yy Today's researchers have made concerted efforts to benefit from biodiesel and to achieve better combustion due to its higher cetane number in comparison to that of diesel. The major drawback of utilizing biodiesel-diesel blend is the corresponding increase in the NOx emission, which can be solved using water. However, water results in higher HC and CO emissions that can be handled by the addition of metal-based nano-particles such as cerium oxide (CeO2). In this study, 36 different cases of these input parameters (different values of biodiesel, water, and nano-particles) have been examined experimentally, and the results are used to train an artificial neural network (ANN) model to produce 8866 data. Then, these data were utilized to find the maximum brake thermal efficiency while the value of output emissions and brake specification fuel consumption are minimum. In this regard, a new parameter called performance evaluation of diesel engine (PEDE) was introduced to decrease the number of output parameters into one. However, the results of sensitivity analysis on the PEDE indicated that the share of output parameters on this newly defined PEDE are not the same, and it demands modifications. Therefore, the exponents of each output parameter were modified by the application of sensitivity analysis. Finally, a modified PEDE that can predict the performance of diesel engines properly was introduced, and the optimum values were presented. Results indicated that the best performance occurs when the amount of cerium oxide nano-particles is 80 ppm, while the shares of biodiesel and water are 6 percent.