GENLS: Co-evolutionary algorithm for nonlinear system of equations

• Published in: Applied mathematics and computation Vol. 197; no. 2; pp. 633 - 642
• Main Authors: Mousa, A.A., El-Desoky, I.M.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.04.2008; Elsevier
• Subjects: Calculus of variations and optimal control; Exact sciences and technology; Genetic algorithms; Mathematical analysis; Mathematics; Nonlinear programming; Nonlinear systems of equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Sciences and techniques of general use; Nonlinear systems of equations; Nonlinear programming; Genetic algorithms; Optimization method; Nonlinear problems; Non linear programming; Non linear system; Implementation; Equation system; Non linear equation; Numerical analysis; Genetic algorithm; Applied mathematics; Mathematical programming
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.08.088

In this paper, we present a new optimization system (GENLS), for nonlinear system of equations. Our approach has two characteristic features. Firstly, nonlinear system of equations is transformed into a nonlinear programming problem (NLP) with additional parameter ε to define 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, efficient co-evolutionary algorithm is implemented for solving the resulting NLP, which combines concept of co-evolution, repairing procedure and 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 nonlinear system of equations.