In this paper, we formulate the task of simultaneous design of molecules and synthetic routes as a general statistical problem in which a forward model is defined as a cascade of reaction prediction models and property prediction models, as in the previous work of Gottipati et al. . In the inverse problem, we seek a set of reactants and a network structure of synthetic reactions such that the resulting products reach a predefined region of desired properties. The overall search space for the reactant sets is spanned by all possible combinations of given commercially available compounds. If the number of commercial compounds is of the order O(10 6 ) and the number of reactants involved in a synthetic route is 10, the size of the search space will reach O(10 60 ). The structure of the reaction network is a design variable as well, involving the number of reaction steps and the network topology.