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Despite the vast research on many-objective optimisation problems, the presence of many objective functions is still a challenge worthy of further study. A way to treat this kind of problem is to incorporate the preferences of the decision maker (DM) into the optimisation process. In this paper, we introduce an interactive ant colony optimisation combined with an ordinal classification method in which classes are described by characteristic profiles. Through several interactions, the DM is supposed to identify some representative solutions of the classes 'satisfactory' and 'dissatisfactory,' which are used to initialise an ordinal classifier that increases the selective pressure by discriminating in favour of the 'satisfactory' class. This method can work with any either asymmetric or symmetric binary preference relation, a feature that confers a very wide generality. As another advantage, the interaction with the DM has minimal cognitive demands, which is an advisable feature for any approach based on interaction. Although the preference model is quite general, the proposal was tested using an eclectic model which combines compensatory preferences, veto conditions, and interval numbers to handle imprecise values; those preferences are aggregated in an asymmetric preference relation. Our approach performs particularly well in 10-objective problems according to the standards in the state-of-the-art literature. Numerical results and tests for statistical significance on the DTLZ and WFG test suites support this claim. [ABSTRACT FROM AUTHOR]