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Optimisation and Evolution


Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: October 2012
  • availability: Available
  • format: Paperback
  • isbn: 9781107410725

£ 53.99

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About the Authors
  • 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.

    • D'Arcy Thompson for the 21st century: path-breaking work on optimisation of network structure
    • Whittle is renowned for his fundamental work on networks and optimisation
    • Comprehensible, realistic design principles that accord with the evolution of networks in nature
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    Reviews & endorsements

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

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    Product details

    • Date Published: October 2012
    • format: Paperback
    • isbn: 9781107410725
    • length: 282 pages
    • dimensions: 244 x 170 x 15 mm
    • weight: 0.45kg
    • availability: Available
  • Table of Contents

    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

  • Author

    Peter Whittle, University of Cambridge

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