Abstract:

In this paper, the geometric relations of differential evolution algorithm in Riemannian manifolds are analyzed and discussed. The convergence of populations in Riemannian manifolds with P-ε is analyzed. A quantum uncertain asymptotic estimation of the convergence accuracy and convergence speed of the iterative individual is obtained as follows

$\Delta_{v}^{2}\cdot \Delta_{x_{\beta}^{\varepsilon}}^{2}\geq\Big(\frac{\sqrt{(\lambda_{\varepsilon})_{1}}+\cdots +\sqrt{(\lambda_{\varepsilon})_{n}}}{2}\Big)^{2},$

where, Δv2 is speed resolution of individual populations, Δxβε2 is position resolution with error ε of individual populations, (λε)i, i=1, 2, …, n. The theorem expression essentially shows that the local eigenvalues of iterated individuals in Riemann manifolds can not achieve high convergent accuracy and convergent speed at the same time.

Key words: DE algorithm, Riemannian manifolds, Convergent accuracy, Convergent speed, Quantum uncertain asymptotic estimation