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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]

Many-objective optimization is an area of interest common to researchers, professionals, and practitioners because of its real-world implications. Preference incorporation into Multi-Objective Evolutionary Algorithms (MOEAs) is one of the current approaches to treat Many-Objective Optimization Problems (MaOPs). Some recent studies have focused on the advantages of embedding preference models based on interval outranking into MOEAs; several models have been proposed to achieve it. Since there are many factors influencing the choice of the best outranking model, there is no clear notion of which is the best model to incorporate the preferences of the decision maker into a particular problem. This paper proposes a hyper-heuristic algorithm—named HyperACO—that searches for the best combination of several interval outranking models embedded into MOEAs to solve MaOPs. HyperACO is able not only to select the most appropriate model but also to combine the already existing models to solve a specific MaOP correctly. The results obtained on the DTLZ and WFG test suites corroborate that HyperACO can hybridize MOEAs with a combined preference model that is suitable to the problem being solved. Performance comparisons with other state-of-the-art MOEAs and tests for statistical significance validate this conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone. [ABSTRACT FROM AUTHOR]