Multi-Objective Evolutionary Algorithm based on decomposition (MOEA/D) has been proposed for a decade in solving complex multi-objective problems (MOP) by decomposing it into a set of single-objective problems. MOEA/D-AGR is one of the improved algorithm introduced recently to substitute the original replacement scheme in MOEA/D with a new adaptive global replacement (GR) scheme so that the neighborhood replacement size Tr is increased among the generation to achieve the shifting of focus from solution diversity to convergence. However, the new replacement scheme only considers the one-way convergence of the objective solutions among all sub-problems. It is hard to re-achieve the solution diversity once the algorithm reaches another steeper landscape of solution from a flatten one while it is focusing on convergence. This paper proposes a new adaptive GR scheme to prolong the period of Tr increment so that it can fit the re-increment of fitness landscape. To compensate the shorten period for solution convergence, local searching is adapted for those individuals which has stopped improving its solution value by Simulated Annealing (SA) algorithm. In order to suppress the degree of local searching at the early stage of focusing solution diversity, Fuzzy Logic is used here to coordinate the frequency of local searching according to the average change of objective solution values. To demonstrate the performance of the proposed algorithm, several common benchmark MOPs are used in this paper for comparing with the several state-of-the-art MOEA/D algorithms in terms of IGD. The performance investigation found that the performance of the proposed algorithm was generally better than the other compared algorithms.