Discrete energy optimization is a NP hard problem. Recent years, the graph cuts based algorithms especially the α-expansion and αβ-swap, become more and more popular. Both the α-expansion and αβ-swap have been widely used in many applications, and they perform extremely well for the Potts energies. However, since all pixels only have a choice of two labels in one move, both the expansion and swap algorithm get approximate solution by a series of iterations and they do not perform well for more general energies, such as the truncated convex energies [1]. In this paper, we analyze the problems of both

the expansion and swap algorithms. The expansion algorithm usually encourages more pixels to get the label fα, since all pixels are only allowed to change their current labels to fα. In contrast, the swap move sometimes cannot swap the labels of pixels reasonably. Based on the analysis, we propose the Interleaved Expansion-Swap Algorithm (IESA) by combining the expansion and swap moves effectively. To prove the effectiveness of the algorithm, we test it on both image restoration and stereo correspondence. The experimental evaluations show that our algorithm gets better optimization compared with both α-expansion and αβ-swap.