Simulated Annealing: Theory and Applications

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Springer Science & Business Media, Jun 30, 1987 - Business & Economics - 186 pages
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It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Oulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks or increasingly specialized topics. However, the "tree" of knowledg~ of mathematics and related fields does not grow only by putting forth new branches. It also ˇhappens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the ~d and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
  

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Contents

Introduction
1
Simulated annealing
7
22 Mathematical model of the algorithm
12
Asymptotic convergence results
17
312 Existence of the stationary distribution
18
313 Convergence of the stationary distribution
20
32 The inhomogeneous algorithm
27
322 Sufficient conditions for convergence
28
63 Probabilistic value analysis
82
64 Performance on combinatorial optimization problems
88
Chapter 7 Applications
99
72 Applications in computeraided circuit design
100
722 Placement
101
723 Routing
110
724 Other applications in computeraided circuit design
118
73 Applications in other areas
128

323 Necessary and sufficient conditions for convergence
35
The relation with statistical physics
39
42 Equilibrium dynamics
40
43 Typical behaviour of the simulated annealing algorithm
44
44 Phase transitions
48
45 Relation with spin glasses
50
Towards implementing the algorithm
55
52 Conceptually simple cooling schedules
59
53 More elaborate cooling schedules
62
54 Improvements of the generation mechanism for transitions
71
Performance of the simulated annealing algorithm
77
62 Worstcase performance results
79
732 Boltzmann machines
131
733 Miscellaneous applications
135
Some miscellaneous topics
139
811 General algorithms
140
812 Tailored algorithms
143
813 Special parallel implementations
147
82 Continuous optimization
148
822 Applications of simulated annealing to continuous problems
151
Summary and conclusions
153
Bibliography
157
Index
177
Copyright

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Page iv - SERIES EDITOR'S PREFACE Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers

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