Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks

TL;DR

This paper demonstrates how tissue growth influences the development of transport networks, enabling systems to escape local minima and achieve near-optimal configurations, explaining biological vascular optimization.

Contribution

It introduces a model coupling tissue growth with network dynamics, revealing how growth guides networks toward global optimization in biological systems.

Findings

Growth-driven models outperform static ones in network optimization

Biological vasculature can be explained by growth-induced optimization

Tissue growth helps networks escape local minima

Abstract

Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that natural selection slowly guides the network towards an optimized state. However, general coarse grained models for flow networks with local positive feedback rules for the vessel conductivity typically get trapped in low efficiency, local minima. In this work we show how the growth of the underlying tissue, coupled to the dynamical equations for network development, can drive the system to a dramatically improved optimal state. This general model provides a surprisingly simple explanation for the appearance of highly optimized transport networks in biology such as leaf and animal vasculature.