This document describes the process of synthesis of a solid shaped reflector mechanically reconfigurable by few actuators that is capable to comply changeable coverage requirements. The method optimizes directly the positions of the actuators with a heuristic technique based in Ant Colony Algorithm. The mechanical and electromagnetic models were integrated in the cost function in a simple and effective way using the mechanical concept of 'stiffness matrix'. To illustrate this technique, we present an example of a reconfigurable reflector antenna which covers South America with a minimum directivity and, for some reduction of this minimum directivity, it is able to increase the directivity in selected regions to respond to rain and other changing conditions in a few seconds.