In recent years, evolutionary algorithms based on the concept of “decomposition” have gained significant attention for solving multi-objective optimization problems. They have been particularly instrumental in solving problems with four or more objectives, which are further classified as many-objective optimization problems. In this paper, we first review the cause-effect relationships introduced by commonly adopted schemes in such algorithms. Thereafter, we introduce a decomposition-based evolutionary algorithm with a novel assignment scheme. The scheme eliminates the need for any additional replacement scheme, while ensuring diversity among the population of candidate solutions. Furthermore, to deal with constrained optimization problems efficiently, marginally infeasible solutions are preserved to aid search in promising regions of interest. The performance of the algorithm is objectively evaluated using a number of benchmark and practical problems, and compared with a number of recent algorithms. Finally, we also formulate a practical many-objective problem related to wind-farm layout optimization and illustrate the performance of the proposed approach on it. The numerical experiments clearly highlight the ability of the proposed algorithm to deliver the competitive results across a wide range of multi-/many-objective design optimization problems.