## 3 Algorithmic Framework
* Mutation operator prevents the GA from a premature convergence in a semi-optimal solution of moderate-quality fuel. In summary, all GA parameters were carefully selected following thorough experimentation and the evaluation of over 100,000 simulations. Their efficacy remains on par with contemporary methods, yielding superior outcomes. ### GA--Chromosome Representation  
The effectiveness of the proposed GA methodology was assessed through two distinct sets of experiments categorized by mixture temperature: 5 \({}^{\circ}\)C, 10 \({}^{\circ}\)C, 15 \({}^{\circ}\)C, 20 \({}^{\circ}\)C, and 25 \({}^{\circ}\)C (referred to as sets henceforth):  
(a) Set 1--Focused on Cost:  
Within Evaluation Function TMFV, the weight value w\({}_{1}\) exceeds or equals 50%, denoted as w\({}_{1}\)\(\geq\) 50% (Table 2). (b) Set 2--Focused on Density:  
Within Evaluation Function TMFV, the weight value w\({}_{2}\) surpasses or equals 50%, denoted as w\({}_{2}\)\(\geq\) 50% (Table 2). (c) Combination of Set 1 and Set 2:  
The population size was fixed at 200, with 300 generations, and the costs of ingredients were set to diesel at 2.0000 EUR/L and biodiesel at 0.8091 EUR/L. The ingredient densities were diesel at 0.8191 g/mL and biodiesel at 0.8855 g/mL at 5 \({}^{\circ}\)C. Ingredient density varies based on temperatures between 5 and 25 \({}^{\circ}\)C (Table 3). (d) The top 10% best-performing chromosomes from the preceding evaluated generation were directly carried over to the subsequent generation. (e) The Crossover operator generated 70% of the population, adjusted by the IPLS value, randomly defined per generation within a range of \(\pm\)5% to 10%. (f) The Mutation operator was applied to the remaining 20% of chromosomes. (g) Each experiment comprised 1000 independent simulations per Set and temperature (e.g., Set 1: 5 \({}^{\circ}\)C-1000 iterations, Set 1: 10 \({}^{\circ}\)C-1000 iterations,..., Set 2: 25 \({}^{\circ}\)C-1000 iterations). In summary, comprehensive experimentation yielded the aforementioned configurations. The algorithm was implemented in the Matlab R2022a environment and executed on an AMD Ryzen 3 2200 G with Radeon Vega Graphics 3.50 GHz and 8.00 GB RAM. Biodiesel, as the secondary ingredient, is comprised of sources from 50% animal fat and 50% vegetable origin. The prices of vegetable origins (rap oil and sun oil) are globally available [42; 43]. Table 2 categorizes the experimental sets according to temperature parameters ranging between 5 and 25 \({}^{\circ}\)C, distinguishing between sets emphasizing Cost (Set 1: w\({}_{1}\)\(\geq\) 50%) and Density (Set 2: w\({}_{2}\)\(\geq\) 50%). For instance, settings such as w\({}_{1}\) = 70% and w\({}_{2}\) = 30% prioritize Cost, as the cost criterion holds greater weight than the density criterion. Further experimental details are outlined in Table 3. Diesel and biodiesel are priced at 2.000 EUR/L and 0.8091 EUR/L, respectively, while their densities range from 0.8191 g/mL \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment Temperatures** & **w\({}_{1}\)/w\({}_{2}\) (Set 1)** & **w\({}_{1}\)/w\({}_{2}\) (Set 2)** \\ \hline  & 50\%/50\% & 50\%/50\% \\
5 \({}^{\circ}\)C, 10 \({}^{\circ}\)C, & 60\%/40\% & 40\%/60\% \\
15 \({}^{\circ}\)C, 20 \({}^{\circ}\)C and 25 \({}^{\circ}\)C & 70\%/30\% & 30\%/70\% \\  & 80\%/20\% & 20\%/80\% \\  & 90\%/10\% & 10\%/90\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: W\({}_{1}\) and w\({}_{2}\) for Set 1 and Set 2 per Temperature between 5 \({}^{\circ}\)C-25 \({}^{\circ}\)C.  
to 0.8915 g/mL, varying with temperature. Additionally, the proportions of ingredients in the mixtures are specified. Diesel percentage ranges from 1% to 99%, and biodiesel percentage ranges from 1% to 30%. The values presented in Table 3 reflect the availabilities and current prices observed during the laboratory experiments.