GPU‐based branch‐and‐bound method to solve large 0‐1 knapsack problems with data‐centric strategies

Summary An out‐of‐core branch‐and‐bound (B&B) method to solve large 0‐1 knapsack problems on a graphics processing unit (GPU) is proposed. Given a large problem that produces many subproblems, the proposed method dynamically swaps subproblems to CPU memory. Because such a CPU‐centric subproblem management scheme increases CPU‐GPU data transfer, we adopt three data‐centric strategies to eliminate this side effect. The first is an out‐of‐order search (O3S) strategy that reduces the data transfer overhead by adaptively transferring subproblems between the CPU and GPU. The second is an explicitly‐managed pipelining strategy that hides the data transfer overhead by overlapping data transfer with GPU‐based B&B operations. The third is a GPU‐based stream compaction strategy that reduces the sparseness of arrays to be transferred. Experimental results demonstrate that the proposed out‐of‐core method stored 41 times as many subproblems as a previous in‐core method that manages subproblems in GPU memory, solving approximately twice as many problem instances on the GPU. In addition, compared to a previous breadth‐first search (BFS) strategy, the proposed O3S strategy achieved an average speedup of 7.5 times.