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An alternative computational optimization technique to solve linear and nonlinear Diophantine equations using discrete WQPSO algorithm

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Abstract

The concept of computational optimization can be used to solve linear and nonlinear Diophantine equations. The goal of this article is to introduce an alternative technique, which is independent of greatest common divisor (g.c.d), to solve linear and nonlinear Diophantine equations by transforming the equations into discrete variable bound constrained optimization problems. To solve these optimization problems, weighted quantum-behaved particle swarm optimization (WQPSO) is developed into discrete variable form. Then, four linear and four nonlinear Diophantine equations are considered from recent literature and solved by using the discrete WQPSO algorithm. Next, the convergence histories of each of the problems are shown. Finally, the results are compared with the same reported by numerous researchers.

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Acknowledgements

Author is thankful to the Editor and the anonymous Reviewers for giving their valuable comments and suggestions for improving the quality of this work.

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  1. Department of Mathematics, The University of Burdwan, Purba Barddhaman, Burdwan, 713104, India

    Nirmal Kumar

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  1. Nirmal Kumar
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Correspondence to Nirmal Kumar.

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Kumar, N. An alternative computational optimization technique to solve linear and nonlinear Diophantine equations using discrete WQPSO algorithm. Soft Comput 26, 12531–12544 (2022). https://doi.org/10.1007/s00500-022-07199-1

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