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

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Sunday, November 10, 2019 - 3:30pm-3:51pm

MAiNGO (** M**cCormick-based

**lgorithm for mixed-**

*A***nteger**

*i***onlinear**

*N***lobal**

*G***ptimization) is a deterministic global**

*O*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

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

Research Field Energy

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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