Modelling min–max–min to the problem of radio base stations location

We report a new proposal to solve the base station location problem. This proposal is related to a non-differentiable min–max–min problem with multi-level nature. In order to overcome these difficulties and, thus, to be able to use more robust and efficient optimization tools, such as Gradient and Newton methods, we have developed a smoothing strategy using a special smoothing function of class C∞. Then, the final solution is obtained by solving a sequence of differentiable sub-problems which gradually approaches the original problem. The use of this technique, called Hyperbolic Smoothing, permits to overcome the main difficulties that arise from the original problem. Besides the initial min–max–min modelling, we propose three variant methods through which other issues of the base station location problem are also taken into account. An algorithm containing the essentialities of the method is also presented together with a set of computational results.