# On Mathematical Modelling of Automated Coverage Optimization in Wireless 5G and beyond Deployments
## 3 Computational Concept
### Employment of Developed Models
The examples of such relaxations are: (i) Dual LP; (ii) Prima-Dual; (iii) Lagrangian relaxation; and (iv) Surrogate relaxation [83; 84; 85]. In the case of large datasets (i.e., \(X>60\)), the meta-heuristic needs to be applied to provide a suitable solution in a reasonable time. The meta-heuristic algorithms are the class of computational methods used for optimization problems, which do not guarantee the optimal but acceptable solution. Since meta-heuristic methods contain a broad range of algorithms, we need to provide a survey on what are the options available at present. Following the literature review, we can divide the meta-heuristic algorithms into three categories: (i) swarm-based algorithms; (ii) evolution-based algorithms; and (iii) hybrid algorithms. Each of these categories contains a plethora of algorithms. The commonly used algorithms for the first category are Ant Colonies Optimization(ACO) [86], Harmony Search (HS) [87], Particle Swarm Optimization (PSO) [88], Artificial Bee Colony (ABC) [89], Gravitational Search Algorithm (GSA) [90], Firefly Algorithm (FA) [91], Teaching Learning Algorithm (TLA) [92], Chemical Reaction Optimization (CRO) [93], Water Cycle Algorithm (WCA) [94]. For the second category, there are Genetic Algorithm (GA), Differential Evolution (DE) [95], evolutionary programming and evolutionary strategies [96], Differential Search Algorithm (DSA) [97], and for the last category we can mention ant colony optimization with variable neighbourhood search and genetic algorithms with variable neighbourhood search. We see that, until now, a lot of meta-heuristic algorithms have been developed. The experiments could be done using any of these, because of the No free lunch theorem [98], it is not possible to expect that any of these algorithms can provide an ideal solution for all the use-cases and datasets. However, for SCP-based problems, it is quite common to employ evolution-based algorithms [99; 100; 101; 102]. Despite the computational complexity presented in Section 3.3, we implemented it in the GAMS optimization tool, as mentioned above, and successfully solved instances with thousands of rows and columns. The results of calculations for such large instances were received in tens of minutes on regular desktop computer (processor: Intel(R) Core(TM) i7-7700 CPU @ 3.60 GHz 3.60 GHz; installed memory (RAM): 16.0 GB; and 64-bit operating system). Since the calculation by GAMS uses deterministic heuristic, there is no need for statistical evaluation of calculations based on dozens of runs of stochastic heuristic methods. Further, on the results from the presented models, we suggest using additional optimization to tune the gNodeB parameters (power, downtilt, height, etc.) to provide the optimal gNodeB configurations. To tune these parameters, we suggest considering the multi-objective genetic algorithm presented in [47]. ```
0:\(S_{C}=\{1,\ldots,m\}\) = the set of all service centres; \(C_{L}=\{1,\ldots,n\}\) = the set of all customer locations; \(E_{s}\) = the set of existing service centres; \(P_{m}\) = selected propagation model; \(D_{m}\) = matrix representing the distances between \(S_{C}\) and \(C_{L}\); \(C_{s}\) = the set of possible capacities of service centres; \(C_{cl}\) = the set of required capacities of customer locations; \(F_{s}\) function computationalConcept() if gNodeB parameters optimization not sufficient then \(I_{m}\leftarrow\) Compute RSPS between all the \(S_{C}\) and \(C_{L}\) using selected \(P_{m}\) for selected scenario; \(R_{m}\leftarrow\) Convert \(I_{m}\) to reachability matrix based on the RSPS; \(C_{m}\leftarrow\) Convert \(R_{m}\) to capacity matrix based on the \(C_{s}\) and \(C_{cl}\); \(F_{s}\leftarrow\) Employ developed models; endif endfunction
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**Algorithm 1** The algorithm representing the whole computational concept to get the best locations to deploy service centres (gNodeB) nodes.