Value-Optimal Sensor Network Design for Steady-State and Closed-Loop Systems Using the Generalized Benders Decomposition

The problem of value-optimal sensor network design for linear systems has been shown to be of the nonconvex mixed integer programming class. While the branch and bound search procedure can be used to obtain a global solution, such a method is limited to fairly small systems. The bottleneck is that during 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, it is demonstrated 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 reductions in computational effort. While the proposed algorithm has to solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by a reduction in the number of SDP problems that must be solved.