A polynomial time solvable algorithm to binary quadratic programming problems with Q being a seven-diagonal matrix and its neural network implementation

Abstract

In this paper, we consider the binary quadratic programming problems (BQP). The unconstrained BQP is known to be NP-hard and has many practical applications like signal processing, economy, management and engineering. Due to this reason, many algorithms have been proposed to improve its effectiveness and efficiency. In this paper, we propose a novel algorithm based on the basic algorithm proposed in [1], [2], [3] to solve problem BQP with Q being a seven-diagonal matrix. It is shown that the proposed algorithm has good performance and high efficiency. To further improve its efficiency, the neural network implementation is realized.