## 5 Conclusions  
In this research article, a novel framework is proposed considering single-tiered EH-WSN with constrained RN deployment. Next, the problem of relay node optimization is considered an NP-hard optimization problem. Further, the designing of effective fault-tolerant routing in EH-WSN constitutes the NP-complete problem. In the proposed novel framework, we have used metaheuristic optimization algorithms, namely, adaptive grey wolf optimizer, adaptive sine cosine optimizer, and adaptive whale optimizer, to provide solutions to the NP-hard and NP-complete problems. The proposed novel framework consists of two phases. In the first phase of the proposed novel framework, maximum node-disjoint routes from all SNs to BS using minimum RNs are explored based on the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework, utilizing a properly designed fitness function; this HA-GWSCO framework also discovers the k-node-disjoint routes from each SN to BS, with k \(\geq\) 2, which enhances the fault-tolerance capability in EH-WSN. In the second phase of the proposed novel framework, out of k-node-disjoint routes from each SN to BS, with k \(\geq\) 2, the most-appropriate reliable route is selected from each SN to BS for routing, which enhances the reliability in routing for EH-WSN based on the hybrid adapted grey wolf whale optimizer (HA-GWWO), utilizing a novel and efficient fitness function covering multiple objective functions. The effectiveness of our proposed novel framework was assessed by considering five metrics, namely, energy consumption, the lifetime of the network, throughput, delay, and the delivery ratio, and the simulation results clearly validate the efficacy of our proposed novel framework. In this way, we finally got the fully connected EH-WSN, ensuring the maximum network life, low latency, efficient distribution of the load for relieving the overloaded sensor nodes, and with minimum energy consumption due to the high connectivity. The proposed novel research effectively handles both the NP-hard (relay node optimization) as well as NP-complete (fault-tolerant reliable routing) optimization problems simultaneously in EH-WSN. This salient feature of the proposed novel research distinguishes it from others existing in the literature. As a future research direction, we would like to implement this novel framework on a real-time EH-WSN, for real-time analysis of the outcomes, by utilizing the optimal number of heterogeneous RNs for maintaining k-connectivity.  
**Author Contributions:** Conceptualization, R.S.R. and O.K.; formal analysis, R.S.R. and O.K.; investigation, R.S.R., O.K., K.N.Q. and I.T.J.; methodology, R.S.R., O.K. and K.N.Q.; supervision, O.K. and K.N.Q.; validation, R.S.R., O.K. and K.N.Q.; writing, R.S.R., O.K., K.N.Q. and I.T.J.; review and editing, R.S.R., O.K., K.N.Q., I.T.J., W.N., A.A. and N.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Deanship of Scientific Research at King Khalid University, as funding for Large Groups (project under grant number (RGP.2/111/43)).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Acknowledgments:** The authors extend their appreciation to Nottingham Trent University, Nottingham, UK.  
**Conflicts of Interest:** The authors declare no conflict of interest.