Adaptive dynamic cost updating procedure for solving fixed charge network flow problems

Authors:
Artyom Nahapetyan;Panos Pardalos
Affiliations:
Center for Applied Optimization, Industrial and Systems Engineering Department, University of Florida, Gainesville, USA;Center for Applied Optimization, Industrial and Systems Engineering Department, University of Florida, Gainesville, USA
Venue:
Computational Optimization and Applications
Year:
2008

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Abstract

We approximate the objective function of the fixed charge network flow problem (FCNF) by a piecewise linear one, and construct a concave piecewise linear network flow problem (CPLNF). A proper choice of parameters in the CPLNF problem guarantees the equivalence between those two problems. We propose a heuristic algorithm for solving the FCNF problem, which requires solving a sequence of CPLNF problems. The algorithm employs the dynamic cost updating procedure (DCUP) to find a solution to the CPLNF problems. Preliminary numerical experiments show the effectiveness of the proposed algorithm. In particular, it provides a better solution than the dynamic slope scaling procedure in less CPU time.