(41a) MAiNGO – McCormick-based Algorithm for Mixed-Integer Nonlinear Global Optimization

MAiNGO (McCormick-based
Algorithm for mixed-integer Nonlinear
Global Optimization) is a deterministic global
optimization software for the solution of mixed-integer nonlinear programs
(MINLPs), to be published open source. It is applicable to MINLPs consisting of
factorable Lipschitz continuous functions. MAiNGO supports procedural modeling and
is thus convenient for formulating optimization problems in a reduced space.
This can result in computational advantages for problems found in flowsheet
optimization (Bongartz & Mitsos, 2017; 2018), optimization with artificial
neural networks embedded (Schweidtmann & Mitsos, 2019; Rall et al. 2018),
and optimization of hybrid data-driven/mechanistic models (Schweidtmann et al.,
2019). The main distinction of MAiNGO compared to state-of-the-art global
solvers such as BARON (Khajavirad & Sahinidis, 2018), ANTIGONE (Misener
& Floudas, 2014), SCIP (Vigerske et al, 2017), COUENNE (Belotti et al.,
2009), and LINDOGLOBAL (Lin & Schrage, 2009), are i) the operation in the
original optimization variable space through the application of McCormick
relaxations (McCormick, 1976; Tsoukalas & Mitsos, 2014) and ii) flexibility
in model formulation that allows to hide parts of the model from the solver. Valid
convex and concave relaxations together with its subgradients (Mitsos et al.,
2009) are computed through the open-source library MC++ (Chachuat et al., 2015).
MAiNGO implements relaxations for various intrinsic functions, in particular functions
relevant to process systems engineering (Najman & Mitsos, 2016; Najman et
al., 2019). In addition to the spatial branch-and-bound and some well-known
bound tightening techniques, MAiNGO also contains specialized methods for
tightening of McCormick relaxations (Najman & Mitsos, 2019). We present the
algorithmic framework of MAiNGO along with computational applications to various
problems from chemical engineering and power systems. Finally, we briefly
introduce the user interface and possibilities for user-implemented heuristics
and extensions.

Acknowledgements: We
would like to thank Benoit Chachuat for providing MC++ and supporting us in
extending it. This work has received funding from the German Research Foundation
(Deutsche Forschungsgemeinschaft, DFG) Improved McCormick Relaxations for
the efficient Global Optimization in the Space of Degrees of Freedom MA
1188/34-1. The authors gratefully acknowledge additional funding by the German
Federal Ministry of Education and Research (BMBF) within the Kopernikus Project
P2X: Flexible use of renewable resources - exploration, validation and
implementation of `Power-to-X' concepts. This work was supported by the Helmholtz Association
under the Joint Initiative Energy System 2050 - A Contribution of the
Research Field Energy. The authors
gratefully acknowledge the financial support of the Kopernikus project SynErgie
by the Federal Ministry of Education and Research (BMBF) and the project
supervision by the project management organization Projektträger Jülich (PtJ).

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