When optimising for more than one parameter of interest, multi-objective Bayesian optimisation (MBO) is an attractive method. A typical example might include finding optimal solutions for stability as well as a functional property quantifying overall performance. In the traditional Bayesian optimisation algorithm, the N best solutions generated by prior calculations are used to rebuild the probabilistic model. For multi-objective problems, it is challenging to decide on the "best" solution and one must develop a ranking scheme to weight individual parameters in the overall score. Non-dominated sorting is a key concept that originated from multi-objective evolutionary algorithms and is widely applied as target ranking schemes in multi-objective Bayesian optimisation. It accounts for a significant proportion of the computational cost when applying selection, comparison and crossover. A multitude of non-dominated sorting methods have been proposed and must be carefully selected based on the functional space in chemical and materials science.