A Deterministic Annealing Neural Network Algorithm for the Minimum Concave Cost Transportation Problem

In this article, a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem. Specifically, the algorithm is derived from two neural network models and Lagrange-barrier functions. The Lagrange function is used to handle linear equality cons...

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Veröffentlicht in:IEEE transaction on neural networks and learning systems Jg. 31; H. 10; S. 4354 - 4366
Hauptverfasser: Wu, Zhengtian, Karimi, Hamid Reza, Dang, Chuangyin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Annealing
Annealing scheme
barrier function
Biological neural networks
combinatorial optimization
Computational modeling
Convergence
Descent
Hierarchies
Iterative methods
Lagrange multipliers
Liapunov functions
Linear programming
Mathematical models
minimum concave cost transportation
neural network
Neural networks
Optimization
Transportation
Transportation networks
Transportation problem
ISSN:2162-237X, 2162-2388, 2162-2388
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Zusammenfassung:In this article, a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem. Specifically, the algorithm is derived from two neural network models and Lagrange-barrier functions. The Lagrange function is used to handle linear equality constraints, and the barrier function is used to force the solution to move to the global or near-global optimal solution. In both neural network models, two descent directions are constructed, and an iterative procedure for the optimization of the neural network is proposed. As a result, two corresponding Lyapunov functions are naturally obtained from these two descent directions. Furthermore, the proposed neural network models are proved to be completely stable and converge to the stable equilibrium state, therefore, the proposed algorithm converges. At last, the computer simulations on several test problems are made, and the results indicate that the proposed algorithm always generates global or near-global optimal solutions.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2019.2955137