Convergence Properties for the Physarum Solver

TL;DR

This paper analyzes the convergence behavior of the Physarum solver, demonstrating its effectiveness in solving linear transshipment problems and its relation to infinity-harmonic solutions in the dual problem.

Contribution

It establishes the convergence of the Physarum solver to the optimal solution and links its electrical potential to infinity-harmonic functions.

Findings

Physarum solver solves linear transshipment problems.

Electrical potential converges to an infinity-harmonic solution.

Provides theoretical foundation for Physarum-based optimization methods.

Abstract

The Physarum solver is an intuitive mechanism for solving optimisation problems based on the idea of an electrical network, whereby the conductivity is reinforced by the current. We show that the Physarum solver obtains the solution to the linear transshipment problem on a digraph and that the electrical potential converges to an infinity-harmonic solution of the dual problem.