Application of finite sampling points in probability based multi – objective optimization by means of the uniform experimental design
Abstract
Introduction/purpose: An approximation for assessing a definite integral is continuously an attractive topic owing to its practical needs in scientific and engineering areas. An efficient approach for calculating a definite integral with a small number of sampling points was newly developed to get an approximate value for a numerical integral with a complicated integrand. In the present paper, an efficient approach with a small number of sampling points is combined to the novel probability–based multi– objective optimization (PMOO) by means of uniform experimental design so as to simplify the complicated definite integral in the PMOO.
Methods: The distribution of sampling points within its single peak domain is deterministic and uniform, which follows the rules of the uniform design method and good lattice points; the total preferable probability is the unique and deterministic index in the PMOO.
Results: The applications of the efficient approach with finite sampling points in solving typical problems of PMOO indicate its rationality and convenience in the operation.
Conclusion: The efficient approach with finite sampling points for assessing a definite integral is successfully combined with PMOO by means of the uniform design method and good lattice points.
References
Fang, K. 1980. Uniform design — Application of Number Theory Method in Experimental Design. Acta Mathematicae Applicatea Sinica, 3(4), pp.363-272..
Fang, K-T., Liu, M-Q., Qin, H. & Zhou, Y-D. 2018. Theory and Application of Uniform Experimental Designs. Beijing: Science Press & Singapore: Springer Nature. Available at: https://doi.org/10.1007/978-981-13-2041-5
Fang, K-T. & Wang, Y. 1994. Number-theoretic Methods in Statistics. London, UK: Chapman & Hall. ISBN: 0-412-46520-5.
Hua, L-K. & Wang, Y. 1981. Applications of Number Theory to Numerical Analysis. Berlin & New York: Springer-Verlag & Beijing: Science Press. ISBN: 9783540103820.
Huang, B. & Chen, D. 2009. Effective Pareto Optimal Set of Multi-objective Optimization Problems. Computer & Digital Engineering, 37(2), pp.28-34 [online]. Available at: https://caod.oriprobe.com/articles/17362139/Effective_Pareto_Optimal_Set_of_Multi_Objective_Op.htm [Accessed: 20 March 2022].
Paskov, S.H. 1996. New methodologies for valuing derivatives. In: Pliska, S. & Dempster, M. & (Eds.) Mathematics of Derivative Securities, pp.545-582. Cambridge: Isaac Newton Institute & Cambridge University Press. Available at: https://doi.org/10.7916/D8TB1FRJ
Paskov, S.H. & Traub, J.F. 1995. Faster valuation of financial derivatives. Journal of Portfolio Management 22(1), pp.113-120. Available at: https://doi.org/10.3905/jpm.1995.409541
Qu, X., Lu, N., & Meng, X. 2004. Multi-objective Fuzzy Optimization of Tower Crane Boom Tie Rods. Journal of Mechanical Transmission, 28(3), pp.38-40 [online]. Available at: https://caod.oriprobe.com/articles/7413876/Fuzzy_Optimization_of_Arm_Link_Rod_in_Tower_Crane.htm [Accessed: 20 March 2022].
Ripley, B.D. 1981. Spatial Statistics. Hoboken, NJ: John Wiley & Sons. ISBN: 0-47169116-X.
Sloan, I.H. & Wozniakowski, H. 1998. When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals?. Journal of Complexity, 14(1), pp.1-33. Available at: https://doi.org/10.1006/jcom.1997.0463
Tezuka, S. 1998. Financial applications of Monte Carlo and Quasi-Monte Carlo methods. In: Hellekalek, P. & Larcher, G. (Eds.) Random and Quasi-Random Point Sets. Lecture Notes in Statistics, 138, pp.303-332. New York: Springer. Available at: https://doi.org/10.1007/978-1-4612-1702-2_7
Tezuka, S. 2002. Quasi-Monte Carlo - Discrepancy between theory and practice. In: Fang, K.T., Niederreiter, H. & Hickernell, F.J. (Eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp.124-140. Heidelberg: Springer-Verlag. Available at: https://doi.org/10.1007/978-3-642-56046-0_8
Wang, Y. & Fang, K. 2010. On number-theoretic method in statistics simulation. Science in China Series A: Mathematics, 53, pp.179-186. Available at: https://doi.org/10.1007/s11425-009-0126-3
Yu, J., Zheng, M., Wang, Y. & Teng, H. 2022. An efficient approach for calculating a definite integral with about a dozen of sampling points. Vojnotehnički glasnik/Military Technical Courier, 70(2), pp. 340-356. Available at: https://doi.org/10.5937/vojtehg70-36029
Zheng, M. 2022. Application of probability-based multi–objective optimization in material engineering. Vojnotehnički glasnik/Military Technical Courier, 70(1), pp.1-12. Available at: https://doi.org/10.5937/vojtehg70-35366
Zheng, M., Teng, H., Yu, J., Cui, Y. & Wang, Y. 2022. Probability-Based Multi-objective Optimization for Material Selection. Singapore: Springer. ISBN: 978-981-19-3350-9.
Zheng, M., Wang, Y. & Teng, H. 2021. A New "Intersection" Method for Multi-objective Optimization in Material Selection. Tehnički glasnik, 15(4), pp.562-568. Available at: https://doi.org/10.31803/tg-20210901142449
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