Abstract
The inherent shortcomings of previously proposed multi-objective optimization methods are employing “additive” algorithm for the normalized evaluation index and weighting factor, which implies to take the form of “union” in the spirit of set theory. In fact, for the evaluation of “simultaneous optimization of multi-performance utility index”, the form of “intersection” in set theory and “joint probability” in probability theory should be more suitable for the problem. The viewpoint of system theory is consistent with this understanding as well. In this chapter, the new idea of preferable probability is introduced to reflect the degree of preference of the candidate’s utility in the selection of multi-objective optimization in viewpoint of system theory; all the utility indexes of candidate schemes are divided into two types, i.e., the beneficial type and the unbeneficial type for the selection of the schemes; each utility index of the candidate scheme contributes a partial preferable probability quantitatively, and the overall/total preferable probability of a candidate scheme is the product of all partial preferable probabilities in the spirit of probability theory, which thus transfers the multi-objective optimization problem into an overall (integrated) single-objective optimization issue naturally. The total preferable probability is the uniquely decisive indicator in the competitive selection process. In addition, examples of applications in material selection and some other businesses in broader and more general fields are given, and the results show the effectiveness of the new methodology.
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References
M.F. Ashby, Materials Selection in Mechanical Design, 4th edn. (Butterworth–Heinemann, Burlington, 2011)
M.M. Farag, Materials and Process Selection for Engineering Design, 4th edn. (CRC Press, New York, 2021)
S. Opricovic, G.H. Tzeng, Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156, 445–455 (2004)
A. Shanian, O. Savadogo, Multiple-criteria decision support analysis for material selection of metallic dipolar plate for polymer electrolyte fuel cell. J. Power Source 159, 1095–1104 (2006)
M.B. Babanli, F. Prima, P. Vermaut, L.D. Demchenko, A.N. Titenko, S.S. Huseynov, R.J. Hajiyev, V.M. Huseynov, in Advances in Intelligent Systems and Computing 896, 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing—ICAFS–2018, ed. by R.A. Aliev, J. Kacprzyk, W. Pedrycz, M. Jamshidi, F.M. Sadikoglu. Material Selection Methods: A Review (Springer Nature, Cham, 2019), pp. 929–936. https://doi.org/10.1007/978-3-030-04164-9_123
B.M. Ayyub, R.H. McCuen, Probability, Statistics, and Reliability for Engineers and Scientists, 3rd edn. (CRC Press, Taylor & Francis Group, A Chapman & Hall Book, Boca Raton, 2011) (978-1-4398-9533-7) (eBook—PDF)
W. Yang, S. Chon, C. Choe, J. Yang, Materials selection method using TOPSIS with some popular normalization methods. Eng. Res. Express 3, 015020 (2021)
V. Modanloo, A. Doniavi, R. Hasanzadeh, Application of multi criteria decision making methods to select sheet hydroforming process parameters. Decis. Sci. Lett. 5(3), 349–360 (2016)
M. Moradian, V. Modanloo, S. Aghaiee, Comparative analysis of multi criteria decision making techniques for material selection of brake booster valve body. J. Traffic. Trans. Eng. 6, 526–534 (2019). https://doi.org/10.1016/j.jtte.2018.02.001
V. Modanloo, V. Alimirzaloo, M. Elyasi, Multi-objective optimization of the stam** of titanium bipolar plates for fuel cell. Int. J. Adv. Des. Manuf. Technol. 12(4), 1–8 (2019)
I.Y. Kim, O. de Weck, Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation. Struct. Multidisc. Opt. 31(2), 105–116 (2006)
J. Ye, System science (Sichuan Academy of Social Sciences Press, Chengdu, 1987)
D. Wang, Probability Theory and Mathematical Statistics (Bei**g Institute of Technology Press, Bei**g, 2020)
G. Derringer, R. Suich, Simultaneous optimization of several response variables. J. Qual. Technol. 12, 214–219 (1980). https://doi.org/10.1080/00224065.1980.11980968
L.R. Jorge, B.L. Yolanda, T. Diego, P.L. Mitzy, R.B. Ivan, Optimization of multiple response variables using the desirability function and a Bayesian predictive distribution. Res. Comput. Sci. 13, 85–95 (2017)
M.A. Maleque, M.S. Salit, Materials Selection and Design (Springer, Heidelberg, 2013), pp.81–98
K. Rajnish, J. Jagadish, R. Amitava, Selection of material for optimal design using multi-criteria decision making. Proc. Mater. Sci. 6, 590–596 (2014)
M. Zheng, Y. Wang, H. Teng, in 7th Virtual International Conference on Science, Technology and Management in Energy Proceedings. Applications of “Intersection” Multi-objective Optimization in Scheme Selection of Energy Engineering (Serbia, Belgrade, 2021), pp. 89–95
X. Wang, S. Zou, B. Pang, The assessing method on site—choosing of NPP about outside artificial event based on fuzzy optimal selection. Value Eng. 4, 8–10 (2009). https://doi.org/10.14018/j.cnki.cn13-1085/n.2009.04.002
M. Chen, X. Lu, Q. Zhu, L. Xu, Evaluation of common chemotherapy regimens in advanced non-small cell lung adenocarcinoma based on multi-attribute utility theory. Chin. J. Drug Appl. Monitor. 18(1), 1–4 (2021)
L. Yang, X. Gao, J. He, A comprehensive method for effectiveness evaluation of a fighter plane. J. Northwestern Polytech. Univ. 21(1), 42–45 (2003)
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Zheng, M., Yu, J., Teng, H., Cui, Y., Wang, Y. (2024). Fundamental Principle of Probability-Based Multi-objective Optimization and Applications. In: Probability-Based Multi-objective Optimization for Material Selection. Springer, Singapore. https://doi.org/10.1007/978-981-99-3939-8_3
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