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Multiobjective evolutionary algorithm based on decomposition MOEA/D and an improved non-dominating sorting multiobjective genetic algorithm NSGA-II is two well known multiobjective evolutionary algorithms MOEAs in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set PS, Pareto front PF are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.