## 1 Introduction  
The excellent advancements in the field of IoT help in applying the latest smart technologies of wireless communications towards agriculture, grids, smart homes, smart industry revolution, military, etc. Currently, researchers are focusing on designing optimal energy-efficient wireless sensor networks (WSNs) consisting of a large number of tiny sensor nodes for monitoring/sensing/detecting particular events, which are operated primarily by limited-capacity batteries [1]. Tiny sensor nodes (SNs) are also known by the name source nodes (SNs). The main applications of WSNs typically occur in very harsh environments and due to these circumstances, the battery of SNs drains out very fast. Therefore, the main reason for node failure in WSNs is due to their deployment in a harsh environment [2]. Energy harvesting (EH) is the prominent solution for providing an alternative source of energy to tiny nodes for resolving energy issues but sometimes fluctuations occur in harvested energy due to environmental conditions and energy optimization again needed for effective utilization in this case [3]. The concept of duty cycle (DC) is also used for energy efficiency but in the case of an energy-harvesting wireless sensor network (EH-WSN), the SNs require a heterogeneous and dynamic DC [4]. Whenever a specific SN involved in routing a data packet to base station (BS) becomes dead, then this data packet is unable to reach the BS and other SNs are selected to route this data packet to the BS; now, these other SNs are taking extra load and their battery is more likely to deplete fast due to the overloaded mechanism and thereby a greater number of SNs becomes dead. Further, this situation creates multiple network partitions [5]. A disjointed, partitioned network may be created due to this type of inherent limitation of EH-WSN. In general terms, this situation is termed as the problem of disjointed networks. If the network partition condition arises, then, in this case, the communication mechanism happens only between the SN and those other SNs that belong to that specific respective partition only; for the remaining part of the network, they are totally cut off [6]. For resolving this condition and maintaining effective connectivity in the partitioned network, we require the placing of a special type of node, called a relay node (RN) [7]. Further, they may be different from traditional SNs in terms of the power of the battery, having the capability of movement, etc. ; also, their uniqueness lies in the fact that, first, they collect data packets from the SNs, and then they forward the data packets to neighboring RNs, and in this way data packets finally reach the sink node [8]. Relay nodes contribute towards enhancing the network life span since they relive the overloaded SNs by distributing their loads [9]. The only limitation in deploying relay nodes is related to increments in the budget of the network since they may be costly compared with traditional SNs. The relay nodes (RNs) can be placed by using two approaches, namely, the random approach or pre-determined approach [10]. The pure random approach is relatively complex since it requires distributed algorithms as well as a routing framework with self-organizing capabilities [11]. It should be noted that a controlled random approach with non-uniform nature is the best solution for the deployment of relay nodes (RNs) [12]. Therefore, for optimal performance with cost-effectiveness for the EH-WSN, we should place the minimum number of relay nodes at appropriate optimal positions. Again, this requirement forms the NP-hard problem, where the relay node optimization problem is having a discrete type nature and a discrete solution is needed for this NP-hard problem [13]. Next, fault-tolerant routing with awareness of the quality of routing is the only solution for the optimal performance of EH-WSN.