The present work aimed at the practical utility of waste hybrid (coconut + fish oil) oil-derived biodiesel with magnesium oxide (MgO) nanoparticles (NPs) fuelled to diesel engines. Central composite design (CCD) experimental matrices with different sets of variables (blend type: 10–40 % vol. of biodiesel; MgO NPs: 60–180 ppm; engine speed: 1000–2000 rpm; engine load: 40–100 %) were used to examine the engine performance (brake specific fuel consumption: BSFC; and brake thermal efficiency: BTE) and emission characteristics (carbon monoxide: CO; unburnt hydrocarbon: UHC; nitrous oxide: NOx). The MgO NPs are characterized by using an X-ray diffractometer: XRD, scanning electron microscope: SEM and transmission electron microscope: TEM and confirm the compositions and the crystallite particle size equal to 132 nm. The models developed for each output showed a better value of coefficient of determination (R2) equal to 0.9843 for BSFC, 0.9859 for BTE, 0.9772 for CO, 0.9777 for NOx, and 0.9368 for UHC. Grey relational analysis (GRA) with quality loss function (QLFs) and principal component analysis (PCA) were used to correlate the multiple responses and transform multiple objective functions to single objective function necessary for optimization. Three population-based search algorithms, such as driving training-based optimization (DTBO) and election-based optimization algorithm (EBOA) and grey wolf optimization (GWO), were applied and evaluated their optimization performances. EBOA, DTBO and GWO determined the same optimal conditions and converged to 1000 iterations with a computational time equal to 2, 5 and 30 s, respectively. The algorithms determined optimal conditions produced better experimental values than GRA-based QLF and PCA with 31.27 % decrease in BSFC, 24.27 % decrease in CO, 4.64 % decrease in HC, 19.82 % decrease in NOx emissions, and 9.82 % decrease in BTE, respectively. MgO NPs addition to biodiesel fuel resulted in better performance and emission characteristics than without MgO NPs.
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