A new methodology that combines the generalized topological indices (GTI) and the down hill simplex optimisation procedure has been developed to search for optimised quantitative structure-property relationship models. The structural interpretation of the optimal molecular descriptors is attained analytically by means of the GTIs decomposition in terms of geodesics (shortest paths) in the molecular graph. This approach provides a clear explanation about the role of topological structure in the study of molecular physico-chemical properties. (c) 2005 Elsevier B.V. All rights reserved.