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Development of some techniques for solving system of linear and nonlinear equations via hybrid algorithm
Author(s) -
Kumar Nirmal,
Shaikh Ali Akbar,
Mahato Sanat Kumar,
Bhunia Asoke Kumar
Publication year - 2021
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/exsy.12669
Subject(s) - computer science , benchmark (surveying) , nonlinear system , algorithm , binary number , basis (linear algebra) , particle swarm optimization , hybrid algorithm (constraint satisfaction) , mathematical optimization , system of linear equations , hybrid system , mathematics , artificial intelligence , constraint satisfaction , machine learning , constraint logic programming , physics , geometry , arithmetic , geodesy , quantum mechanics , probabilistic logic , geography
The objective of this article is to introduce several new methods or techniques for solving simultaneous linear and nonlinear system of equations with the help of a new hybrid algorithm based on advanced quantum behaved particle swarm optimization and the concept of binary tournamenting process. Depending on different options of binary tournamenting, six different variants of hybrid algorithms are proposed. To examine the effectiveness of the proposed hybrid algorithms five well known benchmark bound‐constrained optimization problems are solved. Among the six different variants of hybrid algorithms, the best algorithm is selected on the basis of their performances in these problems. This best algorithm is then applied in solving simultaneous linear and nonlinear system of equations transforming these equations into optimization problems. In case of linear system, just two systems are solved while in case of nonlinear system seven complicated problems are solved and finally a comparison of best found solutions are estimated with the same of existing algorithms provided in the literature.