RLT2-based Parallel Algorithms for Solving Large Quadratic Assignment Problems on Graphics Processing Unit Clusters

This paper discusses efficient parallel algorithms for obtaining strong lower bounds and exact solutions for large instances of the Quadratic Assignment Problem (QAP). Our parallel architecture is comprised of both multi-core processors and Compute Unified Device Architecture (CUDA) enabled NVIDIA Graphics Processing Units (GPUs) on the Blue Waters Supercomputing Facility at the University of Illinois at Urbana-Champaign. We propose novel parallelization of the Lagrangian Dual Ascent algorithm on the GPUs, which is used for solving a QAP formulation based on Level-2 Refactorization Linearization Technique (RLT2). The Linear Assignment sub-problems (LAPs) in this procedure are solved using our accelerated Hungarian algorithm [Date, Ketan, Rakesh Nagi. 2016. GPU-accelerated Hungarian algorithms for the Linear Assignment Problem. Parallel Computing 57 52-72]. We embed this accelerated dual ascent algorithm in a parallel branch-and-bound scheme and conduct extensive computational experiments on single and multiple GPUs, using problem instances with up to 42 facilities from the QAPLIB. The experiments suggest that our GPU-based approach is scalable and it can be used to obtain tight lower bounds on large QAP instances. Our accelerated branch-and-bound scheme is able to comfortably solve Nugent and Taillard instances (up to 30 facilities) from the QAPLIB, using modest number of GPUs.