A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization

TL;DR

This paper introduces quaternion-valued differential evolution algorithms that operate in quaternion space, improving convergence speed and performance in numerical optimization tasks.

Contribution

The paper presents a novel family of quaternion-valued DE algorithms with mutation strategies tailored to quaternion algebra, enhancing optimization performance.

Findings

QDE variants outperform traditional DE on BBOB benchmarks

QDE algorithms achieve faster convergence

Quaternion algebra exploits geometric properties for better optimization

Abstract

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.