Physarum-Inspired Multi-Commodity Flow Dynamics

TL;DR

This paper introduces a Physarum-inspired dynamic model for multi-commodity network design, demonstrating through simulations and analysis that it constructs efficient networks by minimizing combined network and routing costs.

Contribution

It extends Physarum-inspired models from shortest path to multi-commodity network design, providing both computational and theoretical insights.

Findings

The dynamics constructs efficient, elegant networks in simulations.

The model minimizes combined network and routing costs.

An alternative characterization of optimal solutions is provided.

Abstract

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution.