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A deterministic annealing algorithm for the minimum concave cost network flow problem
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DOI：10.1016/j.neunet.2011.03.018.png)
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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. (C) 2011 Elsevier Ltd. All rights reserved.
Keyword:
Concave cost
Network flow
Combinatorial optimization
Lagrange multiplier
Barrier function
Lagrange and barrier function
Descent direction
Iterative method
Deterministic annealing
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