用四元数改进差分进化算法，提升优化速度与精度
A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization
- 在四元数空间直接操作，利用其代数几何特性设计新变异策略
- 在BBOB基准测试中收敛更快，多类函数优化性能超越传统实数算法
- 适合需要高维优化、追求计算效率的科研与工程应用
连续函数的数值优化是机械设计到人工智能训练等多个科学与工程领域的基础任务。差分进化（DE）因其简单性和优异性能而被广泛使用。近年研究显示，将人工智能模型扩展至复数、四元数和几何代数等数系可提升模型紧凑性与准确性，但此类拓展在生物启发式优化算法中仍较少探索。四元数运算在计算智能领域属新兴方向。本文提出一系列新型四元数值差分进化（QDE）算法，在四元数空间内直接运行，并设计了多种针对四元数代数与几何特性的变异策略。实验结果表明，所提出的QDE变体在BBOB基准测试的多个函数类别上，相比传统实数型DE算法展现出更快的收敛速度与更优的性能。
原文摘要 · Abstract (English)
The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used algorithms for this purpose is Differential Evolution (DE), known for its simplicity and strong performance. Recent research has shown that adapting AI models to operate over alternative number systems-such as complex numbers, quaternions, and geometric algebras-can improve model compactness and accuracy. However, such extensions remain underexplored in bio-inspired optimization algorithms. In particular, the use of quaternion algebra represents an emerging area in computational intelligence. This paper introduces a family of novel Quaternion-Valued Differential Evolution (QDE) algorithms that operate directly in the quaternion space. We propose several mutation strategies specifically designed to exploit the algebraic and geometric properties of quaternions. Results show that our QDE variants achieve faster convergence and superior performance on several function classes in the BBOB benchmark compared to the traditional real-valued DE algorithm.
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