This paper is aimed at optimizing the synchronizability of a complex network when the total of its edge weights is given and fixed. We try to allocate edge weights on a complex network to optimize the network's synchronizability from the perspective of spectral graph theory. Most of the existing analysis on multilayer networks assumes the weights of intralayer or interlayer edges to be identical. Such a restrictive assumption is not made in this work. Using the graph comparison based method, different edge weights are allocated according to topological features of networks, which is more reasonable and consistent with most physical complex networks. Furthermore, in order to find out the best edge-weight allocation scheme, we carried out numerical simulations on typical duplex networks and real-world networks. The simulation results show that our proposed edge-weight allocation schemes outperform the average, degree-based, and edge betweenness centrality allocations.