The use of hyper-heuristics is increasing in the multi-objective optimisation domain, and the next logical advance in such methods is to use them in the solution of many-objective problems. Such problems comprise four or more objectives and are known to present a significant challenge to standard dominance-based evolutionary algorithms. We incorporate three comparison operators as alternatives to dominance and investigate their potential to optimise many-objective problems with a hyper-heuristic from the literature. We discover that the best results are obtained using either the favour relation or hypervolume, but conclude that changing the comparison operator alone will not allow for the generation of estimated Pareto fronts that are both close to and fully cover the true Pareto front.