Symmetry

50 pages, 7686 KB

Open AccessArticle

A Multi-Strategy Augmented Newton–Raphson-Based Optimizer for Global Optimization Problems and Robot Path Planning

by Xiuyuan Yi and Chengpeng Li

Symmetry 2026, 18(2), 280; https://doi.org/10.3390/sym18020280 (registering DOI) - 3 Feb 2026

Newton–Raphson-Based Optimizer (NRBO) is a recently proposed metaheuristic that combines mathematical search rules with population-based optimization; however, it still suffers from an insufficient balance between global exploration and local exploitation, limited local refinement accuracy, and weak adaptability in complex optimization scenarios. To address [...] Read more.

Newton–Raphson-Based Optimizer (NRBO) is a recently proposed metaheuristic that combines mathematical search rules with population-based optimization; however, it still suffers from an insufficient balance between global exploration and local exploitation, limited local refinement accuracy, and weak adaptability in complex optimization scenarios. To address these limitations, this paper proposes an Improved Newton–Raphson-Based Optimizer (INRBO), which enhances the original framework through a multi-strategy augmentation mechanism. Specifically, INRBO integrates three complementary strategies: (1) an adaptive differential operator with a linearly decaying scaling factor to dynamically regulate exploration and exploitation throughout the search process; (2) a quadratic interpolation strategy that exploits high-quality individuals to improve local search directionality and precision; and (3) an elitist population genetic strategy that preserves superior solution characteristics while maintaining population diversity and preventing premature convergence. The performance of INRBO is systematically evaluated on the CEC2017 benchmark suite under multiple dimensions and compared with several state-of-the-art metaheuristic algorithms. Experimental results demonstrate that INRBO achieves superior optimization accuracy, convergence efficiency, and robustness across unimodal, multimodal, hybrid, and composite functions, which is further confirmed by statistical significance tests. In addition, INRBO is applied to mobile robot path planning in grid-based environments of different scales, where it consistently generates shorter, smoother, and safer paths than competing algorithms. Overall, the proposed INRBO provides an effective and robust optimization framework for global continuous optimization problems and real-world engineering applications, demonstrating both strong theoretical value and practical applicability. Full article

(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)

25 pages, 506 KB

Open AccessArticle

Solution Dynamics of the (1 + 1)-Dimensional Fisher’s Equation Using Lie Symmetry Analysis

by Phillipos Masindi and Lazarus Rundora

Symmetry 2026, 18(2), 279; https://doi.org/10.3390/sym18020279 - 3 Feb 2026

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Symmetry

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