## 1 Introduction  
Due to the increasing demands for various types of high data rate services, cellular networks are facing the problem of resource limitations. For solving these problems, multicast device-to-device (M-D2D) communications underlaying long-term evolution-advanced (LTE-A) cellular networks have become enormously favorable [1]. In M-D2D communication, nearby devices form an M-D2D group where D2D receivers in the group can receive the same data from the D2D transmitter over a direct link, without relying on the evolved node B (eNB). There are two approaches of M-D2D communications: With network assistance and without network assistance [2]. In the network-assisted M-D2D communications, M-D2D groups are placed in the coverage area of the eNB. Thus, the eNB maintains information to generate peer discovery, mode selection, scheduling, and so on. The key benefits of network-assisted M-D2D communications are: The reusing of resources between M-D2D groups and cellular users, and the reduction of power consumption. On the other hand, in M-D2D communications without network assistance, M-D2D groups are not placed in the coverage area of the eNB. The main limitation of the M-D2D communications without network assistance is that the D2D communication is prone to security issues. Moreover, M-D2D communications can be categorized into: Single rate and multi-rate transmissions [3]. In the single-rate transmission, the D2D transmitter in a multicast group transmits the same data rate to its corresponding receivers. Whereas, in the multi-rate transmission, the D2D transmitter in a multicast group transmits multiple data rates according to the receiver's demands. Compared to a unicast (point-to-point) communication system, where a transmitter sends the signal to a single receiver, M-D2D communication reduces overhead and increases spectral efficiency. This concept is envisaged as the promising solution for the incoming 5G system and Internet of Things (IoT) technology. However, the system faces challenges in coordinating conventional cellular communication and D2D communication over a single resource simultaneously. The interference from the cellular user to D2D receivers in a multicast group and interference from the M-D2D transmitter to the eNB are incorporated as the main challenge. Therefore, there is a need for an effective solution that guarantees D2D communications will not generate deleterious interference to conventional users and also between M-D2D groups [4]. In [5], the authors proposed a multi-carrier code-division multiple access (MC-CDMA) transmission scheme in M-D2D communication. The results showed that their proposed scheme achieves a better signal-to-interference-plus-noise ratio (SINR) compared with a conventional scheme. Interference coordination mechanisms for M-D2D communication underlaying uplink cellular networks are discussed in [6]. A dynamic power control scheme was introduced to mitigate interference from M-D2D to a cellular network. Comparing the result of this scheme with that of a conventional multicast transmission scheme shows the improvement of the system throughput. Cooperative relay-based D2D communications have attracted the interest of new mobile broadband communications systems. In relay-based D2D communications, nearby devices can communicate through multi-hops instead of a single hop over the eNB. Such communication technology can improve cell throughput and coverage for the users located far away from the eNB. In [7], an optimization problem was proposed to find the optimal solution by taking into account both the relay social-trust level and propagation link condition. The problem with this study is: Interference scenarios are not considered distinctly. Some new limitations with respect to D2D communications are high energy consumption and computational complexity. To reap low computational complexity, heuristic algorithms are rapidly gaining popularity as a promising solution.