Abstract Due to the fixed and monotonous search direction, the performance of decomposition-based multiobjective evolutionary algorithms (MOEAs) highly depends on the Pareto front (PF) shape. Recent studies have highlighted the complementary effect of the ideal and nadir points. They roughly employed both as the reference points to diversify the search direction. However, few works investigate whether two points are equally important. This paper thereby proposes a novel decomposition-based MOEA, where the ideal point is consistently considered as the global reference point while the nadir point is conditionally employed as the local one. We show that the nadir point may aid the ideal point in some cases and be recognized as a redundant one in others. More specifically, an assignment strategy is suggested to determine the necessity of using a local reference point for each subproblem , by considering whether the solution found by the nadir point and corresponding weight vector can improve the quality of the population. Experimental results finally verify the effectiveness of the proposed algorithm on 57 benchmark test problems with various PF shapes. In comparison with the state-of-the-art decomposition-based MOEAs, the proposed algorithm is promising to bring a more refined search and prevent redundant search behaviors .