## 3 Algorithmic Framework
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fuel’s Temp.** & \(\mathbf{w_{1}/w_{2}}\) & **Diesel\%** & **Biodiesel\%** & **TMFV** & **Cost** & **Density** \\ \hline \multirow{8}{*}{5 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.00\% & 25.00\% & \(-\)0.0771 & 1.6988 & 0.8340 \\  & w\({}_{1}\): 60\%, w\({}_{2}\): 40\% & 75.00\% & 25.00\% & 0.1104 & 1.6985 & 0.8351 \\  & w\({}_{1}\): 70\%, w\({}_{2}\): 30\% & 74.98\% & 25.02\% & 0.2856 & 1.6978 & 0.8359 \\  & w\({}_{1}\): 80\%, w\({}_{2}\): 20\% & 74.97\% & 25.03\% & 0.4878 & 1.6978 & 0.8364 \\  & w\({}_{1}\): 90\%, w\({}_{2}\): 10\% & 74.95\% & 25.05\% & 0.6322 & 1.6976 & 0.8378 \\ \hline \multirow{8}{*}{10 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.01\% & 24.99\% & \(-\)0.0727 & 1.7377 & 0.8349 \\  & w\({}_{1}\): 60\%, w\({}_{2}\): 40\% & 74.99\% & 25.01\% & 0.1134 & 1.7211 & 0.8355 \\  & w\({}_{1}\): 70\%, w\({}_{2}\): 30\% & 74.97\% & 25.03\% & 0.2987 & 1.7200 & 0.8363 \\  & w\({}_{1}\): 80\%, w\({}_{2}\): 20\% & 74.95\% & 25.05\% & 0.4881 & 1.6993 & 0.8376 \\  & w\({}_{1}\): 90\%, w\({}_{2}\): 10\% & 74.93\% & 25.07\% & 0.6781 & 1.6987 & 0.8379 \\ \hline \multirow{8}{*}{15 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.00\% & 25.00\% & \(-\)0.0715 & 1.7379 & 0.8356 \\  & w\({}_{1}\): 60\%, w\({}_{2}\): 40\% & 74.98\% & 25.02\% & 0.1154 & 1.7216 & 0.8359 \\ \cline{1-1}  & w\({}_{1}\): 70\%, w\({}_{2}\): 30\% & 74.96\% & 25.04\% & 0.2996 & 1.7222 & 0.8368 \\ \cline{1-1}  & w\({}_{1}\): 80\%, w\({}_{2}\): 20\% & 74.95\% & 25.05\% & 0.4897 & 1.7077 & 0.8379 \\ \cline{1-1}  & w\({}_{1}\): 90\%, w\({}_{2}\): 10\% & 74.93\% & 25.07\% & 0.6792 & 1.6991 & 0.8382 \\ \hline \multirow{8}{*}{20 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.01\% & 24.99\% & \(-\)0.0704 & 1.7382 & 0.8367 \\  & w\({}_{1}\): 60\%, w\({}_{2}\): 40\% & 74.98\% & 25.02\% & 0.1155 & 1.7245 & 0.8371 \\ \cline{1-1}  & w\({}_{1}\): 70\%, w\({}_{2}\): 30\% & 74.97\% & 25.03\% & 0.3011 & 1.7233 & 0.8377 \\ \cline{1-1}  & w\({}_{1}\): 80\%, w\({}_{2}\): 20\% & 74.92\% & 25.08\% & 0.4954 & 1.7188 & 0.8385 \\ \cline{1-1}  & w\({}_{1}\): 90\%, w\({}_{2}\): 10\% & 74.91\% & 25.09\% & 0.6808 & 1.6995 & 0.8389 \\ \hline \multirow{8}{*}{25 \({}^{\circ}\)C} & w\({}_{1}\): 50\%, w\({}_{2}\): 50\% & 75.02\% & 24.98\% & \(-\)0.0681 & 1.7386 & 0.8371 \\ \cline{1-1}  & w\({}_{1}\): 60\%, w\({}_{2}\): 40\% & 75.01\% & 24.99\% & 0.1176 & 1.7248 & 0.8373 \\ \cline{1-1}  & w\({}_{1}\): 70\%, w\({}_{2}\): 30\% & 74.95\% & 25.05\% & 0.3225 & 1.7254 & 0.8379 \\ \cline{1-1}  & w\({}_{1}\): 80\%, w\({}_{2}\): 20\% & 74.91\% & 25.09\% & 0.5238 & 1.7195 & 0.8388 \\ \cline{1-1}  & w\({}_{1}\): 90\%, w\({}_{2}\): 10\% & 74.89\% & 25.11\% & 0.7007 & 1.6999 & 0.8395 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Set 1 experiments for temperatures 5 \({}^{\circ}\)C–25 \({}^{\circ}\)C, Emphasis on Mixtures Cost, \(w_{1}\geq 50\%\). Figure 4: Set 1: (**a**) Cost Statistical Analysis and (**b**) Best Cost Solutions Allocation. Figure 3: Set 1: (**a**) TMFV Statistical Analysis and (**b**) Best TMFV Solutions Allocation. In terms of mixtures' density, a series of 1000 independent experiments indicate a minimum mixture density of 0.8378 g/mL and a maximum mixture density of 0.8537 g/mL. The difference between the minimum and maximum densities is 0.0159. The average mixture density across all experiments is 0.8390 g/mL, with a standard deviation of 0.0047 (as shown in Figure 5a). The allocation of Best Density solutions is presented in Figure 5b. Most best solutions, 881 mixtures (881 = 452 + 234 + 121 + 74) or 88.1% is between 0.8378 g/mL and 0.8461 g/mL (minimum mixture density 0.8378 EUR/L), compared to the total 119 (344 = 59 + 34 + 22 + 4) mixtures or 11.9%, which were between 0.8462 g/mL and 0.8545 g/mL (maximum mixture density 0.8537 g/mL).