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Numerical approach to solve imprecisely defined systems using Inner Outer Direct Search optimization technique

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  • Panigrahi, Paresh Kumar
  • Nayak, Sukanta

Abstract

In this paper, the Inner–Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To validate the proposed algorithm, convergence analysis is performed. Further, three different fuzzy system of nonlinear equations are considered to demonstrate the algorithm. The fuzzy system of nonlinear equations is divided into various cases viz. fully fuzzy (when both the coefficient matrix and right-side vector are fuzzy) and only fuzzy (when either of the coefficient matrix or the right-side vector is fuzzy). For each individual case the numerical and graphical convergence of the obtained solutions were established. One electrical circuit problem is investigated to obtain the current in fuzzy environment and the same is compared with an existing method. It is observed that the closed form of the fuzzy solution contains the solution of the corresponding crisp system as well as the compared method. Finally, it can be noted that the proposed IODS approach can be applied to find the united fuzzy solutions for various science and engineering problems with easy implementation.

Suggested Citation

  • Panigrahi, Paresh Kumar & Nayak, Sukanta, 2024. "Numerical approach to solve imprecisely defined systems using Inner Outer Direct Search optimization technique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 578-606.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:578-606
    DOI: 10.1016/j.matcom.2023.08.025
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    References listed on IDEAS

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    1. Mohand Ouamer Bibi & Nacira Ikheneche & Mohand Bentobache, 2020. "A hybrid direction algorithm for solving a convex quadratic problem," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(2), pages 159-178.
    2. Iñigo L. Ansorena, 2019. "Work planning optimisation in ports: a simplex application," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 14(1), pages 146-155.
    3. Raheleh Jafari & Wen Yu, 2017. "Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-10, January.
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