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Network survivability provided at the optical layer is a desirable feature in modern high-speed networks. For example, the wavelength division multiplexed (WDM) self-healing ring (or SHR/WDM) provides a simple and fast optically transparent protection mechanism against any single fault in the ring. Multiple self-healing rings may be deployed to design a survivable optical mesh network by superposing a set of rings on the arbitrary topology. However, the optimum design of such a network requires the joint solution of three subproblems: the ring cover of the arbitrary topology (the RC subproblem); the routing of the working lightpaths between end node pairs to carry the offered traffic demands (the WL subproblem); and the provisioning of the SHR/WDM spare wavelengths to protect every line that carries working lightpaths (the SW subproblem). The complexity of the problem is exacerbated when software and hardware requirements pose additional design constraints on the optimization process. The paper presents an approach to optimizing the design of a network with arbitrary topology protected by multiple SHRs/WDM. Three design constraints are taken into account, namely, the maximum number of rings acceptable on the same line, the maximum number of rings acceptable at the same node, and the maximum ring size. The first objective is to minimize the total wavelength mileage (working and protection) required in the given topology to carry a set of traffic demands. The exact definition of the problem is given based on an integer linear programming (ILP) formulation that takes into account the design subproblems and constraints and assumes ubiquitous wavelength conversion availability. To circumvent the computational complexity of the exact problem formulation, a suboptimal solution is proposed based on an efficient pruning of the solution space. By jointly solving the three design subproblems, it is numerically demonstrated that the proposed optimization technique yields up to 12% reduction of the total wavelength mileage when compared to solutions obtained by sequentially and independently solving the subproblems. The second objective is to reduce the number of wavelength converters required in the solution produced by the ILP formulation. Two approaches- are proposed in this case that trade the required wavelength mileage for the number of wavelength converters.