Branch-and-Refine for Solving Time-Dependent Problems

One of the standard approaches for solving time-dependent discrete optimization problems, such as the traveling salesman problem with time-windows or the shortest path problem with time-windows, is to derive a so-called time-indexed formulation. If the problem has an underlying structure that can be described by a graph, the time-indexed formulation is usually based on a … Read more

A Solution Framework for Linear PDE-Constrained Mixed-Integer Problems

We present a general numerical solution method for control problems with PDE-defined state variables over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs (and if necessary a linearization scheme) to derive constraints for a mixed-integer linear program (MILP) … Read more

An Iterative Graph Expansion Approach for the Scheduling and Routing of Airplanes

A tourism company that offers fly-in safaris is faced with the challenge to route and schedule its fleet of airplanes in an optimal way. Over the course of a given time horizon several groups of tourists have to be picked up at airports and flown to their destinations within a certain time-window. Furthermore the number … Read more