A Benchmark Library of Mixed-Integer Optimal Control Problems

Abstract

Numerical algorithm developers need standardized test instances for empirical studies and proofs of concept. There are several libraries available for finite- dimensional optimization, such as the netlib or the miplib. However, for mixed-integer optimal control problems (MIOCP) this is not yet the case. One explanation for this is the fact that no dominant standard format has been established yet. In many cases instances are used in a discretized form, but without proper descriptions on the modeling assumptions and discretizations that have been applied. In many publications crucial values, such as initial values, parameters, or a concise definition of all constraints are missing. In this contribution we intend to establish the basis for a benchmark library of mixed-integer optimal control problems that is meant to be continuously extended online on the open community web page http://mintoc.de. The guiding principles will be comprehensiveness, a detailed description of where a model comes from and what the underlying assumptions are, a clear distinction between problem and method description (such as a discretization in space or time), reproducibility of solutions and a standardized problem formulation. Also, the problems will be classified according to model and solution characteristics. We do not benchmark MIOCP solvers, but provide a library infrastructure and sample problems as a basis for future studies. A second objective is to formulate mixed-integer nonlinear programs (MINLPs) orig- inating from these MIOCPs. The snag is of course that we need to apply one out of several possible method-specific discretizations in time and space in the first place to obtain a MINLP. Yet the resulting MINLPs originating from control problems with an indication of the currently best known solution are hopefully a valuable test set for de- velopers of generic MINLP solvers. The problem specifications can also be downloaded from http://mintoc.de.