  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.
