Optimization in product design with properties correlated with topological indices

This paper addresses the problem of incorporating topological indices as structural descriptors for correlating properties in the design of product molecules with fine-tuned or optimized property values. Three different types of topological indices are considered: Randic's molecular connectivity indices, Kier's shape indices and the Wiener Index. The adjacency matrix representation which provides a complete description of the connectivity of a molecule is utilized. Thus, complete molecular interconnectivity information is introduced in the optimization framework which, in principle, provides for more accurate property prediction than simple group contributions. The nonlinear expressions for the topological indices are systematically transformed into equivalent linear relations enabling the formulation of the molecular design problem as a Mixed Integer Linear Program (MILP). Two different examples are considered: The first involves the design of alkanes with target physical properties correlated with Kier's shape indices and the second the selection of the best substituent of a compound with desired fungicidal properties correlated with Randic's connectivity index. In both examples, uncertainty in the model regression coefficients is quantitatively taken into account.