The problem of routing logical links (lightpaths) on a physical topology of WDM networks in a way that the logical topology remains connected in the event of single physical link failure is called survivable routing. This paper addresses the survivable routing problem with and without wavelength-continuity constraints by proposing a new Integer Linear Programming (ILP) algorithm, which is based on a simplified necessary and sufficient condition. Numerical results are given and discussed to show that survivable routing solutions of most logical topologies can be found by the algorithm of the authors. Furthermore, comparing with other similar methods, the above algorithm can find out a survivable solution in much shorter time, and it works especially well with sparse-connected logical topologies. The impact of wavelength-continuity constraints and the other factors that influence the probability to find out a survivable solution are also discussed in the paper.