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Transport processes are universal in real-world complex networks, such as communication and transportation networks. As the increase of the traffic in these complex networks, problems like traffic congestion and transport delay are becoming more and more serious, which call for a systematic optimization of these networks. In this paper, we formulate a multi-objective optimization problem (MOP) to deal with the enhancement of network capacity and efficiency simultaneously, by appropriately adjusting the weights of edges in networks. To solve this problem, we provide a multi-objective evolutionary algorithm (MOEA) based on particle swarm optimization (PSO), namely network centrality guided multi-objective PSO (NC-MOPSO). Specifically, in the framework of PSO, we propose a hybrid population initialization mechanism and a local search strategy by employing the network centrality theory to enhance the quality of initial solutions and strengthen the exploration of the search space, respectively. Simulation experiments performed on network models and real networks show that our algorithm has better performance than four state-of-the-art alternatives on several most-used metrics.