Optimization codes and modeling environment

As in part 1 of this paper deliberately standard NLP software was utilized in conjunction with a modeling language to numerically solve the large discrete optimization problems. Modeling languages such as AMPL [13] which will be used below permit the formulation of the problem in a language particularly suitable for this purpose. Subsequently, a number of solvers, written in different programming languages, may be called through an interface which, in the case of AMPL, is provided for free. Below the following solvers will be used: LANCELOT A [12], MINOS-5.5 [26], SNOPT-5.3-4 [14], and LOQO-4.01 [29]. Especially, the only interior point code LOQO proved to be robust and efficient for the type of problems considered. An important feature of AMPL is its automatic differentiation capability. Only function values need to be provided for objective and constraint functions.