Minimum-cost flow algorithms: an experimental evaluation

Abstract

An extensive computational analysis of several algorithms for solving the minimum-cost network flow problem is conducted. Some of the considered implementations were developed by the author and are available as part of an open-source C++ optimization library called LEMON (http://lemon.cs.elte.hu/). These codes are compared to other publicly available solvers: CS2, MCF, RelaxIV, PDNET, MCFSimplex, as well as the corresponding components of the IBM ILOG CPLEX Optimization Studio and the LEDA C++ library. This evaluation, to the author's knowledge, is more comprehensive than earlier studies in terms of the range of considered implementations as well as the diversity and size of problem instances. The presented results demonstrate that the primal network simplex and cost-scaling algorithms are the most efficient and robust in general. Other methods, however, can outperform them in particular cases. The network simplex code of the author turned out to be far superior to the other implementations of this method, and it is the most efficient solver on the majority of the considered problem instances. In contrast, the cost-scaling algorithms tend to show better asymptotic behaviour, especially on sparse graphs, and hence they are typically faster than simplex-based methods on huge networks.