Extreme-Point Search Heuristics for Solving Interval-Flow Transshipment Networks

Interval-flow networks are a special class of network models that can include minimum-flow requirements on some or all active arcs in a feasible solution. While this extension expresses constraints often encountered in practice, the resulting NP-hard problems are challenging to solve by standard means. This work describes a heuristic that explores adjacent extreme-point solutions to quickly find high-quality feasible solutions to large-scale instances of this problem class. Computer software implementing this approach is tested on problems with up to 40,000 nodes and 1 million arcs, giving solution speeds over 400 times faster than a leading commercial optimizer.