| Summary: | Approved for public release; distribution is unlimited === This thesis explores Benders decomposition for solving interdiction problems on electric power grids, with applications to analyzing the vulnerability of such grids to terrorist attacks. We refine and extend some existing optimization models and algorithms and demonstrate the value of our techniques using standard reliability test networks from IEEE. Our implementation of Benders decomposition optimally solves any problem instance, in theory. However, run times increase as Benders' cuts are added to the master problem, and this has prompted additional research to increase the decomposition's efficiency. We demonstrate empirical speed ups by dropping slack cuts, solving a relaxed master problem in some iterations, and using integer but not necessarily optimal master-problem solutions. These mixed strategies drastically reduce computation times. For example, in one test case, we reduce the optimality gap, and the time that it takes to achieve this gap, from 16% in 75 hours to 5% in 16 minutes. === FUNDED BY: 2002-GT-R-057 === Lieutenant Commander, United States Navy
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