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Statistical Physics of Spin Glasses and Information ProcessingAn Introduction$
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Hidetoshi Nishimori

Print publication date: 2001

Print ISBN-13: 9780198509417

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509417.001.0001

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Optimization Problems

Optimization Problems

Chapter:
(p.183) 9 Optimization Problems
Source:
Statistical Physics of Spin Glasses and Information Processing
Author(s):

Hidetoshi Nishimori

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509417.003.0009

A decision-making problem is often formulated as the minimization or maximization of a multivariable function, an optimization problem. This chapter shows that the methods of statistical mechanics are useful to study some types of optimization problems including the number partitioning, the graph partitioning, the knapsack problem, and the satisfiability problem. All these problems are shown to be formulated and solved using the theory of spin glasses, in particular the replica method. Then, discussions are continued on the mathematical properties of simulated annealing, an approximate numerical method for generic optimization problems.

Keywords:   optimization problem, cost function, replica method, satisfiability problem, number partitioning, simulated annealing

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