Computational Evaluation of Cut-Strengthening Techniques in Logic-Based Benders’ Decomposition

Abstract

Cut-strengthening techniques have a significant impact on the computational effectiveness of the logic-based Benders’ decomposition (LBBD) scheme. While there have been numerous cut-strengthening techniques proposed, very little is understood about which techniques achieve the best computational performance for the LBBD scheme. This is typically due to implementations of LBBD being problem specific, and thus, no systematic study of cut-strengthening techniques for both feasibility and optimality cuts has been performed. This paper aims to provide guidance for future researchers with the presentation of an extensive computational study of five cut-strengthening techniques that are applied to three different problem types. The computational study involving 3000 problem instances shows that cut-strengthening techniques that generate irreducible cuts outperform the greedy algorithm and the use of no cut strengthening. It is shown that cut strengthening is a necessary part of the LBBD scheme, and depth-first binary search and deletion filter are the most effective cut-strengthening techniques.