Title: Solving systems of nonlinear equations with real world problems using an advanced hybrid algorithm

Authors: Pooja Verma; Raghav Prasad Parouha

Addresses: Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Madhya Pradesh-484886, India ' Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Madhya Pradesh-484886, India

Abstract: Systems of nonlinear equations (SNLEs) existed in various disciplines like engineering and applied mathematics. Finding solutions to SNLES is one of the most challenging problems. An advanced hybrid algorithm (haDEPSO) is proposed in this paper for finding the solution of SNLEs and real world problems, based on multi-population approach. Suggested advanced differential evolution (aDE) and particle swarm optimisation (aPSO) integrated with haDEPSO where in aDE a novel mutation strategy, crossover probability and slightly changed selection scheme is introduced (to avoid premature convergence) and novel gradually varying parameters familiarised in aPSO (to escape stagnation). Also in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. Performance of proposed haDEPSO as well as its integrating component aDE and aPSO are used to solve three SNLEs and three complex real world problems. Comparative analysis confirms superiority of the proposed algorithms.

Keywords: systems of nonlinear equations; SNLEs; real world applications; meta-heuristics algorithms; hybrid algorithm.

DOI: 10.1504/IJBIC.2022.124333

International Journal of Bio-Inspired Computation, 2022 Vol.19 No.4, pp.238 - 252

Received: 11 Sep 2020
Accepted: 02 Jul 2021
Published online: 22 Jul 2022 *

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