The Optimal Multiple Multicast Problem (OMMP) on wavelength division multiplexing (WDM) ring networks without wavelength conversion is considered in this paper. When the physical network and the set of multicast requests are given, OMMP is the problem that selects a suitable path (or paths) and wavelength (or wavelengths) among the many possible choices for each multicast request such that not any pair of paths using the same wavelength pass through the same link. In this paper, a formulation of OMMP is given; this problem is NP-hard since the famous RWA problem which has been proved NP-hard is a special case of OMMP. In this paper, the OMMP is divided into two subproblems: path routing and wavelength assignment subproblems. For each subproblem, two heuristic algorithms are proposed to solve it. Moreover, a hybrid method which combines heuristic and simulated annealing algorithm is proposed to find the near optimal solution. Experimental results indicate that these algorithms are efficient.