Multi-objective optimisation of particulate matter characteristics from various feedstock biodiesels using symbolic regression and NSGA-II

• Biodiesels reduced PM by 18-68%; coconut showed lowest PM at high load. • Highly unsaturated biodiesels showed load-dependent PM size reversal. • Symbolic regression revealed nonlinear PM drivers with high accuracy (R 2 > 0.93). • NSGA-II identified Pareto-optimal fuel-load conditions balancing PM number and size. • Engine load and palmitic/linoleic acids were dominant nonlinear drivers of PM. Particulate matter (PM) emissions from diesel engines remain a critical environmental health hazard. However, mitigating these emissions using biodiesel is complicated by the non-linear and often conflicting interactions between the fatty acid composition and engine operating parameters. This study addresses black-box limitations by introducing a novel symbolic regression (SR) framework to derive transparent, interpretable models for multi-objective optimisation. Experiments on 10 distinct feedstocks showed that biodiesels reduced the PM concentration by 18%–68% relative to diesel, and the mechanisms underlying this reduction varied significantly. Coconut oil biodiesel emerged as the superior fuel, achieving the lowest PM concentration (0.8–1.8 × 10 7 particle/scm 3 ). This performance was attributed to its exceptionally low viscosity (2.93 cSt) and an extended ignition delay (18.13 CA), which synergistically enhanced air–fuel premixing. In contrast, highly unsaturated biodiesels demonstrated a load-dependent reversal: they produced smaller particles at low loads but generated significantly larger particles (79–84 nm) at 75% load. This detrimental shift resulted from a lower heating value, which required a 15%–20% increase in the injected fuel mass, creating oxygen-deficient zones that favoured soot precursor formation. The developed SR models were exceptionally accurate (R 2 > 0.93) and explicitly identified engine load, palmitic acid, and linoleic acid as the dominant drivers. By integrating these models with the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the critical trade-off between minimising the PM concentration and maximising particle size was resolved. The use of biodiesel with a high linoleic acid concentration (34%–38%) and minimal α-linolenic acid (< 0.2%) and operation at a moderate engine load (56%–64%) was the optimal strategy to minimise adverse health impacts.