In the context of metaheuristic global optimization, we present the definition and development of two new ant colony optimizers (ACO): a single-objective mixed-integer one, called ACOmi, and a multi-objective hypervolume-based one, called MHACO. In particular, after having performed a verification and validation phase over a wide set of problems (including various space missions such as Cassini, Messenger, Rosetta, and others), we focus on their application to a solar polar sailing mission to the Sun, attempting to minimize its mission cost and duration. Therefore, building on previous studies of such a mission scenario, we first constructed a model for simulating the journey of the sail from a geocentric GTO to the Sun, not only accounting for gravitational forces, but also atmospheric forces, the non-ideal solar radiation pressure force, and other environmental aspects. Then, a guidance model for the sail was set up, so that the attitude of the sail could be controlled during its journey to the Sun. This entire framework was formulated as both a single and multi-objective problem. Finally, a trade-off was performed between the newly developed ACO and other state-of-art global optimizers. For the single-objective case, these include artificial bee colony, simple genetic algorithm, self-adaptive differential evolution, particle swarm optimization, and other methods. While for the multi-objective scenario three different optimizers have been tested against the multi-objective ant colony extension: an evolutionary algorithm with decomposition, a nondominated sorting genetic algorithm and a multi-objective variant of particle swarm optimization. The found results are very promising: for the single-objective problem, the ant colony optimizer has managed to outperform all the algorithms. Whilst for the multi-objective case, the genetic algorithm seems to provide the best Pareto fronts, although the results are very competitive with those of the ACO, especially for lower function evaluations. In the end, besides providing the scientific community with new powerful global optimizers for SO and MO problems, we managed to halve the mass of the solar sail compared to previous studies, while still keeping a similar time of flight.