An optimization approach is proposed for suppressing the automoiré, also known as internal moiré, in multi-level periodic screen designs. This artifact can appear when the halftone dots of a rational tangent screen do not have integer offsets in pixels. Starting with an ideal continuous space halftone pattern for a given level, a bounded, constrained convex optimization problem is solved to obtain the best discrete space halftone pattern values on the pixels of the supercell tile. The optimization minimizes a least-squares spatial frequency weighted difference between the pattern when first reconstructed to continuous space by the printing system (e.g. exposure) and the ideal pattern. The resulting halftone pattern has been found to typically contain very little energy outside of the screen's fundamental frequencies and harmonics while preserving the original ideal dot shape reasonably well. A series of such patterns so derived can be converted to multi-level threshold arrays if the pattern values are quantized and the stacking constraint is enforced during optimization.