Optimizing Multilayer Networks Through Time-Dependent Decision-Making: A Comparative Study.

Abstract

This research highlights the importance of accurately analyzing real-world multilayer network problems and introduces effective solutions. Whether simulating protein-protein network, transportation network, or a social network, representation and analysis over these networks are crucial. Multilayer networks, that contain added layers, may undergo dynamic transformations over time akin to single-layer networks that experience changes over time. These dynamic networks, that expand and contract, can be optimized by guidance from human operators if the transient changes are known and can be controlled. For the expansion and contraction of networks, this study introduces two distinct algorithms designed to make optimal decisions across dynamic changes of a multilayer network. The main strategy is to minimize the standard deviation across betweenness centrality of the edges in a complex network. The approaches we introduce incorporate diverse constraints into a multilayer weighted network, probing the network's expansion or contraction under various conditions represented as objective functions. The addition of changing of objective function enhances the model's adaptability to solve a wide array of problem types. In this way, complex network structures representing real-world problems can be mathematically modeled which makes it easier to make informed decisions.