A customized dual ascent algorithm for a class of traffic coordination problems

Lagrangian relaxation has been pursued as a pertinent methodology for many hard scheduling problems. From standard duality theory, the method is known to provide good-quality bounds to the performance of the optimal solutions of these problems, and in certain cases, the optimal Lagrange multipliers can function as a starting point for the construction good suboptimal solutions for the original (primal) problem. In this work we consider the application of the method on a class of novel scheduling problems that concern the routing of a set of mobile agents over the edges of an underlying guidepath network. Besides the introduction of these new scheduling problems and the proposed Lagrangian relaxations, our primary contribution is an “ascent” algorithm for the corresponding dual problem that is characterized by (i) monotonic improvement of the generated solutions and (ii) finite convergence to an optimal solution.