An approximation algorithm for graph partitioning via deterministic annealing neural network

Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a co...

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Published in:	Neural networks Vol. 117; pp. 191 - 200
Main Authors:	Wu, Zhengtian, Karimi, Hamid Reza, Dang, Chuangyin
Format:	Journal Article
Language:	English
Published:	United States Elsevier Ltd 01.09.2019
Subjects:	Combinatorial optimization Deterministic annealing neural network algorithm Graph partitioning Neural network NP-hard problem Graph partitioning Deterministic annealing neural network algorithm NP-hard problem Neural network Combinatorial optimization
ISSN:	0893-6080, 1879-2782, 1879-2782
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Abstract	Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a continuation method that attempts to obtain a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. With the barrier parameter assumed to be any positive number, one minimum solution of the barrier problem can be found by the algorithm in a feasible descent direction. With a globally convergent iterative procedure, the feasible descent direction could be obtained by renewing Lagrange multipliers red. A distinctive feature of it is that the upper and lower bounds on the variables will be automatically satisfied on the condition that the step length is a value from 0 to 1. Four well-known algorithms are compared with the proposed one on 100 test samples. Simulation results show effectiveness of the proposed algorithm.
AbstractList	Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a continuation method that attempts to obtain a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. With the barrier parameter assumed to be any positive number, one minimum solution of the barrier problem can be found by the algorithm in a feasible descent direction. With a globally convergent iterative procedure, the feasible descent direction could be obtained by renewing Lagrange multipliers red. A distinctive feature of it is that the upper and lower bounds on the variables will be automatically satisfied on the condition that the step length is a value from 0 to 1. Four well-known algorithms are compared with the proposed one on 100 test samples. Simulation results show effectiveness of the proposed algorithm. Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a continuation method that attempts to obtain a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. With the barrier parameter assumed to be any positive number, one minimum solution of the barrier problem can be found by the algorithm in a feasible descent direction. With a globally convergent iterative procedure, the feasible descent direction could be obtained by renewing Lagrange multipliers red. A distinctive feature of it is that the upper and lower bounds on the variables will be automatically satisfied on the condition that the step length is a value from 0 to 1. Four well-known algorithms are compared with the proposed one on 100 test samples. Simulation results show effectiveness of the proposed algorithm.Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a continuation method that attempts to obtain a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. With the barrier parameter assumed to be any positive number, one minimum solution of the barrier problem can be found by the algorithm in a feasible descent direction. With a globally convergent iterative procedure, the feasible descent direction could be obtained by renewing Lagrange multipliers red. A distinctive feature of it is that the upper and lower bounds on the variables will be automatically satisfied on the condition that the step length is a value from 0 to 1. Four well-known algorithms are compared with the proposed one on 100 test samples. Simulation results show effectiveness of the proposed algorithm.
Author	Dang, Chuangyin Wu, Zhengtian Karimi, Hamid Reza
Author_xml	– sequence: 1 givenname: Zhengtian orcidid: 0000-0001-7702-5730 surname: Wu fullname: Wu, Zhengtian email: wzht8@mail.usts.edu.cn organization: School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China – sequence: 2 givenname: Hamid Reza surname: Karimi fullname: Karimi, Hamid Reza email: hamidreza.karimi@polimi.it organization: Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy – sequence: 3 givenname: Chuangyin surname: Dang fullname: Dang, Chuangyin organization: Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong
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Keywords	Graph partitioning Deterministic annealing neural network algorithm NP-hard problem Neural network Combinatorial optimization
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Snippet	Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an...
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SubjectTerms	Combinatorial optimization Deterministic annealing neural network algorithm Graph partitioning Neural network NP-hard problem
Title	An approximation algorithm for graph partitioning via deterministic annealing neural network
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