Combining tabu Hopfield network and estimation of distribution for unconstrained binary quadratic programming problem
► This paper combines a tabu Hopfield neural network (THNN) with estimation of distribution algorithm (EDA) for combinatorial optimization problems. ► The short term memory of the tabu mechanism in THNN cooperates with the long term memory mechanism in EDA to help the network escape from local minim...
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| Vydáno v: | Expert systems with applications Ročník 38; číslo 12; s. 14870 - 14881 |
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Elsevier Ltd
01.11.2011
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| ISSN: | 0957-4174, 1873-6793 |
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| Abstract | ► This paper combines a tabu Hopfield neural network (THNN) with estimation of distribution algorithm (EDA) for combinatorial optimization problems. ► The short term memory of the tabu mechanism in THNN cooperates with the long term memory mechanism in EDA to help the network escape from local minima. ► The proposed THNN–EDA is tested on unconstrained binary quadratic programming problems and maximum cut problems.
Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN–EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN–EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN–EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms. |
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| AbstractList | Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0-1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN-EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN-EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN-EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms. ► This paper combines a tabu Hopfield neural network (THNN) with estimation of distribution algorithm (EDA) for combinatorial optimization problems. ► The short term memory of the tabu mechanism in THNN cooperates with the long term memory mechanism in EDA to help the network escape from local minima. ► The proposed THNN–EDA is tested on unconstrained binary quadratic programming problems and maximum cut problems. Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN–EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN–EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN–EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms. |
| Author | Wang, Jiahai Yin, Jian Zhou, Ying |
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| CitedBy_id | crossref_primary_10_1007_s10878_014_9734_0 crossref_primary_10_1155_2016_3420671 crossref_primary_10_1007_s42484_024_00186_9 crossref_primary_10_1016_j_knosys_2017_11_009 crossref_primary_10_1080_00207160_2016_1184256 |
| Cites_doi | 10.1023/A:1013500812258 10.1145/937503.937505 10.1007/BF00339943 10.1109/CEC.2006.1688410 10.1007/s00291-003-0153-3 10.1016/j.dam.2005.05.020 10.1016/j.cor.2007.10.001 10.1137/S1052623400382467 10.1080/1055678021000090033 10.1016/j.orl.2004.04.014 10.1504/IJOR.2009.025005 10.1023/A:1021849410328 10.1109/AICCSA.2009.5069318 10.1109/TSMCB.2008.2010220 10.1016/j.parco.2004.11.002 10.1073/pnas.79.8.2554 10.1007/s10479-005-3449-7 10.1016/j.ejor.2006.06.035 10.1109/TEVC.2004.840835 10.1016/j.biosystems.2004.08.002 10.1023/B:ANOR.0000039522.58036.68 10.1016/j.eswa.2010.02.032 10.1109/TCSII.2008.922373 10.1287/ijoc.1080.0275 10.1137/S1052623497328987 10.1109/TSMCA.2009.2014556 10.15388/Informatica.2006.138 |
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| Keywords | Discrete Hopfield neural network Maximum cut problem Tabu search Estimation of distribution Unconstrained binary quadratic programming problem Combinatorial optimization problem |
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| Snippet | ► This paper combines a tabu Hopfield neural network (THNN) with estimation of distribution algorithm (EDA) for combinatorial optimization problems. ► The... Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0-1 function. It is a well known NP-hard problem and is considered... |
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| SubjectTerms | Algorithms Benchmarking Combinatorial analysis Combinatorial optimization problem Computer simulation Discrete Hopfield neural network Estimation of distribution Mathematical models Maximum cut problem Networks Quadratic programming Searching Tabu search Unconstrained binary quadratic programming problem |
| Title | Combining tabu Hopfield network and estimation of distribution for unconstrained binary quadratic programming problem |
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