Non parameter-filled function for global optimization

Pandiya, Ridwan; Widodo, Widodo; Salmah,; Endrayanto, Irwan

doi:10.1016/j.amc.2020.125642

Cited by 10 publications

(3 citation statements)

References 23 publications

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“…e number of variables and the number of equations are n and m, respectively. All these test functions were described in detail in [34,[41][42][43][44].…”

Section: Test Functions and Results Analysismentioning

confidence: 99%

“…According to [34], selected test function 3 is represented as [44]. Selected test function 4 is represented as…”

Section: Selected Test Functionmentioning

confidence: 99%

“…ey are useful when the search space is enormous, and there are many parameters involved. Several hybridization techniques and combinations were developed based on the GAs [42][43][44][45][46]. ese hybridization techniques aim to benefit the GA's advantages by accelerating the hybrid method, enhancing their initial conditions, reducing their computational burden, or avoiding derivative calculations based on the gradient.…”

Section: Introductionmentioning

confidence: 99%

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

Omar

2021

Mathematical Problems in Engineering

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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.

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“…e number of variables and the number of equations are n and m, respectively. All these test functions were described in detail in [34,[41][42][43][44].…”

Section: Test Functions and Results Analysismentioning

confidence: 99%

“…According to [34], selected test function 3 is represented as [44]. Selected test function 4 is represented as…”

Section: Selected Test Functionmentioning

confidence: 99%