Summary: The damper placement problem for large flexible space truss structures is to determine the \(p\) truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and columns indexed on the truss members we seek to find a set of \(p\) columns such that the smallest row sum, over the \(p\) columns, is maximized. An extension of this model is formulated for the passive damper case. This formulation includes the frequency of maximum displacement as a decision variable for each passive damper. Each formulation can be written as a mixed 0/1 integer linear program. We compare the performance of tabu search and simulated annealing for the damper placement problem on a laboratory test article, the NASA Langley Controls-Structures Interaction Phase I Evolutionary Model (10 modes and 1507 truss members). Tabu search, coupled with the starting solution generated by rounding the solution to a linear programming relaxation, is shown to provide the highest quality solutions in the shortest amount of computing time.