Numerical solution of nonlinear equations systems with improved meta-heuristic ARO algorithm

Articles in Press

Document Type : Original Article

Authors

Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran.

Abstract

In the field of numerical analysis, one of the most difficult problems to solve is nonlinear equations. Traditional numerical techniques like Newton's methods and their variations typically demand a well-informed initial guess to successfully solve these nonlinear systems. An improper initial guess can significantly hinder the performance and convergence of these methods, making it difficult and time-consuming to achieve the desired results in practice. To overcome these issues, this paper presents a novel approach that employed the Improved ARO (IARO) meta-heuristic algorithm for solving nonlinear equation systems numerically. Given that solving nonlinear equation systems can be transformed into an optimization problem, meta-heuristic algorithms exhibit strong potential for finding solutions efficiently. The ARO meta-heuristic algorithm, inspired by the feeding behavior of rabbits, has demonstrated its ability to solve intricate optimization problems within acceptable time. In the proposed method, the ARO algorithm is improved with adding a memory table to have a suitable performance for solving nonlinear equation systems. To assess the effectiveness of the proposed method, it is applied to solve several complex nonlinear equations. The results clearly demonstrate the robust performance of the approach.

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Soft Computing Journal

Articles in Press, Accepted Manuscript
Available Online from 23 October 2024

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History

  • Receive Date: 05 May 2024
  • Revise Date: 20 September 2024
  • Accept Date: 22 October 2024

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