Abstract
Solving systems of nonlinear equations is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications. The convergence and performance characteristics can be highly sensitive to the initial guess of the solution for most numerical methods such as Newton’s method. However, it is very difficult to select reasonable initial guess of the solution for most systems of nonlinear equations. Besides, the computational efficiency is not high enough. Aiming at these problems, an improved particle swarm optimization algorithm (imPSO) is proposed, which can overcome the problem of selecting reasonable initial guess of the solution and improve the computational efficiency. The convergence and performance characteristics of this method are demonstrated through some standard systems. The results show that the improved PSO for solving systems of nonlinear equations has reliable convergence probability, high convergence rate, and solution precision and is a successful approach in solving systems of nonlinear equations.
Highlights
Solving systems of nonlinear equations is one of the most important problems in all of numerical computations, especially in a diverse range of engineering applications
The results show that the improved Particle swarm optimization algorithm (PSO) for solving systems of nonlinear equations has reliable convergence probability, high convergence rate, and solution precision and is a successful approach in solving systems of nonlinear equations
Many different combinations of the traditional numerical methods and the intelligent algorithms are applied to solve the systems of nonlinear equations [12, 13], which can overcome the problem of selecting reasonable initial guess of the solution
Summary
Solving systems of nonlinear equations is one of the most important problems in all of numerical computations, especially in a diverse range of engineering applications. Many different combinations of the traditional numerical methods and the intelligent algorithms are applied to solve the systems of nonlinear equations [12, 13], which can overcome the problem of selecting reasonable initial guess of the solution. Many improved intelligent algorithms, such as particle swarm algorithm and genetic algorithm, are proposed to solve systems of nonlinear equations. Though they overcome the problem of selecting reasonable initial guess of the solution, they lack the sophisticated search capabilities in local area, which may lead to convergence stagnation. An improved particle swarm optimization algorithm (imPSO) is put forward, which can overcome the dependence on reasonable initial guess of the solution and improve the computational efficiency. The unnecessary iterations will be cancelled if the value of G meets the standard (such as G < P), which can improve computational efficiency
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