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Introduction to Uncertain Optimization Design

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Numerical Simulation-based Design

Abstract

Generally, structural analysis and optimization design are implemented based on the deterministic system and models.

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References

  1. Bellman, R. E., & Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141–164.

    Article  MathSciNet  Google Scholar 

  2. Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73–79.

    Article  MathSciNet  Google Scholar 

  3. Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1, 197–206.

    Article  MathSciNet  Google Scholar 

  4. Beale, E. M. L. (1955). On minimizing a convex function subject to linear inequalities. Journal of the Royal Statistical Society, Series B (Methodological), 17(2), 173–184.

    Google Scholar 

  5. Birge, J. R., & Louveaux, F. V. (1997). Introduction to stochastic programming. New York: Springer.

    MATH  Google Scholar 

  6. Takriti, S., & Ahmed, S. (2003). On robust optimization of two-stage systems. Mathematical Programming, 99(1), 109–126.

    Article  MathSciNet  Google Scholar 

  7. Kulkiarni, A., & Shanbhag, U. V. (2012). Recourse-based stochastic nonlinear programming: properties and Bender-SQP algorithms. Computational Optimization and Application, 51(1), 77–123.

    Article  MathSciNet  Google Scholar 

  8. Du, X., & Chen, W. (2004). Sequential optimization and reliability assessment method for efficient probabilistic design. Journal of Mechanical Design, 126(2), 225–233.

    Article  Google Scholar 

  9. Cheng, G. D., Xu, L., & Jiang, L. (2006). A sequential approximate programming strategy for reliability-based structural optimization. Computers & Structures, 84(21), 1353–1367.

    Article  Google Scholar 

  10. Inuiguchi, M., & Ramik, J. (2000). Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111(1), 3–28.

    Article  MathSciNet  Google Scholar 

  11. Moore, R. E., & Moore, R. E. (1979). Methods and applications of interval analysis. Philadelphia: Siam.

    Book  Google Scholar 

  12. Ben-Haim, Y., & Elishakoff, I. (1990). Convex models of uncertainty in applied mechanics. Amsterdam: Elsevier Science Publishers.

    MATH  Google Scholar 

  13. Qiu, Z. P. (2005). The convex method of non-probabilistic set theory and its application. Beijing: National Defense Industry Press.

    Google Scholar 

  14. Jiang, C., Han, X., & Liu, G. P. (2008). A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188(1), 1–13.

    Article  MathSciNet  Google Scholar 

  15. Jiang, C., Zhang, Z. G., Zhang, Q. F., et al. (2014). A new nonlinear interval programming method for uncertain problems with dependent interval variables. European Journal of Operational Research, 238(1), 245–253.

    Article  MathSciNet  Google Scholar 

  16. Elishakoff, I., Haftka, R. T., & Fang, J. (1994). Structural design under bounded uncertainty-optimization with anti-optimization. Computers & Structures, 53(6), 1401–1405.

    Article  Google Scholar 

  17. Guo, X., Bai, W., Zhang, W., et al. (2009). Confidence structural robust design and optimization under stiffness and load uncertainties. Computer Methods in Applied Mechanics and Engineering, 198(41), 3378–3399.

    Article  MathSciNet  Google Scholar 

  18. Jiang, C., Han, X., Lu, G. Y., et al. (2011). Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Computer Methods in Applied Mechanics and Engineering, 200(33), 2528–2546.

    Article  Google Scholar 

  19. Jiang, C., Lu, G. Y., Han, X., & Bi, R. G. (2014). Some important issues on first-order reliability analysis with nonprobabilistic convex mdoels. ASME Journal of Mechanical Design, 136(3), 034501.

    Article  Google Scholar 

  20. Jiang, T., Chen, J. J., & Xu, Y. L. (2007). A semi-analytic method for calculating non-probabilistic reliability index based on interval models. Applied Mathematical Modelling, 31(7), 1362–1370.

    Article  Google Scholar 

  21. Luo, Y., Kang, Z., & Li, A. (2009). Structural reliability assessment based on probability and convex set mixed model. Computers & Structures, 87(21), 1408–1415.

    Article  Google Scholar 

  22. Qiu, Z. P., Yang, D., & Elishakoff, I. (2008). Probabilistic interval reliability of structural systems. International Journal of Solids and Structures, 45(10), 2850–2860.

    Article  Google Scholar 

  23. Jiang, C., Li, W. X., Han, X., et al. (2011). Structural reliability analysis based on random distributions with interval parameters. Computers & Structures, 89(23), 2292–2302.

    Article  Google Scholar 

  24. Jiang, C., Han, X., Li, W. X., et al. (2012). A hybrid reliability approach based on probability and interval for uncertain structures. Journal of Mechanical Design, 134(3), 031001.

    Article  Google Scholar 

  25. Ishibuchi, H., & Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48(2), 219–225.

    Article  Google Scholar 

  26. Sengupta, A., Pal, T. K., & Chakraborty, D. (2001). Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems, 119, 129–138.

    Article  MathSciNet  Google Scholar 

  27. Inuiguchi, M., & Sakawa, M. (1995). Minimax regret solution to linear programming problems with an interval objective function. European Journal of Operational Research, 86(3), 526–536.

    Article  Google Scholar 

  28. Kouvelis, P., & Yu, G. (1997). Robust discrete optimization and its applications. Boston: Kluwer Academic Publishers.

    Book  Google Scholar 

  29. Jiang, C., Han, X., & Liu, G. R. (2007). Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Computer Methods in Applied Mechanics and Engineering, 196, 4791–4800.

    Article  Google Scholar 

  30. Jiang, C., Han, X., & Liu, G. P. (2008). A sequential nonlinear interval number programming method for uncertain structures. Computer Methods in Applied Mechanics and Engineering, 197, 4250–4265.

    Article  Google Scholar 

  31. Jiang, C., Han, X., & Liu, G. P. (2008). Uncertain optimization of composite laminated plates using a nonlinear interval number programming method. Computers & Structures, 86, 1696–1703.

    Article  Google Scholar 

  32. Wu, H. C. (2007). The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. European Journal of Operational Research, 176, 46–59.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Hunan University, Changsha, Hunan, China

    Xu Han

  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan, China

    Jie Liu

Authors
  1. Xu Han
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  2. Jie Liu
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Correspondence to Xu Han .

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Han, X., Liu, J. (2020). Introduction to Uncertain Optimization Design. In: Numerical Simulation-based Design. Springer, Singapore. https://doi.org/10.1007/978-981-10-3090-1_11

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  • DOI: https://doi.org/10.1007/978-981-10-3090-1_11

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3089-5

  • Online ISBN: 978-981-10-3090-1

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