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It is known from single-objective optimization that hybrid variants of local search algorithms and evolutionary algorithms can outperform their pure counterparts. This holds, in particular, in continuous search spaces and for differentiable fitness functions. The same should be true in multiobjective optimization. An efficient gradient-based local algorithm, sequential quadratic programming (SQP) is combined with two well-known multiobjective evolutionary algorithms, strength Pareto evolutionary algorithm (SPEA) and nondominated sorting genetic algorithm (NSGA-II) respectively, by means of a modified ε-constraint method. The resulting two hybrid algorithms demonstrate great success over two sets of well-chosen functions regarding the convergence rate. In addition, from the simulation studies, the hybridization approach also enhances, at least does not ruin, the diversity of the solutions.