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A Simulated Annealing Inequalities Solver

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Control Systems Design
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Abstract

Simulated annealing, based on the statistical mechanical annealing of solids, is a probabilistic method for generating and assessing trial points in the search space. The method is well known and has been used to find the minimum of any function. By defining an energy function for a known simulated annealing method, a probabilistic globally convergent search procedure for solving inequalities is obtained. The method is tested on some numerical test problems and some control design problems. It is found that the method has a high rate of success in finding solutions.

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References

  • Jones, D.F., S.K. Mirrazavi and M. Tamiz (2002), Multi-objective meta-heuristics: An overview of the current state-of-the-art, Eur. J. Op. Research, 137(1):1–9.

    Google Scholar 

  • Kirkpatrick, S., C.D. Gelatt, Jr. and M.P. Vecchi (1983), Optimization by simulated annealing, Science, 220:671–680.

    MathSciNet  Google Scholar 

  • Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller (1953), Equation of state calculations by fast computing machines, J. Chem. Phys., 21:1087–1092.

    Article  Google Scholar 

  • Munro, N. (1972), Design of controllers for open-loop unstable multivariable system using inverse Nyquist array, Proc. IEE, 119(9):1377–1382.

    Google Scholar 

  • Vanderbilt, D. and S.G. Louie (1984), A Monte Carlo simulated annealing approach to optimization over continuous variables, J. Comp. Physics, 56:259–271.

    MathSciNet  Google Scholar 

  • Whidborne, J.F., D.-W. Gu and I. Postlethwaite (1995), Algorithms for the method of inequalities — a comparative study, Proc. 1995 Amer. Contr. Conf., Seattle, WA, pp. 3393–3397.

    Google Scholar 

  • Whidborne, J.F., D.-W. Gu and I. Postlethwaite (1996), Simulated annealing for multi-objective control system design, IEE Proc. Control Theory and Appl., 144(6):582–588.

    Google Scholar 

  • Zakian, V. (1996), Perspectives on the principle of matching and the method of inequalities, Int. J. Control, 65(1):147–175.

    MathSciNet  MATH  Google Scholar 

  • Zakian, V. and U. Al-Naib (1973), Design of dynamical and control systems by the method of inequalities, Proc. IEE, 120(11):1421–1427.

    Google Scholar 

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© 2005 Springer-Verlag London Limited

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Whidborne, J.F. (2005). A Simulated Annealing Inequalities Solver. In: Zakian, V. (eds) Control Systems Design. Springer, London. https://doi.org/10.1007/1-84628-215-2_7

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  • DOI: https://doi.org/10.1007/1-84628-215-2_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-913-5

  • Online ISBN: 978-1-84628-215-7

  • eBook Packages: EngineeringEngineering (R0)

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