Optimizing the layout of sparse planar arrays constrained by minimum element spacing to reduce the peak side lobe level (PSLL) is a difficult and challenging task in engineering applications. Here, a new sparse array design method is proposed under the constraints of aperture size, the number of array elements, and minimum spacing between elements. The approach is based on a new element mutation method which is proposed for mutating the position of any element within the aperture without changing the position of other elements. Because a mutating element can be thought of as being placed inside the board like a black/white stone in Go or crawling somewhere nearby like a caterpillar, we call it Go-Caterpillar-mutation (GCM). Based on GCM, a stochastic optimization algorithm (GCM-OA) is proposed to optimize the layout of sparse planar arrays. Several examples demonstrate the robustness and rapidity of GCM-OA in reducing PSLL by adjusting the array element positions under various constraints.