Testing metric relations on Finsler manifolds via a geodesic detecting algorithm

By using evolutionary techniques (genetic algorithms), we provide a geodesic detecting algorithm in order to test metric relations on a large class of not necessarily reversible Finsler manifolds. In particular, we focus our attention to a rigidity conjecture: any Finsler manifold which is a Busemann NPC space is Berwaldian. Beside of existing theoretical results in the literature, we support this statement by several numerical examples provided by our algorithm.