An evolutionary approach to black-box optimization on matrix manifolds

摘要: Abstract Optimization on matrix manifolds is a class of methods for solving optimization problems, subject to constraints which admit the structure Riemannian manifold. These problems are intractable traditional evolutionary algorithms due non-Euclidean nature. This paper generalizes classical technique covariance adaptation manifolds, and proposes manifold evolution strategy named ManES. By exploiting structure, we turn an originally constrained problem into sequence unconstrained ones in Euclidean subspace. The proposed algorithm coordinate-free, sense that it independent choice basis requires no global coordinate system. All genetic operators take form transformations thus computationally efficient. exhibits state-of-the-art performance four benchmark one real-world application posed three different kinds manifolds.