This work presents the application of the omni-aiNet algorithm-an immune-inspired algorithm originally developed to solve single and multi-objective optimization problems-to the reconstruction of phylogenetic trees. The main goal here is to automatically evolve a population of phylogenetic unrooted trees, possibly with distinct topologies, by minimizing at the same time two optimization criteria: the minimum evolution and the mean-squared error. This proposal generates, in a single run, a set of non-dominated solutions that represent the trade-offs of the two conflicting objectives, and gives the user the possibility of having distinct explanations for the differences observed at the terminal nodes of the trees. A series of experimental results is also reported in this work, in order to illustrate the effectiveness of the proposal and its capability to overcome the restrictive feedback provided by the application of well-known algorithms for phylogenetic reconstruction, such as the Neighbor Joining. Besides, the methodology presented in this work is compared to the popular NSGA-II algorithm, also modified to solve phylogenetic reconstruction problems.