Convex Optimization for Binary Tree-Based Transport Networks

Raoul Sallé de Chou, Mohamed Ali Srir, Laurent Najman, Nicolas Passat, Hugues Talbot, Irene E. Vignon-Clementel

Abstract: Optimizing transport networks is a well-known class of problems that have been extensively studied, with application in many domains. Here we are interested in a generalization of the Steiner problem, which entails finding a graph minimizing a cost function associated with connecting a given set of points. In this paper, we concentrate on a specific formulation of this problem which is applied to the generation of synthetic vascular trees. More precisely, we focus on the Constrained Constructive Optimization (CCO) tree algorithm, which constructs a vascular network iteratively, optimizing a blood transport energy efficiency. We show that the classical incremental construction method often leads to sub-optimal results, and that a better global solution can be reached.