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Profit-based Sensor Network Design using the Generalized Benders Decomposition

The problem of profit-based sensor network design for linear systems has been shown to be of the nonconvex mixed integer programming class. The branch and bound search procedure can be used to obtain a global solution, but such a method is limited to fairly small systems. The bottleneck is that in each iteration of the branch and bound search, a fairly slow Semi-Definite Programming (SDP) problem must be solved to its global optimum. In this paper, we demonstrate that an equivalent reformulation of the nonconvex mixed integer programming problem and subsequent application of the Generalized Benders Decomposition (GBD) algorithm will result in massive computational effort reductions. While the proposed algorithm has to solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by the reduction of SDP problems that must be solved.