Optimaltransport för styrning av en svärm av agenter

Abstract

The purpose of this report is to derive and implement a solver for a multimarginal optimal transport problem. This type of multimarginal optimal transport problem can be used to model and calculate how a swarm of agents should be controlled in an optimal way. Interpolation, entropic regularization and Sinkhorn iterations are used in order to do this. We applied the solver to two different cases. In the first case, the agents started according to a certain distribution inside a 100 × 100 grid and their goal was to evenly spread out. Furthermore, an obstacle was placed in the model that moved through the grid for each time step. In the last case, the algorithm was required to find an optimal way out through a maze.