An Integrated Genetic Algorithm and Homotopy Analysis Method to Solve Nonlinear Equation Systems

Abstract

Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined objective function. This paper proposes a new algorithm for solving square and nonsquare nonlinear systems combining the genetic algorithm (GA) and the homotopy analysis method (HAM). First, the GA is applied to find out the solution. If it is realized, the algorithm is terminated at this stage as the target solution is determined. Otherwise, the HAM is initiated based on the GA stage’s computed initial guess and linear operator. Moreover, the GA is utilized to calculate the optimum value of the convergence control parameter (h) algebraically without plotting the h-curves or identifying the valid region. Four test functions are examined in this paper to verify the proposed algorithm’s accuracy and efficiency. The results are compared to the Newton HAM (NHAM) and Newton homotopy differential equation (NHDE). The results corroborated the superiority of the proposed algorithm in solving nonlinear equation systems efficiently.

The Impact of E-Commerce and Ride Hailing on Emissions from Shopping-Related Transport: A Case Study of the Shopping Habits of University Students from Ningbo University

“…Kesari et al [9] also used a structural equation model to study the impact of utilitarian shopping values and hedonic shopping values on shopper satisfaction in Indian shopping centers and found that the two values both have a significant positive impact on customer satisfaction. Chebat et al [30] investigated the psychological process of the changes in shoppers' consumption behavior caused by renovated shopping malls and discussed the impact of shopping mall renovation on shoppers' consumption, especially the impact of shoppers' perception of shopping mall atmosphere. ey found that the hedonic value contributes more than the utilitarian value to shopper satisfaction.…”

Coupled of Semi Analytic Approach Associated with Laplace Transform First Step for Solving Matrix Differential Equations Quadratic Form when the Time-Delay in Noise Term

“…It's strongly method use for finding solutions of nonlinear form 13 . The application of HAM to solve nonlinear equation systems with integrated genetic algorithm is considered 14 . The quotient HAM for solving nonlinear equations is studied 15 .…”