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Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U′ $$_q$$ ( $$\widehat {\mathfrak{g}}$$ $$_n$$ ). Let B $$_l$$ be the crystal of the U′ $$_q$$ ( $$\widehat {\mathfrak{g}}$$ $$_n$$ )-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = $$B_{l_1 }$$ ⊗ ...⊗ $$B_{l_N }$$ , we prove that the combinatorial R matrix B $$_M$$ ⊗B $$\widetilde \to$$ B⊗B $$_M$$ is factorized into a product of Weyl group operators in a certain domain if M is sufficiently large. It implies the factorization of certain transfer matrix at q=0, hence the time evolution in the associated cellular automata. The result generalizes the ball-moving algorithm in the box-ball systems. [ABSTRACT FROM AUTHOR]