A branch-and-Benders-cut method for nonlinear power design in green wireless local area networks

We consider a problem arising in the design of green (or energy-saving) Wireless Local Area Networks (WLANs). In this context, decisions on powering-on a set of access points, via the assignment of one power level to each opened access point, and decisions on the assignment of the user terminals to the opened access points, have to be taken simultaneously. In particular, the power level assigned to an access point affects, in a nonlinear way, the capacity of the connections between the access point and the user terminals that are assigned to it. We model this problem as an integer program with nonlinear constraints. We solve the proposed nonlinear integer programming model by means of a branch-and-Benders-cut method. The approach has been tested on a large set of instances, and compared to a more traditional Benders decomposition algorithm on a subset of the instances. The computational results show the superiority of the proposed branch-and-Benders-cut approach in terms of solution quality, scalability and robustness.