Thinning a large concentric ring array by an evolutionary algorithm needs to handle a large amount of variables. The computational time to find out the optimum elements set increases with the increase of array size. Moreover, thinning significantly reduces the directivity of the array. In this paper, the authors propose a pattern synthesis method to reduce the peak sidelobe level (peak SLL) while keeping first null beamwidth (FNBW) of the array fixed by thinning the outermost rings of the array based on Gravitational Search Algorithm (GSA). Two different cases have been studied. In the first case only the outermost ring of the array is thinned and in the second case the two outermost rings are thinned. The FNBW of the optimized array is kept equal to or less than that of a fully populated, uniformly excited and 0.5 λ spaced concentric ring array of same number of elements and rings. The directivity of the optimized array for the above two cases are compared with an array optimized by thinning all the rings, while keeping the design criteria same as the above two cases. The optimized array by thinning the outermost rings gives higher directivity over the optimized array by thinning all the rings. Time required for computing the optimum elements state for the above two cases using GSA are shown lesser compared to the optimized array by thinning all the rings using the same algorithm. The peak SLL and the FNBW of the optimized array for the above two cases are also compared with the optimized array by thinning all the rings.