The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has shown a superior performance in tackling some complicated multiobjective optimization problems (MOPs). However, the use of different evolutionary operators and their various parameter settings has a significant impact on its performance. To enhance its algorithmic robustness and effectiveness, this paper proposes an adaptive composite operator selection (ACOS) strategy for MOEA/D. Four evolutionary operator pools are used in ACOS and their advantages are combined to provide stronger exploratory capabilities. Regarding each selected operator pool, an online self-adaptation for the parameters tuning is further employed for performance enhancement. When compared with other adaptive and improved strategies designed for MOEA/D, our proposed algorithm is found to be effective and competitive in solving several complicated MOPs.