A Quantum-Behaved Particle Swarm Optimization Algorithm on Riemannian Manifolds

Yeerjiang Halimu, Chao Zhou, Qi You and Jun Sun ()
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Yeerjiang Halimu: Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, No. 1800, Lihu Avenue, Wuxi 214122, China
Chao Zhou: Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, No. 1800, Lihu Avenue, Wuxi 214122, China
Qi You: Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, No. 1800, Lihu Avenue, Wuxi 214122, China
Jun Sun: Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, No. 1800, Lihu Avenue, Wuxi 214122, China

Mathematics, 2022, vol. 10, issue 22, 1-20

Abstract: The Riemannian manifold optimization algorithms have been widely used in machine learning, computer vision, data mining, and other technical fields. Most of these algorithms are based on the geodesic or the retracement operator and use the classical methods (i.e., the steepest descent method, the conjugate gradient method, the Newton method, etc.) to solve engineering optimization problems. However, they lack the ability to solve non-differentiable mathematical models and ensure global convergence for non-convex manifolds. Considering this issue, this paper proposes a quantum-behaved particle swarm optimization (QPSO) algorithm on Riemannian manifolds named RQPSO. In this algorithm, the quantum-behaved particles are randomly distributed on the manifold surface and iteratively updated during the whole search process. Then, the vector transfer operator is used to translate the guiding vectors, which are not in the same Euclidean space, to the tangent space of the particles. Through the searching of these guiding vectors, we can achieve the retracement and update of points and finally obtain the optimized result. The proposed RQPSO algorithm does not depend on the expression form of a problem and could deal with various engineering technical problems, including both differentiable and non-differentiable ones. To verify the performance of RQPSO experimentally, we compare it with some traditional algorithms on three common matrix manifold optimization problems. The experimental results show that RQPSO has better performance than its competitors in terms of calculation speed and optimization efficiency.

Keywords: Riemannian manifold; retracement operator; quantum-behaved particle swarm optimization; matrix manifold optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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