Modeling Mixed-Integer Constrained Optimal Control Problems in AMPL

Modeling languages and systems for simulation and optimization of continuous ODE/DAE systems are commonly available. For the most part, they focus on convenience of user interaction, and are tightly coupled to one or a few selected numerical methods. Control problems with discrete and hybrid controls, called mixed-integer optimal control problems (MIOCPs), have recently gained increased attention as the potential for optimization is high. The mixed-integer optimization community however most often considers problems without dynamics, and relies on symbolic modeling languages such as AMPL. Access to many advances MI(N)LP codes is provided by the NEOS Server for Optimization through the AMPL modeling language. Addressing this gap, 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 easily realized and do not require intrusive changes to the AMPL language standard or implementation itself. An example of an optimal control problem solver interfaced with AMPL is the “multiple shooting code for optimal control” MUSCOD-II, a direct and simultaneous method for ODE/DAE-constrained optimal control, and its extension MS-MINTOC for mixed-integer optimal control. As an example, we use the described AMPL extensions to model a heavy duty truck control problem.