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polynomial time solvable algorithms to a class of unconstrained and linearly constrained binary quadratic programming problems

引用

NEUROCOMPUTING 2016年 198卷 171-179页

作者： Gu, Shenshen Cui, Rui Peng, Jiao Shanghai Univ Sch Mechatron Engn & Automat 149 Yanchang Rd Shanghai 200072 Peoples R China

Binary quadratic programming (BQP) is a typical integer programming problem widely applied in the field of signal processing, economy, management and engineering. However, it is NP-hard and lacks efficient algorithms. Due to this reason, in this paper, some novel polynomial algorithms are proposed to solve a class of unconstrained and linearly constrained binary quadratic programming problems. We first deduce the polynomial time solvable algorithms to the unconstrained binary quadratic programming problems with Q being a seven-diagonal matrix (UBQP7) and a five-diagonal matrix (UBQP5) respectively with two different approaches. Then, the algorithm to unconstrained problem is combined with the dynamic programming method to solve the linearly constrained binary quadratic programming problem with Q being a five-diagonal matrix (LCBQP5). In addition, the polynomial solvable feature of these algorithms is analyzed and some specific examples are presented to illustrate these new algorithms. Lastly, we demonstrate their polynomial feature as well as their high efficiency. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Binary quadratic programming polynomial time solvable algorithm Dynamic programming

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