A finite set C = c1, c2, . . . , cNC of components is given. The states of the problem are defined in terms of sequences x = [ci, cj, . . . , ck] over the elements ofC. The set of all possible sequences is denoted by S. The length of a sequence x, that is the numberof components in the sequence, is expressed by jxj. The finite set of constraints W defines the set of feasible states c, with ˜c c. A cost f (s, t) is associated with each candidate solution s 2 S. In some cases, a cost, or the estimation of a cost, J(xi, t), can be associated with states other thansolutions. If xj can be obtained by adding solution components to a state xi, then J(xi, t) J(xj, t).Note that J(s, t) = f (s, t).