An Extension of the iMOACO$\mathbb {_R}$ Algorithm Based on Layer-Set Selection.

iMOACO $$\mathbb {_R}$$ is an ant colony optimization algorithm designed to tackle multi-objective optimization problems in continuous search spaces. It is built on top of ACO $$\mathbb {_R}$$ and uses the R2 indicator (to improve its performance on high-dimensional objective function spaces) to rank the pheromone archive of the best previously-explored solutions. Due to the utilization of an R2-based selection mechanism, there are typically a large number of tied-ranks in iMOACO $$\mathbb {_R}$$ ’s pheromone archive. It is worth noting that the solutions of a specific layer share the same importance based on the R2 indicator. A critical issue due to the large number of tied-ranks is a reduction of the algorithm’s exploitation ability. In consequence, in this paper, we propose replacing iMOACO $$\mathbb {_R}$$ ’s probabilistic solution selection mechanism with a mechanism tailored to these layer-sets. Our proposed layer-set selection uses rank-proportionate (roulette wheel) selection to select a layer, with all the solutions in the layer sharing equally in the layer’s probability. Our experimental evaluation indicates that our proposal, which we call iMOACO $$\mathbb {^{\prime }_{R}}$$ , performs better than iMOACO $$\mathbb {_R}$$ to a statistically significant extent on a large number of benchmark problems having from 3 to 10 objective functions.