This work presents the application of the omni-aiNet algorithm - an immune-inspired algorithm originally developed to solve single and multiobjective optimization problems - to the reconstruction of phylogenetic trees. The main goal of this work is to automatically evolve a population of phylogenetic unrooted trees, possibly with distinct topologies, by minimizing at the same time the minimal evolution and the mean-squared error criteria. The obtained set of phylogenetic trees contains non-dominated individuals that form the Pareto front and that represent the trade-off of the two conflicting objectives. Given this set of phylogenetic trees, two multicriterion decision-making techniques were applied in order to try to select the best solution within the Pareto front.