This paper addresses the problem of a moving target search with a discrete allocation of search effort to disjoint cones of observation. A cone covers several regions with different visibilities. This is an important step towards the optimal search with radars on airborne platforms which has not been previously studied. We adapt Forward And Backward (FAB) algorithms to this problem and apply them to compute search plans. We measure the quality of our solution with a continuous relaxation of the problem. In a set of numerical experiments we exhibit that our algorithms have good performance in terms of plan quality and computation time. Finally, we compare the plans optimizing different objective functions.