Optimal networks by mass transportation via points allocation

TL;DR

This paper introduces a method to derive optimal network plans as limits of simpler point allocation problems, which are easier to solve and involve finite variables, using mass transportation theory.

Contribution

It presents a novel approach linking optimal network design to mass transportation problems through point allocations, providing a new computational perspective.

Findings

Optimal network plans can be obtained as limits of point allocation problems.

Point allocation problems are solvable via finite-variable optimization.

The approach simplifies complex network optimization by using mass transportation limits.

Abstract

It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of atoms. Each of these problems can be solved by minimizing a function of a finite, prescribed number of variables.