Applied Mathematics & Information Sciences

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In this paper, Differential Evolution with Powell conjugate direction method (DE-Powell)is proposed in order solve a system of nonlinear equations. A given system of nonlinear equations is formulated as an unconstrained optimization problem. Integrating Powell conjugate direction method into DE improves the performance of DE and enables DE to optimize effectively the system of nonlinear equations. For example, applying DE to solve our formulation of the system of nonlinear equations, in some iterations DE may get trapped in local minima, then Powell conjugate direction method is applied to help DE to overcome local minima by changing the initial solution for Powell with best obtained one by DE. Our proposed algorithm, DE-Powell, has superiority over Powell Conjugate Direction (CD) and Differential Evolution (DE), separately, it it overcomes the inaccuracy of Powell conjugate direction method and DE for solving systems of nonlinear equations. The DE-Powell is tested on nine well known problems and our numerical results show that the proposed algorithm is solving the highly nonlinear problems effectively and outperforms over many algorithms in literature.

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