The working principles of the well-established multi-objective evolutionary algorithm MOEA/D relies on the iterative and cooperative improvement of a number of single-objective sub-problems obtained by decomposition. Besides the definition of sub-problems, selection and replacement are, like in any evolutionary algorithm, the two core elements of MOEA/D. We argue that these two components are however loosely coupled with the maintained population. Thereby, we propose to re-design the working principles of MOEA/D by adopting a set-oriented perspective, where a many-to-one mapping between sub-problems and solutions is considered. Selection is then performed by defining a neighborhood relation among solutions in the population set, depending on the corresponding sub-problem mapping. Replacement is performed following an elitist mechanism allowing the population to have a variable, but bounded, cardinality during the search process. By conducting a comprehensive empirical analysis on a range of combinatorial multi- and many-objective nk-landscapes, we show that the proposed approach leads to significant improvements, especially when dealing with an increasing number of objectives. Our findings indicate that a set-oriented design can constitute a sound alternative for strengthening the practice of multi- and many-objective evolutionary optimization based on decomposition.