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October  2012, 8(4): 1039-1056. doi: 10.3934/jimo.2012.8.1039

State transition algorithm

1. 

School of Information Science and Engineering, Central South University, Changsha, 410083, China

Received  March 2011 Revised  April 2012 Published  September 2012

In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.
Citation: Xiaojun Zhou, Chunhua Yang, Weihua Gui. State transition algorithm. Journal of Industrial & Management Optimization, 2012, 8 (4) : 1039-1056. doi: 10.3934/jimo.2012.8.1039
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show all references

References:
[1]

Mathematics and Computers in Simulation, 43 (1997), 223-228. doi: 10.1016/S0378-4754(96)00069-9.  Google Scholar

[2]

in "Proceedings of IEEE Congress on Evolutionary Computation," 1 (2003), 435-442. Google Scholar

[3]

Analytica Chimica Acta, 181 (1986), 97-106. doi: 10.1016/S0003-2670(00)85224-1.  Google Scholar

[4]

Information Sciences, 176 (2006), 937-971. doi: 10.1016/j.ins.2005.02.003.  Google Scholar

[5]

Handbook of Research on Nature Inspired Computing for Economics and Management, 2006. Google Scholar

[6]

Complex Systems, 9 (1995), 115-148.  Google Scholar

[7]

in "Annual Conference on Evolutionary Programming," San Diego, (1998), 611-616. Google Scholar

[8]

Reading: Addison-Wesley, 1989. Google Scholar

[9]

Applied Mathematics and Computation, 173 (2006), 1323-1333. doi: 10.1016/j.amc.2005.05.002.  Google Scholar

[10]

Applied Mathematical Modeling, 31 (2007), 2189-2198. doi: 10.1016/j.apm.2006.08.015.  Google Scholar

[11]

Journal of the Association for Computing Machinery(ACM), 8 (1961), 212-229. Google Scholar

[12]

in "Proceedings of IEEE International Conference on Neural Networks," IEEE Service Center, Piscataway, NJ, (1995), 1942-1948. Google Scholar

[13]

SIAM J. OPTIM., 9 (1998), 112-147.  Google Scholar

[14]

IEEE Transaction on Evolutionary Computation, 10 (2006), 281-295. Google Scholar

[15]

Computers and Chemical Engineering, 22 (1998), 427-444. Google Scholar

[16]

Journal of Industrial and Management Optimization, 4 (2008), 53-66.  Google Scholar

[17]

Automation and Remote Control, 26 (1965), 246-253.  Google Scholar

[18]

Computers Math. Applic, 23 (1992), 83-94. doi: 10.1016/0898-1221(92)90094-X.  Google Scholar

[19]

Computer Journal, 7 (1965), 308-313. Google Scholar

[20]

IEEE Transactions on Evolutionary Computation, 13 (2009), 398-417. Google Scholar

[21]

IEEE Transactions on Neural Networks, 5 (1994), 96-101. Google Scholar

[22]

Beijing: World Publishing Corporation, 2009. Google Scholar

[23]

Mathematics of Operations Research, 6 (1981), 19-30.  Google Scholar

[24]

Journal of Global Optimization, 11 (1997), 341-359. doi: 10.1023/A:1008202821328.  Google Scholar

[25]

in "Proceedings of the IEEE Congress on Evolutionary Computation," IEEE Press, Seoul, Korea, (2001), 1945-1950. Google Scholar

[26]

in "Workshop Proceedings of the Genetic and Evolutionary Computation Conference," (2010), 1731-1738. Google Scholar

[27]

in "Foundations of Genetic Algorithms" (Ed. G. J. E. Rawlins), (1991), 205-220.  Google Scholar

[28]

IEEE Transactions on Evolutionary Computation, 1 (1997), 67-82. Google Scholar

[29]

Journal of Global Optimization, 28 (2004), 229-238. doi: 10.1023/B:JOGO.0000015313.93974.b0.  Google Scholar

[30]

Wiley, 2010. Google Scholar

[31]

Beijing: Science press, 2008. Google Scholar

[32]

Journal of Industrial and Management Optimization, 7 (2011), 31-51.  Google Scholar

[33]

in "the 2nd International Conference on Digital Manufacturing and Automation(ICDMA)," (2011), 644-647. Google Scholar

[34]

in "the 2nd International Conference on Intelligent Control and Information Processing," (2011), 674-678. Google Scholar

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