An Out-of-Core Branch and Bound Method for Solving the 0-1 Knapsack Problem on a GPU

In this paper, we propose an out-of-core branch and bound (B&B) method for solving the 0-1 knapsack problem on a graphics processing unit (GPU). Given a large problem that produces many subproblems, the proposed method dynamically swaps subproblems out to CPU memory. We adopt two strategies to realize this swapping-out procedure with minimum amount of CPU-GPU data transfer. The first strategy is a GPU-based stream compaction strategy that reduces the sparseness of arrays. The second strategy is a double buffering strategy that hides the data transfer overhead by overlapping data transfer with GPU-based B&B operations. Experimental results show that the proposed method can store 33.7 times more subproblems than the previous method, solving twice more instances on the GPU. As for the stream compaction strategy, an input-output separated scheme runs 13.1% faster than an input-output unified scheme.