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 & Management Optimization, 2012, 8 (1) : 103-115. doi: 10.3934/jimo.2012.8.103
References:
[1]

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W. M. Frank, "Tropical Cyclone Formation. A Global View of Tropical Cyclones,", Edited by R. L. Elsberry, (1987), 53.   Google Scholar

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F. Glover, Future paths for integer programming and links to artificial intelligence,, Computers and Operations Research, 13 (1986), 533.  doi: 10.1016/0305-0548(86)90048-1.  Google Scholar

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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.  doi: 10.3934/jimo.2010.6.177.  Google Scholar

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J. H. Holland, "Adaptation in Natural and Artificial System: An Introductory Analysis with Application to Biology, Control, and Artificial Intelligence,", University of Michigan Press, (1975).   Google Scholar

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W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search,, Journal of Global Optimization, 14 (1999), 331.  doi: 10.1023/A:1008382309369.  Google Scholar

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D. Karaboga, "An Idea Based on Honey Bee Swarm for Numerical Optimization,", Technical Report-TR06, (2005).   Google Scholar

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J. J. Moré and Z. Wu, "Global Smoothing and Continuation for Large-Scale Molecular Optimization,", Argonne National Laboratory, (1995), 539.   Google Scholar

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R. A. Pielke, Jr. and R. A. Pielke, Sr., "Hurricanes: Their Nature and Impacts on Society,", John Wiley & Sons Press, (1997), 68.   Google Scholar

[19]

F. Schoen, A wide class of test functions for global optimization,, in, (1989), 51.   Google Scholar

[20]

A. Törn, M. M. Ali and S. Viitanen, Stochastic global optimization: Problem classes and solution techniques,, Journal of Global Optimization, 14 (1999), 437.  doi: 10.1023/A:1008395408187.  Google Scholar

[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.  doi: 10.3934/jimo.2011.7.183.  Google Scholar

show all references

References:
[1]

Ş.İ. Birbil and S.-C. Fang, An electromagnetism-like mechanism for global optimization,, Journal of Global Optimization, 25 (2003), 263.  doi: 10.1023/A:1022452626305.  Google Scholar

[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.  doi: 10.1007/s10898-004-8270-3.  Google Scholar

[3]

E. W. Cowan, "Basic Electromagnetism,", Academic Press, (1968).   Google Scholar

[4]

L. David, "Encyclopedia of Hurricanes, Typhoons, and Cyclones,", Facts on File, (2008), 112.   Google Scholar

[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.  doi: 10.1023/A:1008384329041.  Google Scholar

[6]

L. C. W. Dixon and G. P. Szegö, eds., "Towards Global Optimization,", Vol. 2, (1978), 1.   Google Scholar

[7]

M. Dorigo, "Optimization, Learning, and Natural Algorithms,", Ph.D Thesis, (1992).   Google Scholar

[8]

N. Forbes, "Imitation of Life: How Biology is Inspiring Computing,", MIT Press, (2004).   Google Scholar

[9]

W. M. Frank, "Tropical Cyclone Formation. A Global View of Tropical Cyclones,", Edited by R. L. Elsberry, (1987), 53.   Google Scholar

[10]

F. Glover, Future paths for integer programming and links to artificial intelligence,, Computers and Operations Research, 13 (1986), 533.  doi: 10.1016/0305-0548(86)90048-1.  Google Scholar

[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.  doi: 10.3934/jimo.2010.6.177.  Google Scholar

[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, (1975).   Google Scholar

[13]

W. Huyer and A. Neumaier, Global optimization by multilevel coordinate search,, Journal of Global Optimization, 14 (1999), 331.  doi: 10.1023/A:1008382309369.  Google Scholar

[14]

D. Karaboga, "An Idea Based on Honey Bee Swarm for Numerical Optimization,", Technical Report-TR06, (2005).   Google Scholar

[15]

J. Kennedy and R. Eberhart, Particle swarm optimization,, in, (1995), 1942.   Google Scholar

[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.  doi: 10.1063/1.1699114.  Google Scholar

[17]

J. J. Moré and Z. Wu, "Global Smoothing and Continuation for Large-Scale Molecular Optimization,", Argonne National Laboratory, (1995), 539.   Google Scholar

[18]

R. A. Pielke, Jr. and R. A. Pielke, Sr., "Hurricanes: Their Nature and Impacts on Society,", John Wiley & Sons Press, (1997), 68.   Google Scholar

[19]

F. Schoen, A wide class of test functions for global optimization,, in, (1989), 51.   Google Scholar

[20]

A. Törn, M. M. Ali and S. Viitanen, Stochastic global optimization: Problem classes and solution techniques,, Journal of Global Optimization, 14 (1999), 437.  doi: 10.1023/A:1008395408187.  Google Scholar

[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.  doi: 10.3934/jimo.2011.7.183.  Google Scholar

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