Switching cost aware rounding for relaxations of mixed-integer optimal control problems: the two-dimensional case

This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more

Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

Feeder Routing for Air-to-Air Refueling Operations

We consider the problem of routing a fleet of feeders for civil air-to-air refueling operations. In the air-to-air refueling problem, a fixed set of cruisers requires refueling by a fleet of feeders at fixed locations and fixed points in time. A typical objective function is to minimize the fuel consumption or the total number of … Read more

A switching cost aware rounding method for relaxations of mixed-integer optimal control problems

This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more

Fast robust shortest path computations

We develop a fast method to compute an optimal robust shortest path in large networks like road networks, a fundamental problem in traffic and logistics under uncertainty. In the robust shortest path problem we are given an $s$-$t$-graph $D(V,A)$ and for each arc a nominal length $c(a)$ and a maximal increase $d(a)$ of its length. … Read more