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首页> 外文期刊>International Journal of Innovative Computing Information and Control >SOLVING POLYNOMIAL SYSTEMS USING A MODIFIED LINE SEARCH APPROACH
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SOLVING POLYNOMIAL SYSTEMS USING A MODIFIED LINE SEARCH APPROACH

机译：使用改进的线搜索方法求解多项式系统

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摘要

This paper proposes a modified line search technique for solving systems of complex nonlinear equations. Line search is a widely used iterative global search method. Since optimization strategies have been (and continue to be) successfully used for solving systems of nonlinear equations, the system is reduced to a one-dimensional equation system for optimization purpose. The proposed line search procedure incorporates a re-start technique, which makes use of derivatives to reduce the search space and to re-generate thereafter the starting points in between the new ranges. Several well known applications such as interval arithmetic benchmark, kinematics, neuropsychology, combustion, chemical equilibrium and economics application are considered for testing the performances of the proposed approach. To validate the strength of the proposed approach, systems having between 5 and 20 equations are considered. Results are compared with an evolutionary algorithm approach, which transforms the problem into a multi-objective optimization problem. Empirical results reveal that the proposed approach is able to deal with high dimensional equations systems very effectively.
机译：本文提出了一种改进的线搜索技术，用于求解复杂的非线性方程组。线搜索是一种广泛使用的迭代全局搜索方法。由于优化策略已（并将继续成功地）用于求解非线性方程组，因此出于优化目的，将系统简化为一维方程组。提议的行搜索过程结合了一种重新启动技术，该技术利用导数来减少搜索空间并在此之后重新生成新范围之间的起点。考虑了几种众所周知的应用程序，例如区间算术基准，运动学，神经心理学，燃烧，化学平衡和经济学应用程序，以测试所提出方法的性能。为了验证所提出方法的强度，考虑了具有5至20个方程的系统。将结果与进化算法方法进行比较，该算法将问题转换为多目标优化问题。实证结果表明，该方法能够非常有效地处理高维方程组。

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    Crina Grosan; Ajith Abraham; Vaclav Snasel;

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    Department of Computer Science Babes-Bolyai University Kogalniceanu 1, Cluj-Napoca 400084, Romania;

    Faculty of Electrical Engineering and Computer Science VSB-Technical University of Ostrava 17. listopadu, 15/2172, Ostrava-Poruba 70833, Czech Republic,Machine Intelligence Research Labs Scientific Network for Innovation and Research Excellence Auburn, Washington, USA;

    Faculty of Electrical Engineering and Computer Science VSB-Technical University of Ostrava 17. listopadu, 15/2172, Ostrava-Poruba 70833, Czech Republic;

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