Solving System of Non-Linear Equations Using Modified Jaya Algorithm

This paper presents application of modified Jaya algorithm for solving system of non-linear equations. The most popular methods for solving system of nonlinear equations are fixed point iteration method and Newton-Raphson (NR) method. The fixed point iteration method may converge to correct solution if problem is formulated in one way, but may not converge if it is formulated in the other way. Moreover, even if the convergence is possible, the method may diverge if the initial choice is far away from the actual solution. The NR method may also diverge, if the initial choice is far away from the actual solution. Application of modified Jaya algorithm overcomes these difficulties. Jaya algorithm is a recently proposed simple optimization algorithm for solving constrained and unconstrained optimization problems. The problem is formulated as an optimization problem, by defining an objective function which aims at minimizing the sum of square of error between the left hand side and right hand side of each nonlinear equation. Modified Jaya algorithm is then applied to solve this optimization problem. It overcomes the drawbacks of fixed point iteration method and NR method. Also, it gives multiple solutions (if exist).