Generalized network design problems

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Combinatorial optimization encompasses a range of problems with significant applications in fields like transportation, telecommunications, and computer networking. Over recent decades, substantial advancements have been made in theory, algorithms, and applications. A key aspect of combinatorial optimization involves generalizing network design problems on clustered graphs, where feasibility constraints are defined by clusters rather than individual nodes. These are known as generalized network design problems (GNDPs). This monograph aims to present a comprehensive overview of mathematical models, methods, propositions, and algorithms related to GNDPs. It includes seven chapters, starting with an introduction and followed by detailed examinations of various generalized network design problems, including the generalized minimum spanning tree, generalized traveling salesman, railway traveling salesman, generalized vehicle routing, generalized fixed-charge network design, and generalized minimum vertex-biconnected network problems. The content is tailored for researchers, practitioners, and graduate students in operations research, optimization, applied mathematics, and computer science. Additionally, the practical significance of the discussed problems will attract interest from researchers in other disciplines.