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The aim of this study is to bring a new perspective for the solutions of non-linear equation systems. So this study handles the non-linear equation systems as a constrained optimization problem, while generally is handled unconstrained optimization problem or multi objective optimization problem. The object is to minimize the sum of the squares of nonlinear equations under the nonlinear equality constraints. A recently developed heuristic optimization algorithm called Grey Wolf Optimizer (GWO) is proposed for the solution of nonlinear equation systems. Two results were obtained. Firstly, it has been seen that GWO can be an alternative solution technique for the solution of nonlinear equation systems. Secondly, modelling the systems of nonlinear equations as constrained optimization gives better results.

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer