On Parallelizing Benson’s Algorithm:

Multiple objective linear programming problems frequently arise in various applications of computational and data science. An important class of iterative techniques for numerically solving these problems is based on Benson’s algorithm. This algorithm starts with an initial outer approximation of a polyhedron and then iteratively refines these outer approximations until a solution is found. This algorithm is an archetype of a class of methods that have been extensively studied serially. Today, however, there is hardly any discussion in the open literature on the difficulties encountered when executing this algorithm in parallel. To fill this gap, we report on numerical experiences when parallelizing Benson’s algorithm on two different shared-memory computers. More precisely, we quantify the performance of a parallelized version of this algorithm on two Intel systems (single socket Core i7-6700 with up to 4 threads and dual socket Xeon E5-2650v4 using up to 24 threads). We show that parallelizing Benson’s algorithm has its performance limitations caused by memory bandwidth saturation. We also sketch opportunities for future research directions on techniques that could improve the performance of Benson-type algorithms on parallel computers.