A deterministic annealing algorithm for the minimum concave cost network flow problem

The existing algorithms for the minimum concave cost network flow problems mainly focus on the single-source problems. To handle both the single-source and the multiple-source problem in the same way, especially the problems with dense arcs, a deterministic annealing algorithm is proposed in this pa...

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Vydáno v:Neural networks Ročník 24; číslo 7; s. 699 - 708
Hlavní autoři: Dang, Chuangyin, Sun, Yabin, Wang, Yuping, Yang, Yang
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Elsevier Ltd 01.09.2011
Témata:
Algorithms
Barrier function
Combinatorial optimization
Computer Simulation
Concave cost
Cost engineering
Descent
Descent direction
Deterministic annealing
Iterative method
Lagrange and barrier function
Lagrange multiplier
Mathematical analysis
Mathematical models
Network flow
Networks
Neural networks
Neural Networks (Computer)
Simulated annealing
Lagrange and barrier function
Lagrange multiplier
Network flow
Barrier function
Concave cost
Iterative method
Combinatorial optimization
Deterministic annealing
Descent direction
ISSN:0893-6080, 1879-2782, 1879-2782
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Shrnutí:The existing algorithms for the minimum concave cost network flow problems mainly focus on the single-source problems. To handle both the single-source and the multiple-source problem in the same way, especially the problems with dense arcs, a deterministic annealing algorithm is proposed in this paper. The algorithm is derived from an application of the Lagrange and Hopfield-type barrier function. It consists of two major steps: one is to find a feasible descent direction by updating Lagrange multipliers with a globally convergent iterative procedure, which forms the major contribution of this paper, and the other is to generate a point in the feasible descent direction, which always automatically satisfies lower and upper bound constraints on variables provided that the step size is a number between zero and one. The algorithm is applicable to both the single-source and the multiple-source capacitated problem and is especially effective and efficient for the problems with dense arcs. Numerical results on 48 test problems show that the algorithm is effective and efficient.
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ISSN:0893-6080
1879-2782
1879-2782
DOI:10.1016/j.neunet.2011.03.018