A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization
Gerardo Altamirano-Gomez, Álvaro Gallardo, Carlos Ignacio Hernández Castellanos
TLDR
This paper introduces Quaternion-Valued Differential Evolution (QDE) algorithms, showing improved convergence and performance for numerical optimization.
Key contributions
- Introduces a new family of Quaternion-Valued Differential Evolution (QDE) algorithms.
- QDE operates directly in quaternion space, leveraging its algebraic and geometric properties.
- Proposes novel mutation strategies specifically designed for quaternion algebra.
- QDE variants achieve faster convergence and superior performance on BBOB benchmarks.
Why it matters
This work extends Differential Evolution into quaternion space, a novel approach for bio-inspired optimization. By leveraging quaternion properties, it offers a path to more compact and accurate AI models. This could lead to significant advancements in numerical function optimization.
Original 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.
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