Parallel implementation of an exact two-phase method for the bi-objective knapsack problem

This paper introduces a parallel implementation of an exact two-phase method for solving the bi-objective knapsack problem on a CPU-GPU system. We utilize the Branch-and-Bound procedure in both phases, along with a highly efficient reduction technique to generate all efficient solutions. However, in the first phase, we focus on identifying all supported extreme efficient solutions, followed by reducing the dimension of the problem using an object efficiency reduction algorithm. The second phase is responsible for generating all unsupported efficient solutions. We develop a combined algorithm incorporating both phases, which is implemented in the CUDA language. Our study investigates the impact of parallel computing performance on various numerical instances compared to other exact methods in the literature. Additionally, we confirm the effectiveness of our proposed parallel-solving method by testing uncorrelated instances.