Reaching Pareto Front Shape Invariance with a Continuous Multi-objective Ant Colony Optimization Algorithm

Generating Pareto Front Approximations with good convergence, uniformity, and spread regardless of the geometry of the Pareto Front remains as an open problem. Many Multi-Objective Evolutionary Algorithms (MOEAs) have been proposed for this aim achieving remarkable results. However, the utilization of Swarm Intelligence algorithms such as Multi-Objective Ant Colony Optimization Algorithms (MOACOs) has been scarcely studied. In this paper, we propose a Geometric-Invariant \(\text {MOACO}_\mathbb {R}\) ( \(\text {GI-MOACO}_\mathbb {R}\) ) designed to tackle multi-objective optimization problems with a continuous decision space. According to our experimental results, \(\text {GI-MOACO}_\mathbb {R}\) outperforms the existing MOACOs for continuous search spaces and it is competitive with respect to state-of-the-art MOEAs on several test suites with regular and irregular Pareto Front geometries. To the best of the author’s knowledge, \(\text {GI-MOACO}_\mathbb {R}\) is the first Pareto-Front-Shape invariant MOACO.