We describe a set of extensions to the AMPL modeling language to conveniently model mixed integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes. Hence, no intrusive changes to the AMPL language standard or implementation itself are required. We describe and provide TACO, a toolkit for optimal control in AMPL that reads AMPL stub.nl files and detects the optimal control problems structure. This toolkit is designed to facilitate the coupling of existing optimal control software packages to AMPL. We discuss requirements, capabilities, and the current implementation. Using the example of the multiple shooting code for optimal control MUSCOD-II, a direct and simultaneous method for DAE-constrained optimal control, we access the problem information provided by the TACO toolkit in order to interface this solver with AMPL. Moreover, we show how the MS-MINTOC algorithm for mixed integer optimal control can be used to efficiently solve mixed integer optimal control problems modeled in AMPL. Three exemplary control problems are modeled using the proposed AMPL extensions to discuss how these affect the representation of optimal control problems. Solutions to these problems are obtained using MUSCOD-II and MS-MINTOC inside the AMPL environment. A collection of further AMPL control models is provided on the web site mintoc.de. Using the TACO toolkit to enable input of AMPL models, MUSCOD-II and MS-MINTOC are made available on the NEOS Server for Optimization.

%B Mathematical Programming Computation %P 1-39 %8 04/2013 %G eng %1 http://www.mcs.anl.gov/papers/P1948-0911.pdf