For the main building block of the proposed method, we employed a sequential Monte Carlo (SMC) algorithm to draw a promising sample set of x = {S, G} from the target π(x). As mentioned above, because the target distribution is defined on a large combinatorial space, an ordinary SMC cannot approximate it adequately. In particular, it is difficult to obtain a diverse set of highly probable molecules with their reaction routes using such ordinary methods, which will be demonstrated later. The proposed method, shown in the next subsection, was developed as an extension of SMC to overcome the difficulty of combinatorial complexity. To clarify the design concept of the proposed method, we briefly describe the general SMC method here.