This work focuses on the generation of optimal fingertip trajectories for a given preshape of a five fingered robot hand, the Anthrobot III. The hand preshape is defined in a ''look ahead'' manner, being related to task properties in manipulating a grasped object and to object constraints such that a performance measure in terms of stability and manipulability is used in the formulation. Stability and manipulability are defined using concepts of vortex theory. The originality of our approach resides not only in the methodology but also in the objective of optimally closing a preshaped hand on an object for a better subsequent grasp. The dual criteria of manipulability and stability are first dem ed in terms of I)vorticities generated by preshape closure and 2) hand divergences. These measures are then applied, together with contact points from possible landing areas of each finger on the object, to the generation of candidate hand-configurations using the optimal search mechanism of genetic algorithms (GA). The surviving hand configurations determine the preshape closure style with optimal performance and by evaluating fingertip trajectories for the closing of the hand which are generated in this paper for different tasks and object constraints. The effects of modifying standard crossover and mutation operators of GAs on finger trajectories are studied on illustrative examples and results are provided with discussions.