OPTIMIZATION IN PRODUCT DESIGN WITH PROPERTIES CORRELATED WITH TOPOLOGICAL INDEXES

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 molecu lar connectivity indices, Kier's shape indices and the Wiener Index. T he adjacency matrix representation which provides a complete descripti on of the connectivity of a molecule is utilized. Thus, complete molec ular interconnectivity information is introduced in the optimization f ramework which, in principle, provides for more accurate property pred iction 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 pro blem as a Mixed Integer Linear Program (MILP). Two different examples are considered: The first involves the design of alkanes with target p hysical properties correlated with Kier's shape indices and the second the selection of the best substituent of a compound with desired fung icidal properties correlated with Randic's connectivity index. In both examples, uncertainty in the model regression coefficients is quantit atively taken into account. (C) 1998 Elsevier Science Ltd. All rights reserved.