A Branch-and-Bound algorithm using multiple GPU-based LP solvers

Abstract

The Branch-and-Bound (B&B) method is a well-known optimization algorithm for solving integer linear programming (ILP) models in the field of operations research. It is part of software often employed by businesses for finding solutions to problems such as airline scheduling problems. It operates according to a divide-and-conquer principle by building a tree-like structure with nodes that represent linear programming (LP) problems. A LP solver commonly used to process the nodes is the simplex method. Nowadays its sequential implementation can be found in almost all commercial ILP solvers. In this paper, we present a hybrid CPU-GPU implementation of the B&B algorithm. The B&B tree is managed by the CPU, while the revised simplex method is mainly a GPU implementation, relying on the CUDA technology of NVIDIA. The CPU manages concurrently multiple instances of the LP solver. The principal difference with a sequential implementation of the B&B algorithm pertains to the LP solver, provided that the B&B tree is managed with the same strategy. We thus compared our GPU-based implementation of the revised simplex to a well-known open-source sequential solver, named CLP, of the COIN-OR project. For given problem densities, we measured a size threshhold beyond which our GPU implementation outperformed its sequential counterpart.