A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization
For researchers in optimization and computational intelligence, this work extends differential evolution to quaternion space, offering a new approach that improves performance on certain benchmark functions.
This paper introduces quaternion-valued differential evolution (QDE) algorithms for numerical optimization, achieving faster convergence and superior performance on several BBOB benchmark function classes compared to traditional real-valued DE.
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.