Letters: Lagrangian object relaxation neural network for combinatorial optimization problems

Authors:
Hiroki Tamura;Zongmei Zhang;Xinshun Xu;Masahiro Ishii;Zheng Tang
Affiliations:
Faculty of Engineering, Toyama University, Japan;Faculty of Engineering, Toyama University, Japan;Faculty of Engineering, Toyama University, Japan;Faculty of Engineering, Toyama University, Japan;Faculty of Engineering, Toyama University, Japan
Venue:
Neurocomputing
Year:
2005

Citing 11
Cited 1

Integer and combinatorial optimization

Integer and combinatorial optimization
On the stability of the travelling salesman problem algorithm of Hopfield and Tank

Biological Cybernetics
Chaotic Potts spin model for combinatorial optimization problems

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A New Relaxation Procedure in the Hopfield Network for Solving Optimization Problems

Neural Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research

INFORMS Journal on Computing
Improving convergence and solution quality of Hopfield-type neural networks with augmented Lagrange multipliers

IEEE Transactions on Neural Networks
Neural techniques for combinatorial optimization with applications

IEEE Transactions on Neural Networks
A parallel algorithm for tiling problems

IEEE Transactions on Neural Networks
A theoretical investigation into the performance of the Hopfield model

IEEE Transactions on Neural Networks
Performance and fault-tolerance of neural networks for optimization

IEEE Transactions on Neural Networks

A new Lagrangian net algorithm for solving max-bisection problems

Journal of Computational and Applied Mathematics

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Abstract

We propose a Lagrangian object relaxation technique that can obtain a more near-optimal solution for the traveling salesman problem (TSP). It consists of two stages. First, a feasible solution is calculated and second, a more near-optimal solution is calculated by a Hopfield neural network (HNN). The Lagrangian object relaxation technique can help the HNN escape from the local minimum by correcting Lagrangian multipliers. The Lagrangian object relaxation neural network is analyzed theoretically and evaluated experimentally through simulating the TSP. The simulation results based on some TSPLIB benchmark problems show that the proposed method can find 100% valid solutions which are near-optimal solutions.