Let d ≥ 2. We consider an i.i.d. supercritical bond percolation on Z^d , every edge is open with a probability p > p_c (d), where p_c (d) denotes the critical point. We condition on the event that 0 belongs to the infinite cluster C_∞ and we consider connected subgraphs of C_∞ having at most n^d vertices and containing 0. Among these subgraphs, we are interested in the ones that minimize the open edge boundary size to volume ratio. These minimizers properly rescaled converge towards a translate of a deterministic shape and their open edge boundary size to volume ratio properly rescaled converges towards a deterministic constant.