This paper contributes (1) to the development of the necessary formalism for the generation of task optimal fingertip trajectories for a multifingered robot hand of a predetermined preshape closing upon an object to be handled; (2) to the generation, in the case of a failing grasp, of an optimal sequence of hand preshapes, differing gradually from each other in terms of manipulability and stability. A "look ahead" preshape control for a robot hand, either in the phase of impacting an object with a certain hand preshape or in the regrasp mode, necessitates the concept of giving the object the suitable motion readiness for a subsequent manipulation behavior; which is a perspective missing in the literature. This work provides a formalism for such a concept and defines the preshaping and the regrasping efficiencies of a robot hand by a performance measure based on both task properties in manipulating a grasped object and on object constraints. This measure is formulated using the dual criteria of manipulability and stability that are derived in terms of vortices, generated by a closing preshape, and hand divergences, respectively. These criteria together with candidate contact points from possible landing areas on an object to be grasped or to be regrasped are then applied to the generation of candidate grasping hand configurations or reshaping configurations using the optimal search mechanism of genetic algorithms (GA). The surviving configurations at the end of each generation, created by the GA-based processing, constitute, with optimal performance, the hand posture sequences closing on an object in a preshaped manner. This work also contributes to the increase in the performance of GAs applied to the generation of optimal hand preshapes, by modifying the classical GA operators and by introducing more disruptive effects to the directed search mechanism. These modifications are tested and sample results are provided and discussed in the paper.