Optimization and Engineering

, Volume 15, Issue 1, pp 267–292 | Cite as

Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving

  • Zhong WanEmail author
  • Shaojun Zhang
  • Kok Lay Teo


In this paper, a polymorphic uncertain nonlinear programming (PUNP) approach is developed to formulate the problem of maximizing the capacity in a system of V-belt driving with uncertainties. The constructed optimization model is found to consist of a nonlinear objective function and some nonlinear constraints with some parameters which are of uncertain nature. These uncertain parameters are interval parameters, random interval parameters, fuzzy parameters or fuzzy interval parameters. To find a robust solution of the problem, a deterministic equivalent formulation (DEF) is established for the polymorphic uncertain nonlinear programming model. For a given satisfaction level, this DEF turns out to be a nonlinear programming involving only interval parameters. A solution method, called a sampling based interactive method, is developed such that a robust solution of the original model with polymorphic uncertainties is obtained by using standard smooth optimization techniques. The proposed method is applied into a real-world design of V-belt driving, and the results indicate that both the PUNP approach and the developed algorithm are useful to the optimization problem with polymorphic uncertainty.


Belt drives Design optimization Polymorphic uncertainty Algorithm Sampling method 



We would like to express our thanks to the anonymous referees for their suggestive comments that greatly improved the presentation of this paper.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.Department of Mathematics and StatisticsCurtin University of TechnologyPerthAustralia

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