The Invisible Hand Heuristic for Origin-Destination Integer Multicommodity Network Flows

TL;DR

This paper introduces an innovative heuristic inspired by economic markets for solving origin-destination integer multicommodity flow problems, significantly improving solution speed and quality on large telecommunications networks.

Contribution

A novel invisible-hand heuristic is proposed for origin-destination multicommodity flows, demonstrating superior speed and solution quality compared to traditional LP relaxation methods.

Findings

Solution times are two orders of magnitude faster than Cplex's LP relaxation.

The heuristic achieves more dramatic MIP ratios.

Solution value differences are small, indicating high solution quality.

Abstract

Origin-destination integer multicommodity flow problems differ from classic multicommodity models in that each commodity has one source and one sink, and each commodity must be routed along a single path. A new invisible-hand heuristic that mimics economic markets' behavior is presented and tested on large-scale telecommunications networks, with solution times two orders of magnitude faster than Cplex's LP relaxation, more dramatic MIP ratios, and small solution value differences.