regarding the cost of the mixtures, a set of 1000 independent experiments suggests a minimal mixture cost of 1.7112 EUR/L and a maximal mixture cost of 1.8598 EUR/L. The difference between the lowest and highest costs is 0.1486. Meanwhile, the average cost of the mixtures across all experiments stands at 1.7322 EUR/L, with a standard deviation of 0.0239 (as indicated in Figure 7a). The allocation of Best Cost solutions is presented in Figure 7b. Most of the best solutions, 954 mixtures (954 = 523 + 227 + 132 + 72) or 95.4% are between 1.7112 EUR/L and 1.7963 EUR/L (minimum mixture cost 1.7112 EUR/L). The above results confirm the GA's effectiveness in providing fuel costs close to the minimum value. Based on the best solutions' allocation, only 46 (46 = 34 + 9 + 3) mixtures (4.6%) were between 1.7964 EUR/L and 1.8602 (maximum mixture cost 1.8598 EUR/L). Figure 6: Set 2: (a) TMFV Statistical Analysis and (b) Best TMFV Solutions Allocation.