This paper proposes a constrained solution update strategy for multiobjective evolutionary algorithm based on decomposition, in which each agent aims to optimize one decomposed subproblem. Different from the existing approaches that assign one solution to each agent, our approach allocates the closest solutions to each agent and thus the number of solutions in an agent may be zero and no less than one. Regarding the agent with no solution, it will be assigned one solution in priority, once offspring are generated (...) closest to its subproblem. To keep the same population size, the agent with the largest number of solutions will remove one solution showing the worst convergence. This improves diversity for one agent, while the convergence of other agents is not lowered. On the agent with no less than one solution, offspring assigned to this agent are only allowed to update its original solutions. Thus, the convergence of this agent is enhanced, while the diversity of other agents will not be affected. After a period of evolution, our approach may gradually reach a stable status for solution assignment; i.e., each agent is only assigned with one solution. When compared to six competitive multiobjective evolutionary algorithms with different population selection or update strategies, the experiments validated the advantages of our approach on tackling two sets of test problems. (shrink)