A Power-Indexed Formulation for Wireless Network Design

Wireless networks have shown a rapid growth over the past two decades and now play an increasingly prominent role in different telecommunication systems. Consequently, scarce resources such as the radio spectrum and the physical sites that accommodate transmitters have become extremely congested and need to be allocated in more effective ways. Since the early 1980s several optimization models have been developed to design wireless networks, that is to localize and configure transmitters by assigning transmission frequencies and emission powers to them. Most such models represent emission powers as continuous decision variables. This choice typically yields ill-conditioned constraint matrices and requires the introduction of very large coefficients to model disjunctive relations. The corresponding relaxations are very weak and the solutions returned by Mixed-Integer Linear Programming solvers are typically far from the optimum and sometimes even infeasible. In order to overcome these difficulties, we introduce a pure 0-1 formulation for the problem that is obtained by considering only a finite set of power values. Basing on such formulation we also developed an iterative, row generation algorithm to solve wireless network design problems. The new approach presents many computational and modeling advantages. First, albeit considering only a subset of feasible solutions, it allows to find better solutions to large practical instances with less computational effort. Second, since the feasible powers are well spaced over the power spectrum, the final plans tend to be robust. Third, it directly models power restrictions that are often imposed by the technology and that sometimes permits two values only (i.e., on/off). Finally, it easily allows for generalizations, such as power consumption minimization.