Increase in the number of users and resources consumed by modern applications results in an explosive growth in the traffic on the Internet. Optical networks with higher bandwidths offer faster and more reliable transmission of data and allows transmission of more data. Fiber optical cables have these advantages over the traditional copper wires. So it is expected that optical networks will have a wide application area. However, there are some physical impairments and optical layer constraints in optical networks. One of these is signal degradation which limits the range of optical signals. Signals are degraded during transmission and below a threshold the signals become useless. In order to prevent this, regenerators which are capable of re-amplifying optical signals are used. Since regeneration is a costly process, it is important to decrease the number of regenerators used in an optical network. To increase the reliability of the network, two edge-disjoint paths between each terminal on the network are to be constructed. So the second path could be used in case of a failure in transmitting data on an edge of the first path. Considering these requirements, selecting the nodes on which regenerators are to be placed is an important decision. In this thesis, we discuss the problem of placing signal regenerators on optical networks with restoration. An integer linear program is formulated for this problem. Due to the huge size and other problems of the formulation, it is impractical to use it on large networks. For this reason, a fast heuristic algorithm is proposed to solve this problem. Three methods are proposed to check the feasibility when a fixed set of regenerators are placed on specific nodes. Additionally, a branch and bound algorithm which employs the proposed heuristic is developed to find the optimal solution of our problem. Performance of both the heuristics and the branch and bound method are evaluated in terms of number of regenerators placed and solution times of the algorithms.