GENLS: Co-evolutionary algorithm for nonlinear system of equations. We present a new optimization system (GENLS), for a system of nonlinear equations. Our approach has two characteristic features. Firstly, the system of nonlinear equations is transformed into a nonlinear programming problem (NLP) with additional parameter ε to define an initial precision of the system. That is, the objective is to reduce the violation of the constraints to an acceptable level (desired precision ε * ) by minimizing a function that measures the maximum violation of the constraints. Secondly, an efficient co-evolutionary algorithm is implemented for solving the resulting NLP, which combines the concept of co-evolution, a repairing procedure and an elitist strategy. Finally, we report numerical results in order to establish the actual computational burden of the proposed method and to assess its performances with respect to classical approaches for solving a system of nonlinear equations.