Problem
Research questions and friction points this paper is trying to address.
numerical optimization
differential evolution
quaternion-valued algorithms
bio-inspired optimization
alternative number systems
A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization
🤖 AI Summary
This study addresses the slow convergence and performance limitations of conventional real-valued differential evolution (DE) algorithms in continuous optimization, as well as the underexplored potential of alternative number systems in intelligent optimization. The work proposes a novel family of quaternion-based differential evolution algorithms (QDE), which operate directly in quaternion space by integrating quaternion algebra into the DE framework for the first time. Several new mutation strategies are designed to leverage both the algebraic and geometric properties of quaternions. Evaluated on the BBOB benchmark suite, QDE variants demonstrate significant improvements over traditional real-valued DE in both convergence speed and solution accuracy, thereby expanding the mathematical foundations and application scope of bio-inspired optimization algorithms.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quaternion-Valued Differential Evolution
quaternion algebra
numerical optimization
mutation strategies
bio-inspired algorithms
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