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Solving Systems of Nonlinear Equations Using an Innovative Hybrid Algorithm

Abstract

In a variety of engineering applications and numerical computation, system of nonlinear equations (SNLEs) is one of the greatest remarkable problems. Among successful metaheuristic algorithms, particle swarm optimization (PSO) and differential evolution (DE) effectively employed in different optimization areas due to their powerful search capacity and simple structure. However, in solving complex optimization problems, still they have some shortcomings such as premature convergence and low search efficiency. An innovative hybrid algorithm of PSO and DE (named ihPSODE) present in this paper, for finding the solution of SNLEs. Besides, a novel inertia weight, acceleration factor and position update structure is adopted in nPSO to increase the population diversity as well as a novel mutation approach and crossover rate is implemented in nDE to help particles escape away from local optima. After population calculation according the fitness function cost recognize the top half member with discard rest half and apply nPSO which help to sustain exploration and exploitation competency of the algorithm. Furthermore, to achieve rapid convergence and fine stability, apply nDE on offspring created by nPSO. The population resultant by nPSO and nDE are combined for repetition. The proficiency of the presented algorithms (nPSO, nDE and ihPSODE) is examined on 23 basic unconstrained benchmark function and 19 scalable high-dimensional continuous functions (200 and 500 dimensions) then solved 7 multifaceted SNLEs. The simulation and relative results have indicated that the presented algorithms offer significant and reasonable performances.

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Acknowledgements

Heartfelt thanks to the Editor in Chief and Reviewers for their highly constructive and insightful suggestions to improve quality of the manuscript.

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Correspondence to Pooja Verma.

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Verma, P., Parouha, R.P. Solving Systems of Nonlinear Equations Using an Innovative Hybrid Algorithm. Iran J Sci Technol Trans Electr Eng (2022). https://doi.org/10.1007/s40998-022-00527-z

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Keywords

  • System of nonlinear equations
  • Metaheuristics algorithm
  • Hybrid algorithm