Tropical sampling is a mathematically streamlined version of the
geometric sector decomposition approach to evaluate algebraic integrals
numerically. If the structure of the Newton polytope of the integrand is
precomputed or known from first principles, then tropical sampling
offers the advantage of a significantly improved performance. In the
case of Euclidean Feynman integrals these polytopes are generalized
permutahedra, a class of polytopes which is well-studied. Employing
this knowledge leads to a highly efficient and practical numerical
Feynman integration algorithm which can compute scalar Euclidean Feynman
integrals with arbitrary kinematics up to loop order ~20 on present-day
hardware.