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Network service outage causes tremendous revenue loss and service disruption for both unicast and multicast traffic. In particular, multicast traffic suffers more in network failures than unicast traffic does, because a link in a multicast tree might carry traffic to multiple destinations. Hence, network survivability is crucial to provisioning of multicast sessions in optical WDM networks. The preconfigured protection cycle (p- cycle) method, originally proposed for unicast traffic protection  by W. D. Grover, combines the rings' simplicity, fast speed in switching, and the meshes' flexibility in routing, efficiency in resource utilization. Although p-cycles have been extensively studied for unicast traffic protection, they have been rarely applied to multicast traffic protection. We have recently proposed applying link p-cycle based approaches, namely Dynamic p-Cycle (DpC) design and link p-cycle based Protected Working Capacity Envelope (PWCE) design to dynamic provisioning of survivable multicast traffic . In this paper, we analyze the existing multicast protection approaches and present Integer Linear Programming (ILP) methods for p-cycle based protection of static multicast sessions. We consider the approaches of p-cycle based ILP joint optimization (JOP) and Non-joint optimization (NJOP), and the approach of p-cycle based ILP optimization of spare capacity (SOP). These ILP optimization methods serve as the bench mark for p-cycle based heuristic algorithms . We also compare the results with that of the Path Pair Protection approach in  . We show that the p- cycle based JOP offers the least total capacity consumption, compared with other optimization approaches.