The high capacity of fibers used in optical networks, can be divided into many channels, using the WDM technology. Any damage to a fiber causes all the channels routed through this link to be broken, which may result; in a serious amount of data loss. As a Solution to this problem, the virtual layer can be mapped onto the physical topology, such that, a failure on any physical link does not disconnect the virtual topology. This is known as the survivable virtual topology mapping problem. In this study, our aim is to design an efficient evolutionary algorithm to find a survivable mapping of a given virtual topology while minimizing the resource usage. We develop and experiment with different evolutionary algorithm components. As a result, we propose a suitable evolutionary algorithm and show that it can be successfully used for this problem. Overall, the results are promising and promote further study.