Networks

Optimisation and Evolution

Peter Whittle (University of Cambridge)

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English

Cambridge University Press
12 June 2007

Mathematics & Sciences; Optimisation; Neural networks & fuzzy systems

Series: Cambridge Series in Statistical and Probabilistic Mathematics

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation 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 Bendsøe and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the World Wide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

By: Peter Whittle (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: No. 21
Dimensions: Height: 260mm, Width: 185mm, Spine: 18mm
Weight: 770g
ISBN: 9780521871006
ISBN 10: 052187100X
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Pages: 282
Publication Date: 12 June 2007
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Peter Whittle is Professor Emeritus at the University of Cambridge. From 1973 to 1986 he was Director of the Statistical Laboratory, Cambridge. He is a Fellow of the Royal Society and this is his 11th book.

Reviews for Networks: Optimisation and Evolution

Review of the hardback: '... a remarkable book ... a pleasure to read ... plenty of interesting results, ideas and inspiration.' Hartmut Noltemeier, Zentralblatt MATH