# A Matheuristic for Joint Optimal Power and Scheduling Assignment in DVB-T2 Networks +
## 5 Computational Tests  
For testing the performance of the new matheuristic, we considered 25 instances corresponding with regional DVB-T networks from Italy. Every instance corresponds to a single frequency network that is based on terrestrial DVB technology and is made up of a number of stations with a power emission belonging to the range \([-40,26]\) dBkW. The number of stations involved in the instances varies from 127 to more than 500 and the number of testpoints vary from about 2000 to more than 7000. We conducted the computational tests on a notebook equipped with the Windows operating system, a 2.70 GHz Intel i7 and 8 GB of RAM. In order to solve the MILP and ILP problems, we used the optimization software IBM ILOG CPLEX 12.5. We implemented the optimization model and solution algorithms by means of C/C++, using IBM Concert Technology for interfacing the code with CPLEX.  
A time limit of 3600 s was set for CPLEX when solving the instances. Also the new matheuristic runs with a time limit of 3600 s. Such computational time budget is distributed in the following way among the two main phases: the GA phase is subject to a time limit of 3000 s, while the ILP-based improvement heuristic exploiting mod-RINS is subject to a time limit of 600 s. The parameters of the algorithm were set as follows, on the basis of preliminary computational experience: (1) In every tournament selection we use \(k=10\) groups; (2) each group includes a fraction \(\alpha=0.1\) of the population _POP_; (3) the best \(m=10\) individuals of every group are chosen for crossover; (4) after having generated the new individuals, a fraction \(\gamma=0.2\) of the population experiences mutation; (5) in mod-RINS, we set \(\rho=0.1\).  
In Table 2, we report the results of the computational tests. ID is the identifier of the instances. _COV-CPLEX_% is the percentage of population covered by the best solution found by the optimizer CPLEX within the time limit. _COV-mathGA_% and _COV-mathGA+ILP_% are instead the percentages of population covered by the matheuristic before and after the execution of the mod-RINS improvement heuristic. Finally, _\(\Delta\)COV-mathGA_% and _\(\Delta\)COV-mathGA+ILP_% denote the percentage coverage increase that the matheuristic grant with respect to CPLEX before and after mod-RINS.  
Considering the values reported in Table 2, it is evident that even an effective and efficient solver like CPLEX finds difficulties in getting feasible solutions of high quality for the DVB model and that for the instances of larger size (with ID from I16 to I25) the percentage coverage is quite low. In contrast, the new matheuristic is able to identify solutions of much higher quality for all instances, both before and after the application of the mod-RINS improvement heuristic. Specifically, before the execution of mod-RINS, the matheuristic grants an average percentage improvement that is about 25% and that reaches almost 40% in the best case. After the execution of the improvement phase, the average percentage increase raises to 48% with peaks that exceed 60% improvement with respect to CPLEX.  
As discussed in the subsection devoted to strengthening the model, this can be explained by the fact that CPLEX must face the combined effect of complicating signal-to-interference constraints with a large number of stations involved, ill-conditioned matrices and weak big-M formulations, which greatly slow the convergence to optimal solutions, whereas the matheuristic can much faster and more effectively explore the discrete space of power emissions. The improvements that we are able to obtain are very remarkable, especially considering that, when dealing with instances that involve large portions of territories like our regional instances, even small increases in coverage may entail that thousands of additional users are able to obtain the service.