Networks: Optimisation and Evolution

by Peter Whittle

• ISBN13: 9780521871006
• ISBN10: 052187100X
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-04-30
• Publisher: Cambridge University Press

Summary

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 Bendsøe 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.

Table of Contents

Tour dÆhorizon

Distribution Networks

Simple flows

Continuum formulations

Multi-class and destination-specific flows

Design optimality under variable loading

Concave costs and hierarchical structure

Road networks

Structural optimisation

Michell structures

Structures: computational experience of evolutionary algorithms

Structure design for variable loading

Artificial Neural Networks

Models and learning

Some particular nets

Oscillatory operation

Processing Networks

Queuing networks

Time-sharing networks

Communication Networks

Loss networks: optimality and robustness

Loss networks: stochastics and self-regulation

Operation of the Internet

Evolving networks and the World-wide Web

Spatial integrals for the telephone problem

Bandit and tax processes

Random graphs and polymer models

References

Index

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