Literature review on Benders cut selection and a multiple cut generation scheme

One way to improve the efficiency of the Benders Decomposition Method is the generation of high-quality cuts. This paper presents a literature review on Benders cut selection methods, followed by the development of a multiple cut generation scheme that remains effective regardless of whether the Subproblem is decomposable or not. The proposed approach builds upon the work of Brandenberg and Stursberg (Mathematical Methods of Operations Research, 94:383–412, 2021), who developed a unifying framework for generating Benders cuts by identifying appropriate parametrizations for the cost vector of the objective function used to optimize over the alternative polyhedron. Our analytical results provide further insights into the structure of those parametrizations. Experiments are conducted to demonstrate the effectiveness of our method compared to the classical Benders Algorithm.