JACIII Vol.19 No.5 pp. 697-707
doi: 10.20965/jaciii.2015.p0697


Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering

Kuntjoro Adji Sidarto and Adhe Kania

Department of Mathematics, Institut Teknologi Bandung
Bandung 40132, Indonesia

April 29, 2015
August 6, 2015
Online released:
September 20, 2015
September 20, 2015
systems of nonlinear equations, root finding problem, spiral dynamics inspired optimization, clustering, Sobol sequence of points

Nowadays the root finding problem for nonlinear system equations is still one of the difficult problems in computational sciences. Many attempts using deterministic and meta-heuristic methods have been done with their advantages and disadvantages, but many of them have fail to converge to all possible roots. In this paper, a novel method of locating and finding all of the real roots from the system of nonlinear equations is proposed mainly using the spiral dynamics inspired optimization by Tamura and Yasuda [1]. The method is improved by the usage of the Sobol sequence of points for generating initial candidates of roots which are uniformly distributed than of pseudo-random generated points. Using clustering technique, the method localizes all potential roots so the optimization is conducted in those points simultaneously. A set of problems as the benchmarks from the literature is given. Having only a single run for each problem, the proposed method has successfully found all possible roots within a bounded domain.

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Last updated on Feb. 24, 2017