The follower optimality cuts for mixed-integer linear bilevel programming problems

We address mixed-integer linear bilevel programming. A discussion ofthe relationships between the optimistic and the pessimistic setting ispresented, providing necessary and sufficient conditions for them to beequivalent. A new class of inequalities, the follower optimality cuts, isintroduced and a related single-level non-compact reformulation of theproblem is derived. The same is done for a revision of … Read more

Efficient approaches for the robust network loading problem

We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. We compare the optimal solution cost and computational cost of the problem when using static routing, volume routing, affine routing, and dynamic routing. For the first three routing types, we compare the compact formulation with a … Read more

Using mixed-integer programming to solve power grid blackout problems

We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. Citation CORC Report TR-2005-07, Columbia University Article Download View Using mixed-integer programming … Read more