# American Institute of Mathematical Sciences

January  2012, 8(1): 103-115. doi: 10.3934/jimo.2012.8.103

## A tropical cyclone-based method for global optimization

 1 Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, 106, Taiwan, Taiwan 2 Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695-7906, United States

Received  October 2010 Revised  July 2011 Published  November 2011

This paper proposes a new heuristic, Tropical Cyclone-based Method (TCM), for solving global optimization problems with box constraints. TCM mimics the formation process of tropical cyclones in the atmosphere to move a set of sample points towards optimality. The formation of a tropical cyclone in nature is still not completely understood by people. Nevertheless, inspired by the known formation factors of a tropical cyclone, TCM is designed to seek optimal solutions by considering airflow, disturbance, and convection in order to traverse the solution space. Experimental results on some well-known nonlinear test functions are included. Compared with the well-known Electromagnetism-like Mechanism (EM), TCM is both effective and efficient for solving the reported test functions.
Citation: Chien-Wen Chao, Shu-Cherng Fang, Ching-Jong Liao. A tropical cyclone-based method for global optimization. Journal of Industrial and Management Optimization, 2012, 8 (1) : 103-115. doi: 10.3934/jimo.2012.8.103
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##### References:
 [1] Ş.İ. Birbil and S.-C. Fang, An electromagnetism-like mechanism for global optimization, Journal of Global Optimization, 25 (2003), 263-282. doi: 10.1023/A:1022452626305. [2] Ş.İ. Birbil, S.-C. Fang and R.-L. Sheu, On the convergence of a population-based global optimization algorithm, Journal of Global Optimization, 30 (2004), 301-318. doi: 10.1007/s10898-004-8270-3. [3] E. W. Cowan, "Basic Electromagnetism," Academic Press, New York, 1968. [4] L. David, "Encyclopedia of Hurricanes, Typhoons, and Cyclones," Facts on File, New York, (2008), 112-115. [5] M. Demirhan, L. Özdamar, L. Helvacĝu and Ş.İ. Birbil, FRACTOP: A geometric partitioning metaheuristic for global optimization, Journal of Global Optimization, 14 (1999), 415-436. doi: 10.1023/A:1008384329041. [6] L. C. W. Dixon and G. P. Szegö, eds., "Towards Global Optimization," Vol. 2, North-Holland Publishing Co., Amsterdam-New York, (1978), 1-15. [7] M. Dorigo, "Optimization, Learning, and Natural Algorithms," Ph.D Thesis, Dip. Elettronica, Politecnico di Milano, Italy, 1992. [8] N. Forbes, "Imitation of Life: How Biology is Inspiring Computing," MIT Press, MA, 2004. [9] W. M. Frank, "Tropical Cyclone Formation. A Global View of Tropical Cyclones," Edited by R. L. Elsberry, U.S. Office of Naval Research, Marine Meteorology Program, Washington, DC, (1987), 53-90. [10] F. Glover, Future paths for integer programming and links to artificial intelligence, Computers and Operations Research, 13 (1986), 533-549. doi: 10.1016/0305-0548(86)90048-1. [11] P. B. Hermanns and N. V. Thoai, Global optimization algorithm for solving bilevel programming problems with quadratic lower levels, Journal of Industrial and Management Optimization, 6 (2010), 177-196. doi: 10.3934/jimo.2010.6.177. [12] J. H. Holland, "Adaptation in Natural and Artificial System: An Introductory Analysis with Application to Biology, Control, and Artificial Intelligence," University of Michigan Press, Ann Arbor, Michigan, 1975. [13] W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search, Journal of Global Optimization, 14 (1999), 331-355. doi: 10.1023/A:1008382309369. [14] D. Karaboga, "An Idea Based on Honey Bee Swarm for Numerical Optimization," Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005. [15] J. Kennedy and R. Eberhart, Particle swarm optimization, in "IEEE International Conference on Neural Networks" Academic Press, (1995), 1942-1948. [16] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equation of state calculations by fast computing machines, Journal of Chemical Physics, 21 (1953), 1087-1092. doi: 10.1063/1.1699114. [17] J. J. Moré and Z. Wu, "Global Smoothing and Continuation for Large-Scale Molecular Optimization," Argonne National Laboratory, Illinois: Preprint MCS-P539-1095, 1995. [18] R. A. Pielke, Jr. and R. A. Pielke, Sr., "Hurricanes: Their Nature and Impacts on Society," John Wiley & Sons Press, London, (1997), 68-91. [19] F. Schoen, A wide class of test functions for global optimization, in "$3^{rd}$ International Conference on Genetic Algorithms," Academic Press, (1989), 51-60. [20] A. Törn, M. M. Ali and S. Viitanen, Stochastic global optimization: Problem classes and solution techniques, Journal of Global Optimization, 14 (1999), 437-447. doi: 10.1023/A:1008395408187. [21] L. Wang, Y. Li and L. Zhang, A differential equation method for solving box constrained variational inequality problems, Journal of Industrial and Management Optimization, 7 (2011), 183-198. doi: 10.3934/jimo.2011.7.183.
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