Different problems in the bioinformatics domain involve the optimization of multiple conflicting criteria. An example of a biologically relevant problem that has benefited from the definition of multiobjective strategies is phylogeny inference. However, this problem is characterized by complex search spaces and differently shaped Pareto fronts that require sophisticated optimization strategies to achieve high-quality outputs. In this work, we explore decomposition-based algorithms that combine the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) with advanced optimization techniques to boost the inference of multiobjective phylogenetic trees. In particular, we investigate the hybridization of MOEA/D with Particle Swarm Optimization (MOPSO/D) and the integration of Dynamic Resource Allocation strategies (MOEA/D-DRA). The results obtained in four real-world datasets highlight MOEA/D-DRA as a highly promising approach to address this problem, attaining hypervolume scores up to 81% while also dominating significant percentages of solutions (up to 90%) with regard to baseline MOEA/D designs and other multiobjective algorithms.