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Generalized Cybernetic Optimization: Solving Continuous Variable Problems

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Meta-Heuristics

Abstract

Cybernetic optimization by simulated annealing (COSA) is a method of parallel processing for solving discrete optimization problems. This paper extends the theory of COSA to the continuous domain. This is done by applying the concept of probabilistic feedback control to the generation of candidate solutions in continuous variable problems. Three general principles of candidate generation are presented leading to the formulation of the candidate generation criterion and its theoretical implications. A practical method of generating candidate solutions is also presented in which the generation of candidate solutions is achieved by making the magnitude of the expected step size to candidate solutions functionally dependent on the proximity of the parallel processors in the solution space. Experimental results show that this method of generating candidate solutions accelerates the convergence of the parallel processors to the global optimum.

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References

  1. E.E. Aarts and J. Korst. Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. Wiley, 1989.

    Google Scholar 

  2. R. Azencott. Simulated Annealing: Parallelization Techniques, chapter Ch. 4 Parallel Simulated Annealing: An Overview of Basic Techniques. Wiley, 1992.

    Google Scholar 

  3. C.J.P. Bélisle. Convergence theorems for a class of simulated annealing algorithms on \({{\mathcal{R}}^{d}}\). J. of Applied Probability, 29:885–895, 1992.

    Article  Google Scholar 

  4. I. Bohachevsky, M. Johnson, and M. Stein. Generalized simulated annealing for function optimization. Technometrics, 28:209–217, 1986.

    Article  Google Scholar 

  5. M.A. Fleischer. Assessing the Performance of the Simulated Annealing Algorithm Using Information Theory. Doctoral Dissertation, Case Western Reserve University, Cleveland, Ohio, 1993.

    Google Scholar 

  6. M.A. Fleischer. Cybernetic optimization by simulated annealing: Accelerating convergence by parallel processing and probabilistic feedback control. Journal of Heuristics, 1:225–246, 1996.

    Article  Google Scholar 

  7. M.A. Fleischer and S.H. Jacobson. Information theory and the finite-time performance of the simulated annealing algorithm: Experimental results. Technical Report, 1994.

    Google Scholar 

  8. M.A. Fleischer and S.H. Jacobson. Using scaling properties in simulated annealing to prove convergence in the continuous domain. Technical Report, 1996.

    Google Scholar 

  9. J. Galambos. The Asymptotic Theory of Extreme Order Statistics. Wiley, 1978.

    Google Scholar 

  10. F.W. Glover. Future paths for integer programming and links to artificial intelligence. Computers & Operations Research, 13:533–549, 1986.

    Article  Google Scholar 

  11. F.W. Glover. Tabu thresholding: Improved search by nonmonotonic trajectories. INFORMS J. on Computing, 7:426–442, 1995.

    Article  Google Scholar 

  12. A.M. Law and W.D. Kelton. Simulation Modeling and Analysis, 2nd Ed. McGraw-Hill, 1991.

    Google Scholar 

  13. N.A. Metropolis, A. Teller, A. Rosenbluth, M. Rosenbluth, and E. Teller. Equation of state calculations by fast computing machines. J. of Chemical Physics, 21:1087–1092, 1953.

    Article  Google Scholar 

  14. D. Mitra, F. Romeo, and A. Sangiovanni-Vincentelli. Convergence and finite-time behavior of simulated annealing. Advances in Applied Probability, 18:747–771, 1986.

    Article  Google Scholar 

  15. I. Osman. Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of OR, 41:421–451, 1993.

    Article  Google Scholar 

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© 1999 Springer Science+Business Media New York

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Fleischer, M.A. (1999). Generalized Cybernetic Optimization: Solving Continuous Variable Problems. In: Voß, S., Martello, S., Osman, I.H., Roucairol, C. (eds) Meta-Heuristics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5775-3_28

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  • DOI: https://doi.org/10.1007/978-1-4615-5775-3_28

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7646-0

  • Online ISBN: 978-1-4615-5775-3

  • eBook Packages: Springer Book Archive

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