A mapping in random structures is defined on the vertices of a generalized hypercube {\cal Q}^n_\alpha. A random structure consists of (i) a random contact graph and (ii) a family of relations inposed on adjacent vertices of the random contact graph. The vertex set of a random contact graph is the set of all coordinates of a vertex V \in {\cal Q}^n_\alpha, {P_1, \ldots, P_n}. The edges of the random contact graph are the union of the edge sets of two random graphs. The first is a random 1-regular graph on 2m vertices {p_{i_1}, \ldots, P_{i_{2m}}} and the second is a random graph G_p with p = {c_2\over n} on {P_1,\ldots,{_n}. The structure of the random contact graphs is investigated and it is shown that for certain values of m and c_2 the mapping in random structures allows systematic search in the set of random structures. Finally the results are applied to evolutionary optimization of biopolymers. <p> Key words. random structure, sequence-structure mapping, random graph, connectivity, branching process, optimization
