A new approximation algorithm for the d-dimensional knapsack problem based on hopfield networks

Abstract

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-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.