Share This Article:

Stochastic Process Optimization Technique

Abstract Full-Text HTML XML Download Download as PDF (Size:3170KB) PP. 3079-3090
DOI: 10.4236/am.2014.519293    5,023 Downloads   5,808 Views   Citations

ABSTRACT

The conventional optimization methods were generally based on a deterministic approach, since their purpose is to find out an accurate solution. However, when the solution space is extremely narrowed as a result of setting many inequality constraints, an ingenious scheme based on experience may be needed. Similarly, parameters must be adjusted with solution search algorithms when nonlinearity of the problem is strong, because the risk of falling into local solution is high. Thus, we here propose a new method in which the optimization problem is replaced with stochastic process based on path integral techniques used in quantum mechanics and an approximate value of optimal solution is calculated as an expected value instead of accurate value. It was checked through some optimization problems that this method using stochastic process is effective. We call this new optimization method “stochastic process optimization technique (SPOT)”. It is expected that this method will enable efficient optimization by avoiding the above difficulties. In this report, a new optimization method based on a stochastic process is formulated, and several calculation examples are shown to prove its effectiveness as a method to obtain approximate solution for optimization problems.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Yoshida, H. , Yamaguchi, K. and Ishikawa, Y. (2014) Stochastic Process Optimization Technique. Applied Mathematics, 5, 3079-3090. doi: 10.4236/am.2014.519293.

References

[1] Kirkpatrick, S., Gelatt Jr., C.D. and Vecchi, M.P. (1983) Optimization by Simulated Annealing. Science, 220, 671-680.
http://dx.doi.org/10.1126/science.220.4598.671
[2] Terasaki, M., Kondo, M., Yoshida, H., Yamaguchi, K. and Ishikawa, Y. (2004) Integrated Optimization of Airplane Design and Flight Trajectory by New Optimization Method Using a Stochastic Process. In: CONPUTATIONAL MECHANICS WCCM VI in Conjunction with APCOM’04, Tsinghua University Press & Springer-Verlag, Beijing, 328.
[3] Yoshida, H., Konno, T., Yamaguchi, K. and Ishikawa, Y. (2005) New Optimization Method Using Stochastic Process Based on Path Integral. Journal of the Japan Society for Computational Methods in Engineering, 5, 145-150. (in Japanese)
[4] Yoshida, H., Yamaguchi, K. and Ishikawa, Y. (2006) Application of a New Optimization Method for System Design. Joint 3rd International Conference on Soft Computing and Intelligent Systems (SCIS) and 7th International Symposium on Advanced Intelligent Systems (ISIS), Tokyo, 20-24 September 2006, 1542-1547.
[5] Yoshida, H., Yamaguchi, K. and Ishikawa, Y. (2007) Design Tool Using a New Optimization Method Based on a Stochastic Process. Transactions of the Japan Society for Aeronautical and Space Sciences, 49, 220-230.
http://dx.doi.org/10.2322/tjsass.49.220
[6] Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path Integrals. McGraw-Hill, New York.
[7] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equation of State Calculations by Fast Computing Machines. Journal of Chemical Physics, 21, 1087-1092.
http://dx.doi.org/10.1063/1.1699114
[8] Nakane, M., Kobayashi, D., Yoshida, H. and Ishikawa, Y. (2009) Feasibility Study on Single Stage to Orbit Space Plane with RBCC Engine. 16th AIAA/DLR/DGLR International Space Planes and hypersonic Systems and Technologies Conference, Bremen, AIAA 2009-7331.
http://dx.doi.org/10.2514/6.2009-7331
[9] Ishimori, Y., Nakane, M., Ishikawa, Y., Yoshida, H. and Yamaguchi, K. (2011) Feasibility Study for Spaceplane’s Concepts in Ascent Phase Using the Optimization Method. Journal of the Japan Society for Aeronautical and Space Sciences, 59, 291-297. (in Japanese)
http://dx.doi.org/10.2322/jjsass.59.291
[10] Suzuki, S. and Kawamura, N. (1996) Simultaneous Optimization of Sailplane Design and Its Flight Trajectory. Journal of Aircraft, 33, 567-571.
http://dx.doi.org/10.2514/3.46982

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.