## 3 Results
### Emissions Results  
Figure 8 exhibits all populations and the Pareto front for the optimization process. According to this figure, the evolution evolves toward decreasing the objective and constraint values of ISFC, PFP objectives, and CO, NOx, and UHC constraints. CO emissions originate from incomplete combustion caused by insufficient oxygen in the combustion chamber. The homogeneity of the air-fuel mixture within the combustion chamber is considered another key factor influencing CO emissions. In some situations, even though oxygen is sufficient in the combustion chamber, a lack of mixture homogeneity leads to rich regions,  
Figure 7: Three-dimensional scatter plot for the effect of operational parameters on ISFC and emissions. resulting in higher CO emissions. Increasing the quantity of diesel fuel might increase the CO emissions due to the deficit of the in-cylinder dynamics in controlling the homogeneous mixing of air/fuel in the cylinder. Additionally, CO emissions may rise as a result of the low-temperature combustion characteristics of the RCCI engine. Meanwhile, UHC emissions primarily result from bulk quenching, wall quenching, and lower combustion temperatures within the combustion chamber. Furthermore, the presence of non-uniform regions within the cylinder can lead to the formation of hydrocarbons (HCs). As seen from row 1 in Figure 8, most infeasible solutions happened in the range of PFP < 7 MPa and PFP > 9 MPa. This happens at lower PFP due to incomplete combustion since the UHC and CO emissions results are out of the acceptable range of optimization constraints, while infeasible solutions happen at higher PFP mostly because of the NOx emissions being out of the range due to high temperature. Figure 8, row 2 shows the influence of each UHC, CO, and NOx emission on IFSC. It seems that both UHC and CO follow approximately the same pattern as ISFC, starting from high and low values of ISFC; all outcomes are infeasible, which might be because of high NOx emissions while at ISFC in the feasible range, an infeasible outcome due to the combined effect of NOx, CO, and UHC emissions. Figure 8, row 3, shows the Pareto outcomes between HC and CO, which have a nearly linear relationship. In contrast, both UHC and CO emissions show a trade-off relationship with nitrogen oxide (NOx) emissions. This study will briefly discuss elective optimum cases, where case (A) shows the optimum case that emits the lowest UHC and CO emissions and gives the lowest ISFC; case (B) is the optimum case that emits less NOx; case c is the optimum result of soot; and case D is the optimum case in terms of power. It can be noticed that all cases were at an SOI of \(-35\) aTDC, except case D, which was at \(-34\) aTDC, which means these values are the optimum values for SOI. In case A, the high temperature is settled for a longer duration in the cylinder, which is why the CO and UHC emissions and ISFC have the lowest values because of enhanced combustion. For this case, the SOC, CA 50, and CD are (\(-0.919\), \(3.03\)), CA aTDC, and 8.739 CA, respectively, with noting that the CA10 is defined as the start of combustion (SOC). This case gives the lowest power of 5.36 kW and a higher IE of 51% and utilizes less diesel fuel at 1.71 mg injected at a pressure of 150 bars at 2270 rpm. The high-temperature range in case B is lower than in the other cases. It settles within a short time in the chamber, which is why the NOx emissions in this case are less than in other cases, even though all cases are considered optimum cases of this study. The emissions in case B are within the EURO VI standards. Moreover, the start of combustion (SOC) is at 2.56 CA aTDC, the CA 50 is retarded to 8.25 CA aTDC, and the combustion duration is 9.74 CA. This case gives a power of 5.97 kW, an IE of 50%, and a utilized diesel fuel of 1.82 mg injected at a pressure of 272.3 bars at 2540 rpm. Case C emits lower soot emissions because it has the most prolonged combustion duration at 8.078 CA.