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Sparse arrays offer a means for reducing the cost and complexity of beamforming systems. Most of the work in the literature has focused on sparse linear arrays with isotropic transducer elements, which simplifies analysis greatly. In this paper, we will focus on multibeam cylindrical arrays using highly directive elements for use in fishery applications, which requires a direction- ally independent imaging performance in the azimuth direction as well as beam steerability in the elevational direction. To populate such an array, we suggest a low periodicity in the azimuth direction of the array, which ensures a (near) directionally independent imaging performance in this direction. At the same time it reduces the complexity of the problem so that a suggested iterative method can find the optimal layout under the given constraints, within reasonable time. The optimality of the constrained solution is verified using a stochastic optimization procedure, with a "loosened" periodicity constraint. Simulations then show that the proposed layout, having low periodicity in the azimuth direction, has a reduced peak sidelobe level compared to the fully sampled array. All of the layouts have been required to support beam steering from -30deg to 0deg in elevation and in all 360deg in azimuth, without deterioration in performance.