Networks Optimisation and Evolution

Point-to-point vs. hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimizing design - nearly all work concerns optimizing flow assuming a given design. This foundational book tackles optimization of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an arterial or hierarchical net. Its determination requires a continuum formulation, which can however be simplified once a discrete structure begins to emerge. Connections are made with the masterly work of Bends?e and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the Worldwide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

Tour d'horizon; Part I. Distribution Networks: 1. Simple flows; 2. Continuum formulations; 3. Multi-class and destination-specific flows; 4. Design optimality under variable loading; 5. Concave costs and hierarchical structure; 6. Road networks; 7. Structural optimisation: Michell structures; 8. Structures: computational experience of evolutionary algorithms; 9. Structure design for variable loading; Part II. Artificial Neural Networks: 10. Models and learning; 11. Some particular nets; 12. Oscillatory operation; Part III. Processing Networks: 13. Queuing networks; 14. Time-sharing networks; Part IV. Communication Networks: 15. Loss networks: optimality and robustness; 16. Loss networks: stochastics and self-regulation; 17. Operation of the Internet; 18. Evolving networks and the World-wide Web; Appendix 1. Spatial integrals for the telephone problem; Appendix 2. Bandit and tax processes; Appendix 3. Random graphs and polymer models; References; Index.

Foundational book on optimization of network structure, not just function, deriving comprehensible and realistic design principles. Connections are made with optimal mechanical structures, formation of bone structure, and neural, processing and communication networks, including the Internet and the Web. A masterful unification of theory from disparate fields and lessons from nature.