# A Neural Network Based Global Optimal Algorithm for Unconstrained Binary Quadratic Programming Problem

## Abstract

Unconstrained binary quadratic programming problem is a classical integer optimization problem and is well known to be NP-hard. In order to improve the performance of global optimal algorithms for unconstrained binary quadratic programming problem, in this paper, we proposed a new exact solution method. By investigating the geometric properties of the original problem, the quality of the algorithms for calculating the upper bound and lower bound are improved. And then, for the new derived upper bound algorithm and lower bound algorithm, their recurrent neural network models are proposed and applied respectively in order to speed up the computation. The numerical results shows that the proposed algorithm of a branch-and-bound type is quite effective and efficient.

## Keywords

Binary quadratic problem Branch-and-bound Recurrent neural network## Notes

### Acknowledgments

The work described in the paper was supported by the National Science Foundation of China under Grant 61503233.

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