Backup trees (BTs) are a promising approach to network protection in optical networks. BTs allow us to protect a group of working paths against single network failures, while reserving only a minimum amount of network capacity for backup purposes. The process of constructing a set of working paths together with a backup tree is computationally very expensive, however. In this paper we propose a multi-agent approach based on ant colony optimization (ACO) for solving this problem. ACO algorithms use a set of relatively simple agents that model the behavior of real ants. In our algorithm multiple types of ants are used. Ants of the same type collaborate, but are in competition with the ants of other types. The idea is to let each type find a path in the network that is disjoint with that of other types. We also demonstrate a preliminary version of this algorithm in a series of simple experiments.