Cooperative annealing Hopfield network for unconstrained binary quadratic programming problem
► This paper first proposes an annealing HNN (AHNN) that permits temporary energy ascent to help the HNN escape from local minima. ► From a cooperative perspective, a population of the AHNN processes are then simultaneously implemented and coupled by their acceptance probabilities. ► The proposed Co...
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| Vydáno v: | Expert systems with applications Ročník 38; číslo 11; s. 13894 - 13905 |
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01.10.2011
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| Abstract | ► This paper first proposes an annealing HNN (AHNN) that permits temporary energy ascent to help the HNN escape from local minima. ► From a cooperative perspective, a population of the AHNN processes are then simultaneously implemented and coupled by their acceptance probabilities. ► The proposed CoAHNN is validated on 21 unconstrained binary quadratic programming problems with the size ranging from 3000 to 7000, and 48 maximum cut problems with the size ranging from 512 to 3375.
The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) 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. The 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. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristic algorithms and state-of-the-art algorithms. |
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| AbstractList | The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) 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. The 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. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristic algorithms and state-of-the-art algorithms. ► This paper first proposes an annealing HNN (AHNN) that permits temporary energy ascent to help the HNN escape from local minima. ► From a cooperative perspective, a population of the AHNN processes are then simultaneously implemented and coupled by their acceptance probabilities. ► The proposed CoAHNN is validated on 21 unconstrained binary quadratic programming problems with the size ranging from 3000 to 7000, and 48 maximum cut problems with the size ranging from 512 to 3375. The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) 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. The 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. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristic algorithms and state-of-the-art algorithms. |
| Author | Wang, Jiahai Yin, Jian Zhou, Ying |
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| Cites_doi | 10.1109/AICCSA.2009.5069318 10.1109/ICNN.1995.488968 10.1080/1055678021000090033 10.15388/Informatica.2006.138 10.1016/j.biosystems.2004.08.002 10.1109/TNN.2006.887556 10.1023/A:1021849410328 10.1007/BF01022991 10.1109/TCSII.2008.922373 10.1016/j.cor.2007.10.001 10.1007/BF00339943 10.1007/s00291-003-0153-3 10.1109/72.857776 10.1023/B:ANOR.0000039522.58036.68 10.1137/S1052623497328987 10.1007/978-1-4615-6089-0 10.1007/s10479-005-3449-7 10.1109/TSMCB.2009.2020435 10.1504/IJOR.2009.025005 10.1016/j.orl.2004.04.014 10.1137/S1052623400382467 10.1016/j.eswa.2010.02.032 10.1109/TSMCB.2008.2010220 10.1287/ijoc.1080.0275 10.1007/978-3-540-37275-2_156 10.1073/pnas.79.8.2554 10.1016/j.ejor.2006.06.035 10.1109/TSMCB.2009.2025775 10.1016/j.parco.2004.11.002 10.1016/S0377-2217(97)00130-6 |
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| Issue | 11 |
| Keywords | Annealing Hopfield neural network Maximum cut problem Cooperative search Unconstrained binary quadratic programming problem Combinatorial optimization problem |
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| Snippet | ► This paper first proposes an annealing HNN (AHNN) that permits temporary energy ascent to help the HNN escape from local minima. ► From a cooperative... The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima... |
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| SubjectTerms | Algorithms Annealing Annealing Hopfield neural network Combinatorial analysis Combinatorial optimization problem Computer simulation Cooperative search Maximum cut problem Minima Networks Neural networks Quadratic programming Unconstrained binary quadratic programming problem |
| Title | Cooperative annealing Hopfield network for unconstrained binary quadratic programming problem |
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