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A study of exploratory and stability analysis of artificial electric field algorithm

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Abstract

The theoretical convergence, exploratory, and stability analysis of any heuristic algorithm is an important aspect to make it more efficient and reliable to the research community. The artificial electric field algorithm (AEFA) (Yadav et al. ,Swarm Evol Comput 48:93–108, 54) is a new optimization algorithm in the class of heuristics optimization algorithms. It is inspired by the Coulombs law of electrostatic force. In this article, a study of the convergence and stability analysis of the particle trajectory of the AEFA algorithm is established. A theoretical study of first and second-order stability of the AEFA algorithm is established which is represented by a stochastic recurrence relation. The convergence of expectation and variance of particle positions is proved and discussed in detail. Further, the boundary conditions for the convergence of expectation and variance of particle positions are established along with their first and second-order stability. These boundary conditions suggest better parameter values for the AEFA algorithm. The coefficient boundaries for particle positions associated with different kinds of oscillation behavior e.g. mono-oscillation, harmonic, and zigzagging are discussed in both the time and frequency domain. Also, the theoretical findings are validated by solving 23 benchmark optimization problems and some real-world optimization problems.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Uttarakhand, Srinagar, 246174, Uttarakhand, India

    Anita Sajwan

  2. Department of Mathematics, Dr. B.R. Ambedkar, National Institute of Technology Jalandhar, Jalandhar, 144011, Punjab, India

    Anupam Yadav

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  1. Anita Sajwan
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Sajwan, A., Yadav, A. A study of exploratory and stability analysis of artificial electric field algorithm. Appl Intell 52, 10805–10828 (2022). https://doi.org/10.1007/s10489-021-02865-7

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