This paper discusses how a backup VP between each pair of a sourcenode and a destination node is set up such that when some nodes and links in primary VP's fail, primary VP's are changed to backup VP's rapidly. Then, this paper proposes a multiagent-based method for such rapid restoration from primary VP's to backup VP's.The proposed method consists of the following three steps. The first step enumerates candidates of backup VP between each pair of a source node and a destination node. In the second step, capacities of shared links in backup VP candidates between different pairs of a source node and a destination node are obtained. The last step determines a backup VP with the minimum capacities of shared links between each pair of a source node and a destination node. The proposed method has potentially good adaptability for change of both network resource such as topology and link capacity and requirements such as capacities of primary VP capacity and backup VP.