# A Matheuristic for Joint Optimal Power and Scheduling Assignment in DVB-T2 Networks +
## 6 Conclusions and Future Work  
Optimally designing DVB-T networks by means of Mathematical Programming is a very challenging task and resulting models may prove very tough even for state-of-the-art optimization commercial software. With the aim of tackling the unsatisfying performance of commercial solvers, we presented a new matheuristic for DVB network design that combines mathematical optimization with exact and heuristic solution strategies. Specifically, we combined a genetic algorithm with a linear relaxation-based variable fixing strategy and an exact large neighborhood search formulated as an Integer Linear Programming problem. The obtained matheuristic refers to a Power-Indexed formulation, a strong and numerically stable pure Binary Linear Programming model for a DVB network design that is obtained through discretization of the power emissions of the DVB stations from a Mixed Integer Linear Programming model that explicitly include signal-to-interference ratios. Computational tests on realistic instances indicate that our matheuristic is able to identify solutions of much higher quality than those identified by a state-of-the-art solver, thanks to a more efficient exploration of the power emission solution space.  
As future work, we plan to further increase the performance of the matheuristic, in particular through integration of it within a branch-and-cut approach. To this end, we would plan also to consider more refined lifting techniques of the considered GUB cover inequalities, to obtain stronger valid inequalities that could improve the upper bounds available on the problem. Moreover, we would aim also at improving the lower bounds, by studying refinements of the matheuristic, in particular  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **COV-CPLEX\%** & **COV-mathGA\%** & **\(\Delta\)COV-mathGA\%** & **COV-mathGA+ILP\%** & **\(\Delta\)COV-mathGA+ILP\%** \\ \hline I1 & 48.6 & 60.5 & 24.5 & 70.6 & 45.3 \\ I2 & 55.3 & 67.9 & 22.7 & 77.4 & 40.0 \\ I3 & 54.7 & 65.5 & 19.7 & 78.9 & 44.3 \\ I4 & 49.2 & 57.2 & 16.3 & 70.6 & 43.5 \\ I5 & 50.0 & 66.8 & 33.7 & 75.5 & 51.1 \\ I6 & 56.4 & 69.9 & 24.0 & 80.8 & 43.3 \\ I7 & 53.9 & 70.0 & 30.0 & 83.1 & 54.1 \\ I8 & 62.4 & 67.6 & 8.4 & 84.3 & 35.2 \\ I9 & 55.5 & 75.2 & 35.5 & 85.3 & 53.8 \\ I10 & 46.3 & 64.7 & 39.8 & 73.4 & 58.7 \\ I11 & 57.2 & 65.4 & 14.3 & 80.2 & 40.2 \\ I12 & 57.7 & 73.9 & 28.0 & 79.6 & 37.9 \\ I13 & 51.4 & 71.6 & 39.3 & 81.7 & 59.0 \\ I14 & 62.5 & 70.3 & 12.5 & 82.7 & 32.4 \\ I15 & 58.8 & 71.5 & 21.7 & 84.0 & 42.8 \\ I16 & 39.5 & 50.9 & 28.9 & 64.0 & 62.2 \\ I17 & 46.3 & 58.5 & 26.3 & 68.0 & 47.0 \\ I18 & 48.9 & 57.7 & 18.0 & 76.2 & 55.9 \\ I19 & 35.8 & 45.8 & 27.9 & 51.7 & 44.5 \\ I20 & 33.0 & 43.2 & 31.0 & 49.4 & 49.9 \\ I21 & 38.5 & 53.3 & 38.6 & 63.5 & 65.0 \\ I22 & 43.0 & 50.7 & 18.0 & 66.4 & 54.5 \\ I23 & 36.6 & 43.3 & 18.4 & 50.8 & 38.8 \\ I24 & 40.3 & 51.4 & 27.7 & 61.0 & 51.4 \\ I25 & 41.7 & 54.9 & 30.9 & 64.7 & 55.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational results.  
by investigating alternative integrations of the GA-phase with suitable exact ILP searches. Last but not least, we also plan to tackle the uncertainty of signal propagation by means of Multiband Robust Optimization [63; 64], a robust model that allows the ability to easily represent empirical discrete distributions commonly built in real-world applications on the basis of historical data.  
Conceptualization, F.D., H.L. and A.N.; Methodology, F.D., H.L. and A.N.; Validation, F.D., H.L. and A.N.; Writing--original draft, F.D., H.L. and A.N. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.