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April  2012, 8(2): 493-505. doi: 10.3934/jimo.2012.8.493

## Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive

 1 School of Mathematical Sciences and Computing Technology, Central South University, Hunan Changsha, 410083, China 2 School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083

Received  February 2011 Revised  December 2011 Published  April 2012

In this paper, a polymorphic uncertain nonlinear programming (PUNP) model is constructed to formulate the problem of maximizing the V-belt's fatigue life according to the practical engineering design conditions. The model is converted into an equivalent interval programming only involved with interval parameters for any given degree of membership and confidence level. Then, a deterministic equivalent formulation (DEF) for the original model is obtained based on the concept of possibility degree for the order of two interval numbers. An algorithm, called sampling based algorithm, is developed to find a robust optimal design scheme for maximizing the fatigue life of the V-belt. Case study is employed to demonstrate the validity and the practicability of the constructed model and the algorithm.
Citation: Shaojun Zhang, Zhong Wan. Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive. Journal of Industrial & Management Optimization, 2012, 8 (2) : 493-505. doi: 10.3934/jimo.2012.8.493
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##### References:
 [1] H. T. Banks, R. A. Everett, Neha Murad, R. D. White, J. E. Banks, Bodil N. Cass, Jay A. Rosenheim. Optimal design for dynamical modeling of pest populations. Mathematical Biosciences & Engineering, 2018, 15 (4) : 993-1010. doi: 10.3934/mbe.2018044 [2] Xiaohu Qian, Min Huang, Wai-Ki Ching, Loo Hay Lee, Xingwei Wang. Mechanism design in project procurement auctions with cost uncertainty and failure risk. Journal of Industrial & Management Optimization, 2019, 15 (1) : 131-157. doi: 10.3934/jimo.2018036 [3] K.F.C. Yiu, K.L. Mak, K. L. Teo. Airfoil design via optimal control theory. Journal of Industrial & Management Optimization, 2005, 1 (1) : 133-148. doi: 10.3934/jimo.2005.1.133 [4] Boris P. Belinskiy. Optimal design of an optical length of a rod with the given mass. Conference Publications, 2007, 2007 (Special) : 85-91. doi: 10.3934/proc.2007.2007.85 [5] Yannick Privat, Emmanuel Trélat. Optimal design of sensors for a damped wave equation. Conference Publications, 2015, 2015 (special) : 936-944. doi: 10.3934/proc.2015.0936 [6] Wei Xu, Liying Yu, Gui-Hua Lin, Zhi Guo Feng. Optimal switching signal design with a cost on switching action. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2019068 [7] Xueling Zhou, Bingo Wing-Kuen Ling, Hai Huyen Dam, Kok-Lay Teo. Optimal design of window functions for filter window bank. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020014 [8] Bin Li, Kok Lay Teo, Cheng-Chew Lim, Guang Ren Duan. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1101-1117. doi: 10.3934/dcdsb.2011.16.1101 [9] Jesús Fabián López Pérez, Tahir Ekin, Jesus A. Jimenez, Francis A. Méndez Mediavilla. Risk-balanced territory design optimization for a Micro finance institution. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2018176 [10] Yingjing Shi, Rui Li, Honglei Xu. Control augmentation design of UAVs based on deviation modification of aerodynamic focus. Journal of Industrial & Management Optimization, 2015, 11 (1) : 231-240. doi: 10.3934/jimo.2015.11.231 [11] Robert Ebihart Msigwa, Yue Lu, Xiantao Xiao, Liwei Zhang. A perturbation-based approach for continuous network design problem with emissions. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 135-149. doi: 10.3934/naco.2015.5.135 [12] Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435 [13] Martha Garlick, James Powell, David Eyre, Thomas Robbins. Mathematically modeling PCR: An asymptotic approximation with potential for optimization. Mathematical Biosciences & Engineering, 2010, 7 (2) : 363-384. doi: 10.3934/mbe.2010.7.363 [14] Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074 [15] Xinwen Luo, Weize Liu, Zhiyi Huo, Dayong Xu. Modeling and control algorithm design for power-assisted steering stability of electric vehicle. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020205 [16] Harish Garg. Solving structural engineering design optimization problems using an artificial bee colony algorithm. Journal of Industrial & Management Optimization, 2014, 10 (3) : 777-794. doi: 10.3934/jimo.2014.10.777 [17] Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095 [18] Yuhe Du, Jianwei Ji, Yu Liao, Yichu Liu. Design of energy storage coordination optimization algorithm for distributed power distribution network operation planning. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020206 [19] Lars Grüne, Manuela Sigurani. Numerical event-based ISS controller design via a dynamic game approach. Journal of Computational Dynamics, 2015, 2 (1) : 65-81. doi: 10.3934/jcd.2015.2.65 [20] Jae Man Park, Gang Uk Hwang, Boo Geum Jung. Design and analysis of an adaptive guard channel based CAC scheme in a 3G-WLAN integrated network. Journal of Industrial & Management Optimization, 2010, 6 (3) : 621-639. doi: 10.3934/jimo.2010.6.621

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