Phylogenetic networks can represent evolutionary phenomena that phylogenetic trees cannot describe, such as parallelism, convergence, reversion, hybridisation, recombination, and horizontal transference. The phylogenetic inference problem can be seen as an optimisation problem, searching for the most qualified network among the possible topologies, based on an inference criterion. However, different criteria may result in several topologies of networks, which could conflict with each other. Multi-objective optimisation can handle conflicting objectives, reducing the bias associated with the dependency on a specific criterion. In this work, we define the multi-objective phylogenetic inference problem based on networks to consider reticular phenomena and propose an ad-hoc evolutionary algorithm to treat it: MO-PhyNet. This algorithm is based on the Non-dominated Sorting Genetic Algorithm II designed to infer rooted phylogenetic networks by minimising three criteria: (1) parsimony hardwired, (2) parsimony softwired, and (3) the number of reticulations. The formalisation of the phylogenetic inference based on networks as a multi-objective optimisation problem allows us to obtain solutions considering conflicting inference criteria, resulting in different reticulated topologies representing distinct evolutionary hypotheses. The MO-PhyNet results identify Pareto set of solutions that show a relationship between the hardwired parsimony and the minimum reticulations criteria. Additionally, MO-PhyNet obtains better solutions than other strategies in terms of the optimised criteria by allowing to visualise incongruences and horizontal phenomena. This work is the first attempt to address the inference of phylogenetic networks considering multi-objective optimisation concerning the current literature to the best of our knowledge.