This paper presents an optimization of IP load-balanced routing for the hose model. We present an IP load-balanced routing scheme based on the two-phase routing over shortest paths. It is called a fine two-phase routing (F-TPR) scheme. In F-TPR, traffic is distributed from a source node to intermediate nodes more finely, compared to the original TPR. F-TPR introduces the distribution ratio to node mthat is determined for each source-destination pair of (p, q), kmpq. To determine an optimum set of kmpq, an linear programming (LP) formulation is first derived. However, the formulation is difficult to solve as a simple LP problem. This is because each element of the traffic matrix is not determined because of the hose model and there are too many possible parameters for us to consider. By introducing a duality theorem, we successfully formulate our problem a quadratic constraint programming (QCP) formulation that can be solved to determine the split ratios by using a mathematical programming solver. We compare F-TPR with TPR and the Multi-Protocol Label Switching (MPLS)-Traffic Engineering (TE). Numerical results show that F-TPR reduces the network congestion ratio compared to TPR. Numerical results show that F-TPR greatly reduces the network congestion ratio compared to TPR, and provides comparable routing performances to that of MPLS-TE. © 2011 National Institute of Informatics.