Most research to date in survivable optical network design and operation, focused on the failure of a single component such as a link or a node. A double-link failure model in which any two links in the network may fail in an arbitrary order was proposed recently in literature.(1) Three loop-back methods of recovering from double-link failures were also presented. The basic idea behind these methods is to pre-compute two backup paths for each link on the primary paths and reserve resources on these paths. Compared to protection methods for single-link failure model, the protection methods for double-link failure model require much more spare capacity. Reserving dedicated resources on every backup path at the time of establishing primary path itself would consume excessive resources. In Ref. 2 and 3, we captured the various operational phases in survivable WDM networks as a single integer programming based (ILP) optimization problem. In this work, we extend our optimization framework to include double-link failures. We use the double-link failure recovery methods available in literature, employ backup multiplexing schemes to optimize capacity utilization, and provide 100% protection guarantee for double-link failure recovery. We develop rules to identify scenarios when capacity sharing among interacting demand sets is possible. Our results indicate that for the double-link failure recovery methods, the shared-link protection scheme provides 10-15% savings in capacity utilization over the dedicated link protection scheme which-reserves dedicated capacity on two backup paths for each link. We provide a way of adapting the heuristic based double-link failure recovery methods into a mathematical framework, and use techniques to improve wavelength utilization for optimal capacity usage.