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.

中文翻译：

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混合算法求解线性和非线性方程组的一些技术的发展

本文的目的是借助基于高级量子行为粒子群优化和二元博弈过程概念的混合算法，介绍几种用于同时求解线性和非线性方程组的新方法或技术。根据二进制锦标赛的不同选择，提出了六种不同的混合算法变体。为了检验所提出的混合算法的有效性，解决了五个众所周知的基准约束约束优化问题。在混合算法的六个不同变体中，根据它们在这些问题中的性能来选择最佳算法。然后将此最佳算法应用于求解同时线性和非线性方程组，将这些方程式转换为优化问题。