A projection exposure apparatus for microlithography includes a projection lens which includes a plurality of optical elements for imaging mask structures onto a substrate during an exposure process. The projection exposure apparatus also includes at least one manipulator configured to change, as part of a manipulator actuation, the optical effects of at least one of the optical elements within the projection lens by changing a state variable of the optical element along a predetermined travel. The projection exposure apparatus further includes an algorithm generator configured to generate a travel generating optimization algorithm, adapted to at least one predetermined imaging parameter, on the basis of the at least one predetermined imaging parameter.