Multiprotocol Label Switching (MPLS) can improve the routing efficiency of Internet Protocol (IP) networks through its intrinsic Traffic Engineering (TE) capabilities. In this paper, a centralised and a distributed virtual-flow routing algorithms are proposed, which aggregate IP flows entering the MPLS domain and optimally partition them among virtual flows that are routed on multiple paths. The routing algorithms dynamically select multiple Label Switched Paths (LSPs), taking into account the available bandwidth of links in the network to balance the traffic load and avoid network congestion. The multipath routing problem is formulated as a Multicommodity Network Flow (MCNF) problem, and is solved by implementing online the Dantzig–Wolfe decomposition method. The proposed multipath algorithms are shown through simulations to outperform single-path routing solutions, such as the Constraint Shortest Path First (CSPF) and the Bandwidth-Based Shortest Path (BSPR) routing algorithms.