The two-archive 2 algorithm(Two_Arch2)is a many-objective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA)and con-vergence archive(CA).However,the individuals in DA are selec-ted based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional problems.The traditional algorithm even cannot converge due to the weak se-lection pressure.Meanwhile,Two_Arch2 adopts DA as the out-put of the algorithm which is hard to maintain diversity and cov-erage of the final solutions synchronously and increase the com-plexity of the algorithm.To increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions,an ε-domination based Two_Arch2 algorithm(ε-Two_Arch2)for many-objective problems(MaOPs)is proposed in this paper.In ε-Two_Arch2,to decrease the computational complexity and speed up the convergence,a novel evolutionary framework with a fast update strategy is proposed;to increase the selection pressure,ε-domination is assigned to update the individuals in DA;to guarantee the uniform distribution of the solution,a boundary protection strategy based on Iε+indicator is designated as two steps selection strategies to update individu-als in CA.To evaluate the performance of the proposed al-gorithm,a series of benchmark functions with different numbers of objectives is solved.The results demonstrate that the pro-posed method is competitive with the state-of-the-art multi-ob-jective evolutionary algorithms and the efficiency of the al-gorithm is significantly improved compared with Two_Arch2.