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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]

This paper presents Outranking-based Particle Swarm Optimisation (O-PSO) a novel metaheuristic to address the multi-objective Unrelated Parallel Machine Scheduling Problem. It is a particle swarm optimisation algorithm enriched with the preferences of the Decision Maker (DM), articulated in a fuzzy relational system based on ELECTRE III. Unlike other multi-objective metaheuristics, O-PSO searches for the Region of Interest (RoI) instead of approximating a sample of the complete Pareto frontier. The RoI is the subset consisting of those Pareto-efficient solutions that satisfy the outranking relations, that is, they are the best solutions in terms of the DM's system of preferences. Therefore, O-PSO not only approximates the Pareto solutions but also supports multicriteria decision analysis of the schedules. The efficiency of O-PSO is validated on a benchmark of synthetic instances from the scientific literature, where the Wilcoxon rank-sum test provides statistical evidence that O-PSO offers high-quality solutions when compared with two state-of-the-art metaheuristics; specifically, O-PSO is capable of generating a greater proportion of solutions (on average, ranging from 7% to 14%) dominating those of the state-of-the-art algorithms, as well as finding more solutions (from 13% to 18%) that satisfy the DM's preferences. O-PSO is also applied to a real-world case study in the transport industry to provide evidence for its applicability. [ABSTRACT FROM AUTHOR]