iMOACO\(_\mathbb {R}\): A New Indicator-Based Multi-objective Ant Colony Optimization Algorithm for Continuous Search Spaces

Ant colony optimization (ACO) is a metaheurisitc which was originally designed to solve combinatorial optimization problems. In recent years, ACO has been extended to tackle continuous single-objective optimization problems, being ACO\(_\mathbb {R}\) one of the most remarkable approaches of this sort. However, there exist just a few ACO-based algorithms designed to solve continuous multi-objective optimization problems (MOPs) and none of them has been tested with many-objective problems (i.e., multi-objective problems having four or more objectives). In this paper, we propose a novel multi-objective ant colony optimizer (called iMOACO\(_\mathbb {R}\)) for continuous search spaces, which is based on ACO\(_\mathbb {R}\) and the R2 performance indicator. Our proposed approach is the first specifically designed to tackle many-objective optimization problems. Moreover, we present a comparative study of our proposal with respect to NSGA-III, MOEA/D, MOACO\(_\mathbb {R}\) and SMS-EMOA using standard test problems and performance indicators adopted in the specialized literature. Our preliminary results indicate that iMOACO\(_\mathbb {R}\) is very competitive with respect to state-of-the-art multi-objective evolutionary algorithms and is also able to outperform MOACO\(_\mathbb {R}\).