## 2 Related Work
Further, they have presented the NP-hard problems of connectivity and survivability in EH-WSNs. They aimed at achieving connectivity or survivability in EH-WSNs by utilizing the least number of RNs. Next, they proposed the polynomial-time O(1)-approximation frameworks for solving NP-hard problems of connectivity and survivability in EH-WSNs. The proposed approximation frameworks are having low approximation ratios. Next, [PERSON] et al. [24] have presented an efficient local search approximation framework for providing the solution to the problem of a RN single cover. The proposed connectivity-aware approximation framework for the placement of RNs aimed at reducing the system overhead. Further, [PERSON] et al. [25] have conducted studies for the RN placement problem. They aimed at achieving the optimal connectivity in ST-WSN by deploying the least possible RNs. First, they construct the neighbor components by utilizing the Voronoi Graph and Delaunay Triangle. Next, they utilized the Steiner heuristic with the Spanning tree for optimizing the placement algorithm. In the latter, all these components are combined for maintaining effective connectivity. The next paragraph will illustrate the heuristics-based frameworks for relay node optimization. [PERSON] et al. [26] have proposed frameworks for maximizing the fault tolerance in ST-WSNs. In the proposed frameworks they assumed sensors having different ranges. Next, [PERSON] et al. [27] have proposed an efficient framework for achieving effective connectivity in ST-EH-WSNs. They aimed at deploying the least possible RNs at a subspace of candidate areas. Further, the constrained deployment RNs constitute the constrained RN placement problem. Further, [PERSON] et al. [28] have proposed an efficient framework for deploying the least possible RNs in ST-WSNs known as the branch-and-cut framework. In the proposed framework, they assumed a bound of predefined delay in between the SNs and BS. Furthermore, [PERSON] et al. [29] have proposed an effective coverage scheme for mobile SNs in ST-WSNs, which are randomly deployed. The proposed effective self-healing coverage scheme is based on fuzzy logic. The proposed effective scheme is aimed at reducing the coverage hole. First, the proposed effective coverage scheme explores the uncovered areas of the sensing. In the next step, the coverage hole issue is effectively handled by selecting the best mobile SNs. Besides, [PERSON] et al. [30] have proposed dual efficient frameworks known as Greedy-MSP and GRASP-MSP for providing the solution to placement problems related to multiple sinks. Further, the two proposed frameworks are also used for providing the solution to the problem of RNs' deployment, with the ultimate aim of reducing the cost of deployment. Next, the proposed frameworks assure the double-coverage of each SN. Moreover, [PERSON] et al. [31] have proposed an efficient framework for providing the solution to constrained RN placement problems in ST-WSNs by effectively handling the deployment of RNs in ST-WSNs. The proposed framework aimed at reducing the outage probabilities during the construction of the routing tree with the addition of the least possible RNs for effective connectivity. Also, [PERSON] et al. [32] have proposed an effective heuristic scheme for enhancing the life of the network. The proposed effective heuristic scheme provides the solution to the constrained RN placement problem. In the proposed heuristic scheme, the life of the network in ST, as well as TT-WSNs, has been significantly enhanced with the deployment of extra SNs and RNs. The next paragraph will illustrate the frameworks based on metaheuristics for relay node optimization. [PERSON] et al. [33] have conducted extensive studies for understanding the problem of optimal deployment. They proposed the framework utilizing the particle swarm algorithm for integer planning.