## 2 Related Works  
The basic optimization problem related to the design of translucent optical networks is regenerator placement (RPL). The RPL problem consists of selecting regeneration nodes in the network and deciding on the number of regenerators that should be installed in each of these nodes. This problem is addressed under the consideration of the transmission reach in optical networks. An optical signal can only travel a maximum distance before its quality deteriorates to the point that it must be regenerated using an installed regenerator. As the regenerator cost is high, the objective is to deploy in the network as few regenerators as possible while ensuring all nodes can communicate with each other [4; 13]. In Reference [14], four regenerator placement algorithms were proposed: two of them were topology based (i.e., information on the network topology is utilized in the algorithms), and two methods were traffic prediction based (i.e., certain information about foreseen network traffic is available). The problem of network planning with routing and wavelength assignment (RWA) and RPL for a set of static traffic demands was studied in translucent WDM networks in Reference [15]. Moreover, various RWA methods were verified together with the RPL methods in order to find the best combination of RPL and RWA methods guaranteeing the lowest blocking probability. The authors of Reference [13] showed that the RLP is NP-Complete and developed three heuristics for the RLP based on various graph theory approaches. In Reference [16], analytical results showing the complexity of the RPL problem were presented. Four cases were considered with an upper bound on the number of regenerators installed at each node and where information on routing and/or information on the requests were given. The authors of Reference [17] proposed two new strategies for sparse regenerator placement in translucent optical networks, named most-used regenerator placement (MU-RP) and most-simultaneous-used regenerator placement (MSU-RP). Both proposed methods are based on preliminary simulations of the network to obtain statistics on regenerator usage, which are next applied for regenerator placement. The reported results showed that the MSU-RP algorithm outperformed all previous approaches. In Reference [18], four strategies for regenerator predeployment in WDMnetwork were presented, starting with a basic uniform distribution of regenerators followed by three topology-based methods that can be enriched with information on network traffic. However, it should be underlined that all of the abovementioned papers were focused on fixed-grid WDM networks. Now, we briefly discuss previous research on regenerator placement in EONs. In Reference [19] in which the spectrum allocation and regenerator placement problem was considered, a heuristic method was proposed for a static optimization scenario. The reported results showed that use of regenerators considerably decreases the utilization of spectrum resources in a translucent EON. The authors of Reference [20] addressed jointly power management and regenerator placement in mixed line rate (MLR) optical networks, and they formulated an integer linear program for the regenerator placement problem. The authors of Reference [7] proposed a dynamic algorithm for energy-efficient routing and spectrum assignment in EONs with regenerator placement. The algorithm is based on a virtual graph, and the cost is computed according to the energy consumption of the corresponding links and intermediates routers. In Reference [21], four algorithms of regenerator placement for cloud-ready EONs were described. Two of the proposed methods utilize additional knowledge of data center location and these methods provide better performance results than simpler approaches. The author of Reference [22] described an approach for regenerator placement, routing, modulation level selection, and spectrum allocation in translucent EONs.