A new global optimization algorithm based on space-filling curve and auxiliary function approach and its applications

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-12 DOI:10.1016/j.cnsns.2025.108920

Nurullah Yilmaz

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引用次数: 0

Abstract

Global optimization is a topic of great interest because of the many practical problems in real life. This article focuses on the unconstrained global minimization of multi-modal continuously differentiable functions, an important subclass of global optimization problems. In order to solve these problems, we develop a new global optimization technique that utilizes two fundamental concepts. The first one is the reducing dimension technique, which uses space-filling curves, while the second one involves utilizing an auxiliary function approach. We propose a new continuously differentiable auxiliary function with direct control of the slope and present the theory behind it. The auxiliary function method is combined with the space-filling curve methodology. We construct a new global optimization algorithm based on the proposed auxiliary function, space-filling curves, and local searches. We implement a comprehensive numerical test procedure to evaluate the numerical stabilization and efficiency of the proposed algorithm. For this purpose, the proposed algorithm is applied to test problems, and the obtained numerical results are compared with the results obtained by some recently proposed algorithms. Moreover, the proposed algorithm is applied to two different economic load dispatch problems, and promising results are obtained.

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一种基于空间填充曲线和辅助函数的全局优化算法及其应用

由于现实生活中存在许多实际问题，全局优化是一个备受关注的话题。研究了多模态连续可微函数的无约束全局最优问题，这是全局优化问题的一个重要子类。为了解决这些问题，我们开发了一种新的全局优化技术，它利用了两个基本概念。第一种是使用空间填充曲线的降维技术，第二种是使用辅助函数方法。我们提出了一种新的直接控制斜率的连续可微辅助函数，并给出了其背后的理论。将辅助函数法与空间填充曲线法相结合。我们基于所提出的辅助函数、空间填充曲线和局部搜索构造了一种新的全局优化算法。我们实施了一个全面的数值测试程序来评估所提出算法的数值稳定性和效率。为此，将提出的算法应用于测试问题，并将得到的数值结果与最近提出的一些算法得到的结果进行了比较。并将该算法应用于两种不同的经济负荷调度问题，取得了较好的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.