Source code for the case study presented in the paper "Approximating Nonlinear Relationships for Optimal Operation of Natural Gas Transport Networks". The case study involves solving the compressor fuel cost minimization problem (FCMP) on three simple natural gas networks. For each gas network three different formulations of the FCMP are tested: a common simplified FCMP model (FCMP_S), the novel approximation FCMP model (FCMP_N) that is developed in the paper, and a partially rigorous FCMP model (FCMP_PR) that models components of the model using their most rigorous calculations where feasible. The FCMP for each of these tests was optimized using GAMS, for which the code is provided. The accuracy of each of the three models was then assessed by comparing them to a rigorous simulation. The rigorous simulation was coded in Matlab and is provided, where separate files are used to calculate the rigorous gas pressure drop along a pipeline, and the energy input required for gas compression... [more]

Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.