## 2 Related Work
The proposed novel framework utilized three metaheuristic optimization algorithms, namely grey wolf optimizer, sine cosine optimizer, and whale optimizer. It should be noted that metaheuristic algorithms are considered a specific category of stochastic algorithms and the unique features of these algorithms are that they are problem-independent techniques. The names of the two pillars of stochastic algorithms are exploration or diversification, and exploitation or intensification. Further, the exploration or diversification component aims at exploring the search space while the exploitation or intensification component aims at searching a near-optimal solution. These are the main powerful attributes of these metaheuristic algorithms. There are three classifications of metaheuristics algorithms, such as swarm intelligence algorithms, physics-based, and evolutionary algorithms. In the stage of exploration, the complete solution space is covered by the search agents with the help of their unique style of random walk. Next, at the stage of exploitation, a local search is carried out with a focused approach for candidate position by covering only a particular part of the solution space. There does not exist any predefined way in which these algorithms can work and therefore their approach is similar to the black-box approach in which we do not have awareness of the internal structure; instead, we give input and get output. Metaheuristic algorithms such as Ant Colony Optimization (ACO), Moth Flame Optimization (MFO), Interior Search Algorithm (ISA), Tabu Search (TS), Whale Optimization Algorithm (WOA), Simulated Annealing (SA), Plant Propagation Algorithm, Genetic Algorithm (GA), Firefly Algorithm, Grey Wolf Optimization (GWO), Cuttlefish Algorithm, Bat Algorithm, Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Cuckoo Search (CS), Sine Cosine Algorithm (SCA), and Intelligent Weeds Optimization (IWO), etc., have a discrete nature,and therefore these metaheuristics algorithms are suitable for solving discrete-type NP-hard as well as NP-complete optimization problems. Next, Figure 1. illustrates the phases of the proposed novel framework with steps taken in each phase. The proposed novel framework comprises two phases. In the first phase of the proposed novel framework, maximum node-disjoint routes from all the SNs to BS using minimum RNs are explored based on the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework, utilizing the properly designed efficient fitness function, and this HA-GWSCO framework also discovers \(k\)-node-disjoint routes from each SN to BS, with \(k\geq 2\), which enhances the fault-tolerance capability in EH-WSN. The first phase starts by initializing the EH-WSN. Next, RNs are deployed by adopting the strategy of a controlled random distribution with non-uniform nature. The efficient fitness function is designed and then the hybrid adapted grey wolf sine cosine optimizer (HA-GWSCO) framework is applied. The output of this hybrid framework is the maximum number of node-disjoint routes from all SNs to BS in EH-WSN using the least number of RNs and \(k\)-node-disjoint routes from each SN to BS. This output is given as input to the second phase of the proposed novel framework. The aim of the second phase is to discover the most appropriate reliable route out of \(k\)-node-disjoint routes from each SN to BS. 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 hybrid adapted grey wolf whale optimizer (HA-GWWO). Utilizing a novel and efficient fitness function covering multiple objective functions, the newly designed efficient fitness function consists of six objective functions, namely, the remaining available energy of the SNs, the distance of the edge, the energy consumption of the edge, delay in communication for the node, relay hops, and also the reliability index.