# Adaptive Energy Management in 5G Network Slicing: Requirements, Architecture, and Strategies
## 6 Heuristic Strategies Discussion  
Given the \(\mathcal{NP}\)-hard nature of the problem (Section 4.3) and due to the intractability of OptTsNS for large values of \(u_{k,j}^{i}\) and/or \(q_{k,j}^{i}\) (Section 5.2.1), in this section, we introduce different strategies to find feasible solutions within a reasonable computing time. Considering that the minimization of power consumption from non-renewable energy sources in the proposed adaptive energy management model falls in the category of a multiple-choice Knapsack Problem, as proven in Section 4.3, a number of techniques could be used to produce computationally efficient heuristic strategies [36]. In this regard, and based on the literature surveyed, we propose four strategies, which, according to their degree of difficulty in implementation are: (i) a pre-partition strategy, based on a divide-and-conquer method; (ii) a greedy approach, based on a constructive algorithm; (iii) a genetic algorithmic solution based on a metaheuristic template; and (iv) a dynamic programming approach, which is a general optimization and programming technique. These approaches have been selected to cover as far as possible the main categories of methods or techniques developed to solve this kind of problem. Table 7 shows a summary of the features and implementation challenges of these strategies in the context of the proposal. The implementation and evaluation of these strategies can be addressed in future work.  
Figure 8: Performance evaluation of the OptTsNS for case study of Figure 7: (**a**) AR metric OptTsNS; (**b**) \(E_{A_{U}}\) metric OptTsNS; and (**c**) \(P_{LACK}\) metric OptTsNS. Parameters: According Table 6.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Strategy/Technique** & \multicolumn{1}{c}{**General Description**} & \multicolumn{1}{c}{**Features and Challenges**} \\ \hline Pre-Partitioning & Strategy based on a divide-and-conquer method. The original problem is divided into sub-problems of less complexity that are solved iteratively. The final solution is a combination of partial solutions. & - Easy implementation. Few modifications on OptTSNS are required. \\  & & - The strategy can be seen as a generalization of OptTSNS. \\  & & - The size of the search space decreases as divisions increase. \\  & & - Control of the accuracy and running time based on the number of divisions. \\ \hline Greedy Approach & Iterative and constructive algorithm, in which the _VarSer_ to be processed, one at time, is selected based on the value of a parameter, \(g\), \(F_{ij}\), \(F_{ij}\), or the ratio between \(F_{ij}\) and \(d_{ij}\), & - Easy implementation. The strategy must be built from scratch and there are many possible implementations. \\  & & - Good running time performance. However, there is no guarantee on the quality of the solution, because it can vary widely according to the parameter used to select the _VarSer_. \\ \hline Genetic Algorithm & Strategy inspired in the behavior of biological systems. First, an initial population of chromosomes is created, where each chromosome represents a possible _ConvSer_ (solution) formed by randomly selected _VarSer_. Later, the population evolves along with generations considering the action of the generation operators (consored and mutation) and the selection of effects that individuals (communations with the best performance metrics). Finally, in the last generation, the solution with the best fitness function (minimum \(P_{\text{N}\alpha}\)) is selected. \\ \hline Dynamic & Strategy that uses a dynamic programming method. The algorithm simplifies the analysis of \(N\) simultaneous services by analyzing and solving them one at a time. Systematically, using a bottom-up approach, the results of a previous set of services (considering their _VarSer_) are stored and used for solving a greater number of services. \\ \hline \hline \end{tabular}
\end{table}
Table 7: Heuristics strategies analyzed to solve the \(P_{\text{N}R}\) minimization problem efficiently.