Abstract
Rescaled Simulated Annealing (RSA) has been adapted to solve combinatorial optimization problems in which the available computational resources are limited. Simulated Annealing (SA) is one of the most popular combinatorial optimization algorithms because of its convenience of use and because of the good asymptotic results of convergence to optimal solutions. However, SA is too slow to converge in many problems. RSA was introduced by extending the Metropolis procedure in SA. The extension rescales the state's energy candidate for a transition before applying the Metropolis criterion. The rescaling process accelerates convergence to the optimal solutions by reducing transitions from high energy local minima. In this paper, structural optimization examples using RSA are provided. Truss structures of which design variables are discrete or continuous are optimized with stress and displacement constraints. The optimization results by RSA are compared with the results from classical SA. The comparison shows that the numbers of optimization iterations can be effectively reduced using RSA.
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References
Aarts, E. and Kost, J., 1989, Simulated Annealing and Boltzmann Machines, John Wily & Sons Inc.
Aarts, E. and van Laarhoven, P., 1987, Simulated Annealing : Theory and Applications, Kluwer Academic Publishers.
Balling, R. J., 1991, “Optimal Steel Frame Design by Simulated Annealing,”Journal of Structural Engineering, Vol. 117, pp. 1780–1795.
Bennage, W. A. and Dhingra, A. K., 1995, “Single and Multi Objective Structural Optimization in Discrete-Continuous Variables using Simulated Annealing,”International Journal for Numerical Methods in Engineering, Vol. 38, pp. 2753–2773.
Cerny, V., 1985, “Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulated Algorithm,”Journal of Optimization Theory and Applications, Vol. 45, No. 1, pp. 41–51.
Cui, G. Y. and Tai, K., 2000, and Wang, Topology Optimization for Maximum Natural Frequency using Simulated Annealing and Morphological Representation, 41st AIAA Structures, Structural Dynamics and Materials Conference and Exhibit, Atlanta, GA, AIAA-2000-1393.
Gelatt, C. D., Kirkpatrick, S. and Vecchi, M. P., 1983, Optimization by Simulated Annealing, Science 220, pp. 671–680.
Haug, E. J. and Arora, J. S., 1979, Applied Optimal Design, Wiley-Interscience Publication.
Herault, L., 2000, “Rescaled Simulated Annealing-Accelerating Convergence of Simulated Annealing by Rescaling the States Energies,”Journal of Heuristics, Vol. 6, No. 2, pp. 215–252.
Ingber, L., 1995, “Adaptive Simulated Annealing : Lessons Learned,”Journal of Control and Cybernetics, Vol. 25, No. 1.
Kincaid, R. K. and Padula, S. L., 1990, Minimizing Distortion and Internal Forces in Truss Structures by Simulated Annealing, AIAA 1095-CP.
Lundy, M., 1986, Convergence of an Annealing Algorithm, Mathematical Programming, Vol. 34, pp. 111–124.
Park, J. S. and Song, S. B., 2002, “Optimization of a Composite Laminated Structure by Network-based Genetic Algorithm,”KSME International Journal, Vol. 16, No. 8, pp. 1033–1038.
Rao, S. S., 1996, Engineering Optimization Theory and Practice, 3rd Ed., John Wily & Sons Inc.
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Park, J., Ryu, M. Optimal design of truss structures by rescaled simulated annealing. KSME International Journal 18, 1512–1518 (2004). https://doi.org/10.1007/BF02990365
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DOI: https://doi.org/10.1007/BF02990365