## 3 Methodology
### Correlated Multi-Objective Energy-Efficient Routing Scheme for SDWSN-IoT  
While most decision problems actually have multiple objectives, most algorithms dealing with agents that need to interact with sequential decision problems focus on optimizing a single objective. Dealing with multi-objective problems (MOP) requires the simultaneous optimization of multiple feedback signals or objectives. Most research on multi-objective optimization is focused on solving problems with conflicting objectives, and rightly so, as these are hard problems with many possible Pareto optimal trade-off solutions. To nonetheless deal with the multiple objectives of the real world, a common approach to creating decision-theoretic agents is to combine all the important aspects together into a single, scalar, additive reward function. The scalarization functions involve assigning an individual weight to \(m\) objectives, allowing the reward function designer to have control over the trade-off of the objectives. This trade-off is parametrized by \(w_{o}\in[0,1]\) for objective \(o\), in a linear combination \(\sum_{o=1}^{m}w_{o}\cdot Q_{0}(s,a)\) whereby \(\sum_{o=1}^{m}w_{o}=1\). This iterative process, which is done repeatedly until the behavior is acceptable, lacks explainability of the decision-making process and is often subjected to a retraining process when preferences between objectives change. Furthermore, assigning weights to objectives is a challenging task that often demands extensive weight tuning and a thorough comprehension of each objective's preference. Failure to properly set these weights often results in biased or suboptimal solutions, highlighting the complexity involved in achieving an effective objective weighting strategy. For example, when trying to train an agent in a network environment, the reward function designer may wish to double the weight of one objective. Even when the objectives are linearly weighted in the reward function, doubling the weight of one objective for a specific aspect of performance might not guarantee a better performance of that objective due to the potential non-linear relationship between the reward weights and the actual objective outcomes. Applying typical _RL_ frameworks to determine optimal routing paths for multi-objective optimization, while using a vector of conflicting objectives as a reward function, presents challenges in managing trade-offs among the objectives, which can lead to suboptimal routing paths. For instance, in the context of routing paths for multi-objective optimization, conflicting objectives may include minimizing delay and maximizing throughput. Improving delay might involve choosing longer paths with less congestion, while maximizing throughput may require selecting shorter paths that could be more congested. Achieving a balance between such competing objectives is challenging since enhancing one objective often comes at the expense of sacrificing performance in another. The study focuses on identifying multi-objective solutions with correlated objectives, where the limited Pareto front makes it challenging to discern clear trade-offs. The reward function designer prioritizes the fast discovery of a near-optimal policy and its closeness to optimality over distinguishing very similar optimal trade-offs. To optimize the performance, a reinforcement learning agent leverages both signals in combination rather than relying solely on one. To address this, the study transforms a single-objective MDP into a _Correlated Multi-Objective Markov Decision Process_ (CMOMDP) by incorporating multiple potential- based shaped reward functions. In this study, we have chosen to implement the CMOMDP approach due to its ability to address multiple correlated optimization objectives, providing comprehensive information about the system. The primary objective of achieving energy efficiency is the optimization of the average energy consumption of nodes.