Abstract
BackgroundIn this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm.ResultsTwelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes.ConclusionsAccuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.
Highlights
In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search
Six different problems are taken for the study and proposed methods base on twelve variants of memetic computing using GAs and SQP algorithms are applied for these equations
Problem 1: generic nonlinear system of equations In this case, a generic system of nonlinear equations based on four equations with four unknowns is taken and it is represented by the following mathematical relations (Grosan and Abraham 2008b) f1(t1, t2, t3, t4 )
Summary
Bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. Conclusions: Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity. Introduction Solving system of non-linear equations in particular based on large set are generally considered to be the most difficult and a challenging problem for the research community in the field of numerical computation. These systems arise frequently in a spectrum of applied mathematics and engineering applications including trajectory planning, kinematics, combustion theory and neurophysiology etc. Many researchers, including Jaffari and Gejji, Abbasbandy, Sharma et al, Vahidi et al have given an updated version of methods to solve the nonlinear system of equation reliably and efficiently (Jafari and Gejji 2006; Abbasbandy 2005; Vahidi et al 2012; Sharma and Guha 2013; Sharma and Gupta 2013, 2014; Sharma and Arora 2014)
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