The NEOS Server offers MUSCOD-II (Multiple Shooting
CODe for Optimal Control) for the solution of mixed integer
nonlinear ODE- or DAE-constrained optimal control problems in an
extended AMPL format.
The AMPL modeling language itself does not allow the formulation of
differential equations. Hence, the TACO Toolkit has been
designed to implement a small set of extensions for easy and convenient
modeling of optimal control problems in AMPL, without the need for
explicit encoding of discretization schemes (e.g. collocation).
Both the TACO Toolkit and the NEOS interface to MUSCOD-II are still
Your feedback is appreciated.
MUSCOD-II is not in the public domain, but can be licensed from the
Simulation and Optimization group
Interdisciplinary Center for Scientific Computing (IWR)
Heidelberg University, Germany.
It is a joint development effort by many current and
former members of the Simulation and Optimization group at Heidelberg:
with contributions from many others.
The TACO Toolkit and the NEOS driver for MUSCOD-II were written and are
Christian Kirches and Sven Leyffer.
Developers of optimal control problem solvers can download
the TACO Toolkit source code.
- Hans Georg Bock and Johannes P. Schlöder,
- Daniel B. Leineweber, Moritz Diehl, and Andreas Schäfer,
- Christian Hoffmann, Christian Kirches, Andreas Potschka, Sebastian Sager, and Leonard Wirsching,
The class of tractable problems is described in the
MUSCOD-II User's Manual.
Mixed-integer optimal control problems (MIOCPs) should be submitted in
their Partial Outer Convexification reformulation. Then, an
approximation theorem holds for the convexified and relaxed problem's
solution. A variety of algorithms and strategies may be invoked using
the bflag option to obtain an integer feasible solution.
Compared to the C/Fortran interface to MUSCOD-II, the AMPL interface to
MUSCOD-II provided through the NEOS server exposes limited functionality
only. Restrictions are due to the need to express the model in AMPL
syntax. Moreover, some algorithms and problem classes such as
model-predictive control and moving horizon estimation don't fit well
into the NEOS concept. Users interested in tackling such online
optimization problems with direct multiple shooting algorithms are
invited to contact us.
Using the NEOS Server for MUSCOD-II
The user must submit a model in AMPL
format using the TACO Toolkit for AMPL Control
Optimization extensions, to solve a mixed integer nonlinear ODE- or
DAE-constrained optimal control problem. Examples of models in AMPL/TACO
format can be found in the open mixed-integer optimal control problem
collection at mintOC.de.
The model is specified by a model file, and optionally, a data file and
a commands file. If the command file is specified it must contain the
AMPL solve command.
Quality software requires constant feedback and testing on a realistic set
of problems. We hence
may collect models you submit, for benchmarking and
Solutions are reported in a separate plain-text file. The
TACO Toolkit paper
describes the simple file format and
shows a small AMPL script for reading it. Values for ODE/DAE state
trajectories and controls trajectories are reported at shooting node
positions. Be aware that ODE/DAE state values are initial values for
ODE/DAE initial value problems, and should not simply be interpolated
Setting Options for MUSCOD-II
MUSCOD-II has a variety of options that can alter the algorithm's
behavior. The TACO Toolkit paper
has a complete list of
those options accessible from AMPL. There are two ways to set options to
MUSCOD-II through NEOS. First, the AMPL commands file can contain AMPL
commands to set options for MUSCOD-II. Second, the user can specify the
name of a local options file muscod.opt that will be used.
Printing directed to standard out is returned to the user with the