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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Veröffentlicht in:Expert systems with applications Jg. 38; H. 11; S. 13894 - 13905
Hauptverfasser: Zhou, Ying, Wang, Jiahai, Yin, Jian
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.10.2011
Schlagworte:
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
Annealing Hopfield neural network
Maximum cut problem
Cooperative search
Unconstrained binary quadratic programming problem
Combinatorial optimization problem
ISSN:0957-4174, 1873-6793
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Zusammenfassung:► 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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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2011.04.195