Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking

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.