A New Approximation Algorithm for the d-dimensional Knapsack Problem Based on Hopfield Networks
In this paper, we study the d-dimensional knapsack problem (d-KP). The problem d-KP is a generalized version of the well-known knapsack problem (1-KP) which is known to be an NP-complete problem. It is also known that there is no fully polynomial-time approximation scheme for d-KP for \(d >1\) unless \(P=NP\). In this work, we design an approximation algorithm for d-KP based on the Hopfield networks. Experimental results show that our proposed algorithm outperforms a well-known greedy algorithm in many cases.
Keywordsd-dimensional knapsack problem Hopfield network Approximation algorithm NP-complete
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