# A Matheuristic for Joint Optimal Power and Scheduling Assignment in DVB-T2 Networks +
#### Related Works  
The use of mathematical optimization techniques in the context of wireless network design is not new and can be traced back to at least twenty years ago, as highlighted and surveyed for quite a wide range of problems in [13] and in [14]. Also, the adoption of bio-inspired and genetic heuristics is not new: if we focus on genetic and evolutionary algorithms, we can report the remarkable cases of: [15], which addresses the problem of the optimal positioning of base stations in a mobile network, encoding the location of base stations in the chromosomes of the genetic algorithm; [16], which addresses the decision problem of how establishing the optimal assignment of users to deployed transmitters, in particular in the context of WiMAX networks, encoding the assignment in the chromosomes; [17], which focuses on the frequency assignment problem (FAP), proposing a permutation-based genetic algorithm to solve minimum span and fixed spectrum variants of the FAP; [18], which focuses on the problem of setting the power emissions of base stations, proposing two distributed power control algorithms that are based on evolutionary computation techniques to fast solve the linear equation systems associated with power updates of the stations; [19], which proposes a genetic algorithm for addressing the joint problem of power, frequency and modulation scheme assignment in fixed networks based on the WiMAX technology. Moreover, it is interesting to note that other works have also tried to tackle sources of data uncertainty within wireless network design problems, such as [20; 21], which adopt a stochastic optimization approach to find a robust location plan of base stations to deal with fluctuations in traffic demand, [22], which deals with the stochastic scheduling of 5G multimedia services and [23; 24; 25], which propose stochastic programming and robust optimization approaches to deal with signal propagation uncertainty of wireless technologies in real-world environments. After having discussed the previous works, it is very interesting to note that, to our best knowledge, in literature there are no matheuristics proposed for DVB network design problems. More specifically, it is also very important to remark that there are no cases of matheuristic expressly designed for tackling the numerical difficulties (ill-conditioned matrices and big-M coefficients) associated with classical optimization models for wireless network design problems (we refer the reader to Section 3 for a discussion about such numerical difficulties). Our new matheuristic, which combines genetic algorithms and ILP heuristics, is thus the first of its genre in the wireless network design context that we study. Within the DVB network design context, we can position our matheuristic between exact optimization algorithms, guaranteeing, at least theoretically, convergence to an optimal solution, and (bio-inspired) heuristics, which instead produce solutions without quality guarantees. Concerning exact algorithms, we can cite the case of [26], which proposes an innovative cutting-plane method based on generalized-upper bound cover inequalities that eliminates sources of numerical instabilities, and [27] which proposes a packing reformulation of the single frequency network design problem arising in DVB-T. Concerning heuristics, besides the already discussed case of [19], we can cite the cases of: [28], which proposes particle swarm optimization and adaptive simulated annealing algorithms for optimizing the coverage of a DVB-T/H network; [29], which proposes a genetic algorithm to solve a service coverage problem of single frequency digital radio and television networks, considering also the energy efficiency and carbon footprint; [30], which attempts to reduce interference in single frequency networks, by optimizing the orientation of transmitters exploiting a simulated annealing algorithm.