📝 SummarXiv

Abstract

We show how to extract alternative solutions for optimization problems solved by Benders Decom- position. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative solutions but none appear to support such generation when using Benders Decomposition. We propose a new post-processing method that extracts multiple optimal and near-optimal solutions using the cut-pool generated during Benders Decomposition. Further, we provide a geometric framework for understanding how the adaptive approximation in Benders Decomposition re- lates to alternative solutions. We demonstrate this technique on stochastic programming and interdiction modeling, and we highlight use cases that require the ability to enumerate all optimal solutions.