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Azmi, Ana Ulul
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Mathematics

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PERBANDINGAN ALGORITMA PARTICLE SWARM OPTIMIZATION (PSO) DAN ALGORITMA GLOWWORM SWARM OPTIMIZATION (GSO) DALAM PENYELESAIAN SISTEM PERSAMAAN NON LINIER Azmi, Ana Ulul; Hidayat, Rusli; Arif, M Ziaul
Majalah Ilmiah Matematika dan Statistika Vol 19 No 1 (2019): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v19i1.17263

Abstract

Non-linear equation system is one of the mathematics problems which difficult to solve. Several methods have been introduced to solve the problems. Newton-Raphson method is the most common and widely used as the basis for evolving the latest numerical methods. However, this method requires the derivative of each equation with respect to every variable when calculating the Jacobian. Naturally, obtaining the derivative is challenging in certain cases. In addition, it needs a proper initial value to obtain the converged solution. Therefore, the new technique with a simple random initial value is urgently needed. In this study, it is shown the implementation of the two metaheuristic optimization methods, including Particle Swarm Optimization (PSO) and the Glowworm Swarm Optimization (GSO) to estimate the solution of a non-linear equation system. Several examples of nonlinear equation system were used for evaluating and testing the performance and the accuracy of both algorithms. In this simulation, the results show that PSO converged to the exact solution (global optimum) better than Glowworm Swarm Optimization (GSO). Keywords: Non-Linear Equation Systems, Particle Swarm Optimization (PSO), Glowworm Swarm Optimization (GSO)
Co-Authors M Ziaul Arif, M Ziaul Rusli Hidayat