The mathematical framework of multiplex networks has been increasinglyrealized as a more suitable framework for modelling real-world complex systems.In this work, we investigate the optimization of synchronizability in multiplexnetworks by evolving only one layer while keeping other layers fixed. Our mainfinding is to show the conditions under which the efficiency of convergence tothe most optimal structure is almost as good as the case where both layers arerewired during an optimization process. In particular, inter-layer couplingstrength responsible for the integration between the layers turns out to becrucial factor governing the efficiency of optimization even for the cases whenthe layer going through the evolution has nodes interacting much weakly thanthose in the fixed layer. Additionally, we investigate the dependency ofsynchronizability on the rewiring probability which governs the networkstructure from a regular lattice to the random networks. The efficiency of theoptimization process preceding evolution driven by the optimization process ismaximum when the fixed layer has regular architecture, whereas the optimizednetwork is more synchronizable for the fixed layer having the rewiringprobability lying between the small-world transition and the random structure.
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