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A Multi-Simplex Imperialist Competitive Paradigm for Solving Nonlinear Physical Systems

Javaid Ali1, Shaukat Iqbal2, Salem Alkhalaf3,*

1 Department of Mathematics, Govt. Graduate College Township, Lahore, Pakistan
2 School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan
3 Department of Computer, College of Science and Arts in Ar Rass, Qassim University, Ar Rass, Saudi Arabia

* Corresponding Author: Salem Alkhalaf. Email:

Intelligent Automation & Soft Computing 2022, 32(1), 149-166.


This paper proposes a novel gradient free multi-simplex topology fabric aided imperialist competitive algorithm (ICA) for solving nonlinear systems of algebraic equations by transforming them to equivalent global optimization problems. The high dependence of traditional gradient based solvers of such systems on initial guesses and the Jacobeans resulting in false convergence is the main motivation behind the present work. The present work provides a mechanism for enhancing exploitation powers of imperialist search phase of the algorithm and hence improves the convergence speed. The variants emerging from the proposed approach are applied to diverse nonlinear systems arising in different scientific areas and the results so obtained are analyzed in details. Based on the analysis of empirical results on complex benchmark models, it is observed that the proposed enhancement of ICA has not only boosted the problem solving power of the imperialist system when applied multidimensional nonlinear physical systems but also emerged as an efficient gradient/initial guess free alternative solver with high accuracy for nonlinear systems.


Cite This Article

J. Ali, S. Iqbal and S. Alkhalaf, "A multi-simplex imperialist competitive paradigm for solving nonlinear physical systems," Intelligent Automation & Soft Computing, vol. 32, no.1, pp. 149–166, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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