Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Combining interior-point and pivoting algorithms for linear programming
Management Science
An efficient implementation of a scaling minimum-cost flow algorithm
Journal of Algorithms
Primal-dual interior-point methods
Primal-dual interior-point methods
Algorithms for Network Programming
Algorithms for Network Programming
A Specialized Interior-Point Algorithm for Multicommodity Network Flows
SIAM Journal on Optimization
A Study of Preconditioners for Network Interior Point Methods
Computational Optimization and Applications
A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems
INFORMS Journal on Computing
New Preconditioners for KKT Systems of Network Flow Problems
SIAM Journal on Optimization
A Computational Study of Cost Reoptimization for Min-Cost Flow Problems
INFORMS Journal on Computing
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Interior point (IP) algorithms for Min Cost Flow (MCF) problems have been shown to be competitive with combinatorial approaches, at least on some problem classes and for very large instances. This is in part due to availability of specialized crossover routines for MCF; these allow early termination of the IP approach, sparing it with the final iterations where the Karush Kuhn-Tucker (KKT) systems become more difficult to solve. As the crossover procedures are nothing but combinatorial approaches to MCF that are only allowed to perform few iterations, the IP algorithm can be seen as a complex 'multiple crash start' routine for the combinatorial ones. We report our experiments of allowing one primal-dual combinatorial algorithm to MCF to perform as many iterations as required to solve the problem after being warm-started by an IP approach. Our results show that the efficiency of the combined approach critically depends on the accurate selection of a set of parameters among very many possible ones, for which designing accurate guidelines appears not to be an easy task; however, they also show that the combined approach can be competitive with the original combinatorial algorithm, at least on some 'difficult' instances.