Applying genetic algorithms for solving nonlinear algebraic equations

作者：Pourrajabian Abolfazl^*; Ebrahimi Reza; Mirzaei Masoud; Shams Mehrzad

来源：Applied Mathematics and Computation, 2013, 219(24): 11483-11494.

DOI：10.1016/j.amc.2013.05.057

• Nonlinear equations
• Genetic algorithm
• Augmented Lagrangian function
• Optimization
• Initial interval

Solving of nonlinear algebraic equations is a prominent problem in science and engineering. In this study, the systems of these equations were solved using genetic algorithms. Three distinctive groups of the equations were studied: a single nonlinear equation, a simple set of nonlinear equations and a complex set of nonlinear equations. In the two first cases, the problem was converted into the unconstrained optimization problem with some simple mathematical relations. Then, the genetic algorithm was used to solve the problem. In the complex nonlinear equations, the problem was changed into the constrained optimization problem and genetic algorithm, in conjunction with augmented Lagrangian function has been used to find the solution. The proposed scheme has been evaluated with five benchmarks with different applications. Moreover, the sensitivity analysis of the method to initial interval and size of population has been studied. The results have a high precision and show good agreement in comparison with conventional methods.

• 出版日期2013-8-15