Multi- or many-objective evolutionary algorithm- s(MOEAs), especially the decomposition-based MOEAs have been widely concerned in recent years. The decomposition-based MOEAs emphasize convergence and diversity in a simple model and have made a great success in dealing with theoretical and practical multi- or many-objective optimization problems. In this paper, we focus on update strategies of the decomposition- based MOEAs, and their criteria for comparing solutions. Three disadvantages of the decomposition-based MOEAs with local update strategies and several existing criteria for comparing solutions are analyzed and discussed. And a global loop update strategy and two hybrid criteria are suggested. Subsequently, an evolutionary algorithm with the global loop update is implement- ed and compared to several of the best multi- or many-objective optimization algorithms on two famous unconstraint test suites with up to 15 objectives. Experimental results demonstrate that unlike evolutionary algorithms with local update strategies, the population of our algorithm does not degenerate at any generation of its evolution, which guarantees the diversity of the resulting population. In addition, our algorithm wins in most instances of the two test suites, indicating that it is very compet- itive in terms of convergence and diversity. Running results of our algorithm with different criteria for comparing solutions are also compared. Their differences are very significant, indicating that the performance of our algorithm is affected by the criterion it adopts.