## 1 Introduction  
Orthogonal frequency division multiple access (OFDMA) combines the orthogonal frequency division multiplexing (OFDM) and frequency division multiple access (FDMA) technology for multiple access of multiple users at a high data rate. The OFDMA scheme in the fourth generation mobile communication system (4G) long-term evolution (LTE) technology has not only upgraded spectrum efficiency but also provided high resistance for frequency-selective fading channels [1]. The Device-to-Device (D2D) is a developing key technique for next generation (5G) mobile communication systems [2]. The D2D technique allows unauthorized users equipment (UEs) to access unused authorized cellular UE bands, thereby improving the utilization efficiency of bandwidth resources. The D2D can maximize communications services in adjacent areas due to the transfer of data without going through the base station. For example, the regional transmission and Wi-Fi combined [3; 4] can provide more neighboring users with multimedia services; allow them to find a nearby friend; allow for real-time communications conversations; and permit product advertising. It also has the potential to be applied in settings of emergency medicine [5] and disaster situations [6] where patients far outnumber healthcare providers and the outreaching communication bandwidth is limited. Several resource allocation algorithms have been developed to allocate system's subcarriers and users' transmission powers in the uplink of Single-carrier Frequency-Division Multiple Access (SC-FDMA) wireless networks [7]. The various resource allocation algorithms are categorized into four major classes based on the ultimate goal/objective of the resource allocation process as follows: (i) throughput optimization, (ii) fairness, (iii) satisfaction of users' QoS requirements and (iv) joint power and subcarriers allocation [7]. Moreover, the multi-sharing D2D communication allows any cellular user equipment to share its radio resource with multiple D2D devices [8]. In reference [9], the maximum independent set based and Stackelberg game based (MISS) algorithm has been developed by jointly considering resource block reuse and power control. In reference [10], the maximum independent set based and Stackelberg power based (MiSo) algorithm has been developed for the radio resource share of cellular user equipment to multiple D2D devices with joint spectrum reuse and power control. In this study, the resource blocks (RBs) are allocated to UEs according to the evolutional algorithms for LTE systems. The advantages of D2D techniques include increased energy efficiency of transmission, energy saving [11] and coverage rate improvement [6]. When there is serious interference from the environments of communication systems, most UEs with direct transmission cannot reach the transmission rate requirement when the UEs is far from the base station. However, with the addition of a relay station for transmission, most UEs can reach the minimum requirements of transmission rate [10]. Therefore, after the application of a relay station for transmission in the serious interference environment, the performance of the system outperforms the direct transmission systems. Particle Swarm Optimization (PSO) algorithm [12] is one of the evolutionary algorithms, which imitates the foraging behavior of a flock of birds through learning and grouping the best experience. PSO for lowering Service Delay in Edge Cloud Computing has been proposed for improvement while still maintaining a low execution time for scenarios of multiple cloudlets [12]. In reference [13], a Simple PSO (SPSO) algorithm was developed for resources allocation to achieve a high quality of service (QoS) and to maximize system capacity. Therefore, in this paper, we further proposed a Refined PSO (RPSO) to enhance the throughput of UEs and to improve the system capacity performance. The GA is a stochastic search algorithm whose procedures are based on the Darwinian models of natural selection and evolution [14].