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An enhanced nonlinear interval number programming method considering correlation of interval variables

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Abstract

Based on decoupling strategy, a novel efficient method is proposed to solve the nonlinear interval uncertainty optimization problem with correlated interval design variables or parameters. This method is applicable to cases where both objective function and constraints are nonlinear with uncertain parameters, and design variables and parameters can be correlated or independent. The uncertainty of design variables and interval parameters is expressed by a multidimensional parallelepiped model, with which the correlated variables and parameters can be converted into independent interval parameters, thus constituting the traditional interval optimization model for independent interval parameters. Based on the idea of sequential optimization and reliability assessment (SORA), the two-layer nested optimization involved in the above interval optimization model can be converted into a single loop problem which can be solved efficiently by the sequential deterministic optimization algorithm. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed model.

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Funding

This work is supported by the Open Funds for State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, China (Grant No. 31515010).

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Authors and Affiliations

  1. College of Material Science and Engineering, Central South University of Forestry and Technology, Changsha, 410004, People’s Republic of China

    H. C. Xie

  2. College of Mechanical and Electrical Engineering, Central South University of Forestry and Technology, Changsha, 410004, People’s Republic of China

    D. H. Liao

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  1. H. C. Xie
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  2. D. H. Liao
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Correspondence to D. H. Liao.

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Xie, H.C., Liao, D.H. An enhanced nonlinear interval number programming method considering correlation of interval variables. Struct Multidisc Optim 60, 2021–2033 (2019). https://doi.org/10.1007/s00158-019-02307-6

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  • DOI: https://doi.org/10.1007/s00158-019-02307-6

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