A partitioning parallelization of the multi-objective evolutionary algorithm based on decomposition, pMOEA/D, is proposed in this letter to achieve significant time reductions for expensive bi-objective optimization problems (BOPs) on message-passing clusters. Each sub-population of pMOEA/D resides on a separate processor in a cluster and consists of a non-overlapping partition and some extra overlapping individuals for updating neighbors. Additionally, sub-populations cooperate across separate processors by the hybrid migration of elitist individuals and utopian points. Experimental results on two benchmark BOPs and the wireless sensor network layout problem indicate that pMOEA/D achieves satisfactory performance in terms of speedup and quality of solutions on message-passing clusters.