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Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions

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Abstract

Geometric programming is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a geometric programming problem are deterministic and accurate. However, in the real-world geometric programming problem, the parameters are frequently inaccurate and ambiguous. To tackle the ambiguity, this paper investigates the geometric programming problem in an uncertain environment, with the coefficients as triangular and trapezoidal twofold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated twofold uncertainties to propose triangular and trapezoidal twofold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal twofold uncertain variables into singlefold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the geometric programming problem with twofold uncertainty into the geometric programming problem with singlefold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced singlefold uncertain geometric programming problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures.

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Data sharing is not applicable to this article as no datasets were generated. A random data set is taken for the numerical example given in this paper.

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Acknowledgements

The authors are extremely thankful to the editor and anonymous reviewers for their insightful comments and suggestions. The first author is thankful to CSIR for financial support of this work through file No: 09\1059(0027)\2019-EMR-I.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India

    Tapas Mondal, Akshay Kumar Ojha & Sabyasachi Pani

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  1. Tapas Mondal
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  2. Akshay Kumar Ojha
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  3. Sabyasachi Pani
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Correspondence to Tapas Mondal.

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Mondal, T., Ojha, A.K. & Pani, S. Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions. J Optim Theory Appl 200, 978–1016 (2024). https://doi.org/10.1007/s10957-023-02347-5

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  • DOI: https://doi.org/10.1007/s10957-023-02347-5

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