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An Efficient Sampling Approach to Multiobjective Optimization

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  • Yan Fu
  • Urmila Diwekar

Abstract

This paper presents a new approach to multiobjective optimization based on the principles of probabilistic uncertainty analysis. At the core of this approach is an efficient nonlinear multiobjective optimization algorithm, Minimizing Number of Single Objective Optimization Problems (MINSOOP), to generate a true representation of the whole Pareto surface. Results show that the computational savings of this new algorithm versus the traditional constraint method increase dramatically when the number of objectives increases. A real world case study of multiobjective optimal design of a best available control technology for Nitrogen Oxides (NOx) and Sulfur Oxides (SOx) reduction illustrates the usefulness of this approach. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Yan Fu & Urmila Diwekar, 2004. "An Efficient Sampling Approach to Multiobjective Optimization," Annals of Operations Research, Springer, vol. 132(1), pages 109-134, November.
    • Handle: RePEc:spr:annopr:v:132:y:2004:i:1:p:109-134:10.1023/b:anor.0000045279.46948.dd
    DOI: 10.1023/B:ANOR.0000045279.46948.dd
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    Citations

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    Cited by:

    1. Ellen H. Fukuda & L. M. Graña Drummond & Fernanda M. P. Raupp, 2016. "An external penalty-type method for multicriteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 493-513, July.
    2. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    3. N. Mahdavi-Amiri & F. Salehi Sadaghiani, 2017. "Strictly feasible solutions and strict complementarity in multiple objective linear optimization," 4OR, Springer, vol. 15(3), pages 303-326, September.
    4. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
    5. G. Cocchi & M. Lapucci, 2020. "An augmented Lagrangian algorithm for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 29-56, September.
    6. Julio B. Clempner, 2018. "Computing multiobjective Markov chains handled by the extraproximal method," Annals of Operations Research, Springer, vol. 271(2), pages 469-486, December.
    7. Esra Karasakal & Murat Köksalan, 2009. "Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making," Operations Research, INFORMS, vol. 57(1), pages 187-199, February.
    8. Diwekar, Urmila, 2005. "Green process design, industrial ecology, and sustainability: A systems analysis perspective," Resources, Conservation & Recycling, Elsevier, vol. 44(3), pages 215-235.
    9. Xiaopeng Zhao & Markus A. Köbis & Yonghong Yao & Jen-Chih Yao, 2021. "A Projected Subgradient Method for Nondifferentiable Quasiconvex Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 82-107, July.
    10. Rafael Lazimy, 2013. "Interactive Polyhedral Outer Approximation (IPOA) strategy for general multiobjective optimization problems," Annals of Operations Research, Springer, vol. 210(1), pages 73-99, November.

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