Hierarchically Accelerated Dynamic Programming with Applications to Transportation Networks

In this paper, we propose a scheme called Hierarchically Accelerated Dynamic Programming (HADP) which gives signiicant speed up of Dynamic Programming (up to several orders of magnitude) for Discrete Event Systems (DES) modelled by nite state machines: this is at the cost of a degree of sub-optimality. This methodology is based upon a dynamical abstraction of the given DES by state aggregation which generates a so-called partition machine (Caines and Wei, 1995, 1998). We discuss necessary and suucient conditions for the HADP procedure to generate global optimal solutions and, further, give bounds on the degree of sub-optimality which can occur. Finally, we use an example called the Broken Manhattan Grid to illustrate our software implementation of HADP with a three level hierarchy.