The multidimensional multi-choice knapsack problem (MMKP) is an extension of the 0-1 knapsack problem. The knapsack kernel has been used to design efficient algorithms for solving the knapsack problem. The purpose is to study how to obtain a knapsack kernel and use it to efficiently solve the multidimensional multi-choice knapsack problem. First, a method is given to determine the kernel of the MMKP. Then, the B&B algorithm that uses the kernel to accurately solve the MMKP problem is explained, and the specific algorithm steps are listed. After analyzing the storage complexity of the algorithm, the running results of the algorithm on various instances are compared with the running results of the commonly used algorithms for solving the MMKP problem. It is found that the performance of this algorithm is better than any previous algorithm.
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