Let $B,B'$ be affine finite crystals. Combinatorial $R$ is a unique map $R:B\otimes B'\longrightarrow B'\otimes B$ commuting with Kashiwara operators $\tilde{e}_i,\tilde{f}_i$. If $B$ and $B'$ have a coordinate representation, the image of $R$ is written as a set of piecewise linear functions in these coordinates. Following Kirillov's slogan ``Tropical Combinatorics" we tackle this problem of obtaining the explicit formula of $R$ by replacing the notions crystal and combinatorical $R$ with geometric crystal, introduced by Berenstein and Kazhdan, and tropical $R$.

This is a joint work with A.Kuniba, T.Takagi and Y.Yamada.