Here, R ∈ C k denotes an element of cluster k, where the cluster members vary with step t; however, we omit the subscript indicating the dependence of the cluster on t. The model η 0 (x t |x t-1 ) for the neighborhood search in the proposal distribution selects x t = {S 1,t , S 2,t } with equal probability from cluster R ∈ C k(Si,t-1) (i = 1, 2) to which each reactant S 1,t-1 or S 2,t-1 in x t-1 belongs. The explicit form of the probabilistic model can be expressed as