In ATM networks with high capacity, the effect of failures on transmission links or nodes can be catastrophic, so that the issue of survivability is of great importance. In this paper. we consider the routing problem for working and backup virtual paths(VPs). To accomplish a higher survivability. routing the two kinds of VPs should be taken into account at the same time because backup VP routing depends on the working VP routing. A coevolutionary algorithm is employed to solve the problem for simultaneously routing of working and backup VPs. To develop an efficient coevolutionary algorithm for the problem. structure of populations, encoding method, neighborhood, and genetic operators are studied in this paper. The results of extensive experiments are reported. The performance comparison of the proposed algorithm with a conventional genetic algorithm and existing heuristics shows that our approach is promising.