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In this paper, we apply EMO (Evolutionary Multiobjective Optimization) algorithms with a generalized dominance relation-based local search (GDR-LS) procedure to MOO (Multi-Objective Optimization) test problems. In the GDR-LS procedure, we generalize the Pareto dominance relation, which is usually used to determine Pareto optimal solutions for MOO problems, for accepting candidate solutions in the local search. We have already applied EMO algorithms with the GDR-LS procedure to well-known multi-objective knapsack problems. In this paper, we examine the effectiveness of the GDR-LS procedure in EMO algorithms through computational experiments on function optimization problems.