This work studies and compares the effects on performance of local dominance and local recombination applied with different locality in multiobjective evolutionary algorithms on combinatorial multiobjective problems. For this purpose, we introduce a method that creates a neighborhood around each individual and assigns a local dominance rank after rotating the principal search direction of the neighborhood by using polar coordinates in objective space. For recombination a different neighborhood determined around a random principle search direction is created. The neighborhood sizes for dominance and recombination are separately controlled by two different parameters. Experimental results show that the optimum locality of dominance is different from the optimum locality of recombination. Additionally, it is shown that the performance of the algorithm that applies local dominance and local recombination with different locality is significantly better than the performance of algorithms applying local dominance alone, local recombination alone, or dominance and recombination globally as conventional approaches do.