Multi-objective evolutionary algorithms based on decomposition (MOEA/D) has demonstrated excellent performance in dealing with multi-objective optimization problems. As two essential issues in MOEA/D, mating neigh- borhood sizes and reproduction operators determine the exploitation and exploration abilities of the algorithm. This paper proposes a new decomposition-based multi-objective evolutionary algorithm with mating neighborhood sizes and reproduction operators adaptation (MOEA/D-ATO), which adaptively assigns the suitable combination of mating neigh- borhood size and reproduction operator to each subproblem at different searching stages. Numerical results indicate that the proposed adaptation is effective. Moreover, compari- son with other adaptive steady-state MOEA/D variants and state-of-art generational MOEA/D variants shows that the proposed MOEA/D-ATO algorithm performs significantly better in terms of solution quality and CPU time.