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.

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

Karimi H. R.;
2020-01-01

Abstract

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.
2020
Annealing scheme
barrier function
combinatorial optimization
Lagrange multipliers
minimum concave cost transportation
neural network
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1167209
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