Solving ramified optimal transport problem in the bayesian influence diagram framework

Abstract

The goal of the ramified optimal transport is to find an optimal transport path between two given probability measures. One measure can be identified with a source while the other one with a target. The problem is well known to be NP-hard. We develop an algorithm for solving a ramified optimal transport problem within the framework of Bayesian networks. It is based on the decision strategy optimisation technique that utilises self-annealing ideas of Chen-style stochastic optimisation. Resulting transport paths are represented in the form of tree-shaped structures. The effectiveness of the algorithm has been tested on computer-generated examples. © 2012 Springer-Verlag Berlin Heidelberg.