Some more general information on MAiNGO can be found in the latest MAiNGO report:
- D. Bongartz, J. Najman, S. Sass, and A. Mitsos, MAiNGO - McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization. Technical Report, Process Systems Engineering (AVT.SVT), RWTH Aachen University (2018).
Relaxations
The relaxations implemented in MC++ that are used in MAiNGO were introduced in the following works (details on the implementation can be found in the documentation of MC++):
- G.P. McCormick, Computability of global solutions to factorable nonconvex programs: Part I - Convex underestimating problem, Mathematical Programming 10 (1976) 145-175.
- A. Mitsos, B. Chachuat, and P.I. Barton, McCormick-Based Relaxations of Algorithms, SIAM Journal on Optimization 20 (2009) 573-601.
- J.K. Scott, M.D. Stuber, and P.I. Barton, Generalized McCormick Relaxations, Journal of Global Optimization 51 (2011) 569-606.
- A. Tsoukalas and A. Mitsos, Multivariate McCormick Relaxations, Journal of Global Optimization 59 (2014) 633-662.
- J. Najman, D. Bongartz, A. Tsoukalas, and A. Mitsos, Erratum to: Multivariate McCormick Relaxations, Journal of Global Optimization 68 (2017) 219-225.
- A. Wechsung and P.I. Barton, Global optimization of bounded factorable functions with discontinuities, Journal of Global Optimization 58 (2014) 1-30.
A discussion of their convergence properties can be found in:
- A. Bompadre and A. Mitsos, Convergence rate of McCormick relaxations, Journal of Global Optimization 52 (2012) 1-28.
- J. Najman and A. Mitsos, Convergence analysis of multivariate McCormick relaxations, Journal of Global Optimization 66 (2016) 597-628.
- J. Najman and A. Mitsos, On tightness and anchoring of McCormick and other relaxations, Journal of Global Optimization 74 (2019) 677-703.
Examples for the construction of tighter relaxations for special functions can be found in:
- J. Najman and A. Mitsos, Convergence Order of McCormick Relaxations for LMTD function in Heat Exchanger Networks, In: 26th European Symposium on Computer Aided Process Engineering (2016) 1605-1610.
- A. Schweidtmann and A. Mitsos, Global Deterministic Optimization with Artificial Neural Networks Embedded, Journal of Optimization Theory and Applications 180(3) (2019).
- J. Najman, D. Bongartz, and A. Mitsos, Relaxations of thermodynamic property and costing models in process engineering. Computers & Chemical Engineering 130 (2019) 106571.
- J. Najman, D. Bongartz, and A. Mitsos, Convex Relaxations of Componentwise Convex Functions. Computers & Chemical Engineering 130 (2019) 106527.
Further extensions that are currently not implemented include the following:
- M.D. Stuber, J.K. Scott, and P.I. Barton, Convex and concave relaxations of implicit functions, Optimization Methods and Software 30 (2015) 424-460.
- A. Wechsung, J.K. Scott, H.A. Watson, and P.I. Barton, Reverse propagation of McCormick relaxations, Journal of Global Optimization 63 (2015) 1-36.
- K.A. Khan, H.A. Watson, and P.I. Barton, Differentiable McCormick Relaxations, Journal of Global Optimization 67 (2017) 687-729.
Branch-and-Bound
Branch-and-Bound for continuous optimization is attributed to:
- J.E. Falk and R.M. Soland, An algorithm for separable nonconvex programming problems, Management Science 15 (1969) 550-569.
Basic results about convergence properties as well as a discussion of node selection, branching schemes etc can be found in:
- R. Horst and H. Tuy, Global Optimization: Deterministic approaches, Springer Science & Business Media, Berlin (1996).
- M. Locatelli and F. Schoen, Global Optimization: Theory, algorithms, and applications, MIS-SIAM, Philadelphia (2013).
- M. Tawarmalani and N.V. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming, Kluwer Academic Publishers (2002).
The structure of MAiNGO's algorithm (in particular the iterative application of node pre-processing, LBP, UBP, and node post-processing) is analogous to the one described in the latter.
Range Reduction
An overview of range reduction techniques can be found in:
- Y. Puranik and N.V. Sahinidis, Domain reduction techniques for global NLP and MINLP optimization, Constraints (2017), doi:10.1007/s10601-016-9267-5.
- M. Locatelli and F. Schoen, Global Optimization: Theory, algorithmy, and applications, MIS-SIAM, Philadelphia (2013).
Duality-based bound tightening (DBBT) as well as probing are taken from:
- H.S. Ryoo and N.V. Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Computers & Chemical Engineering 19 (1995) 551-566.
- H.S. Ryoo and N.V. Sahinidis, A branch-and-reduce approach to global optimization, Journal of Global Optimization 8 (1996) 107-138.
A detailed discussion of optimization-based bound tightening (OBBT) as well as the trivial filtering and greedy heuristic implemented in MAiNGO can be found in:
- A.M. Gleixner, T. Berthold, B. Müller, and S. Weltge, Three enhancements for optimization-based bound tightening, Journal of Global Optimization 67 (2017) 731-757.
McCormick subgradient-based interval heuristic:
- J. Najman, A. Mitsos, Tighter McCormick relaxations through subgradient propagation. Journal of Global Optimization (2019).
Uses of MAiNGO
Examples of applications of earlier versions of MAiNGO can be found in:
- D. Bongartz and A. Mitsos, Deterministic Global Optimization of Process Flowsheets in a Reduced Space Using McCormick Relaxations, Journal of Global Optimization 69 (2017) 761-796.
- D. Bongartz and A. Mitsos, Infeasible Path Global Flowsheet Optimization Using McCormick Relaxations, In: Proceedings of the 27th Symposium on Computer Aided Process Engineering - ESCAPE27 (2017) 631-636.
- D. Bongartz and A. Mitsos, Deterministic Global Flowsheet Optimization: Between Equation-Oriented and Sequential-Modular Methods, AIChE Journal 65 (2019) 1022-1034.
- W.R. Huster, D. Bongartz, and A. Mitsos, Deterministic Global Optimization of the Design of a Geothermal Organic Rankine Cycle, Energy Procedia 129 (2017) 50-57.
- W.R. Huster, A.M. Schweidtmann and A. Mitsos, Impact of accurate working fluid properties on the globally optimal design of an organic Rankine cycle, Computer Aided Chemical Engineering 47 (2019) 427-432.
- W.R. Huster, A.M. Schweidtmann and A. Mitsos, Working fluid selection for organic rankine cycles via deterministic global optimization of design and operation, Optimization and Engineering (2019) in press.
- D. Rall, D. Menne, A.M. Schweidtmann, J. Kamp, L. von Kolzenberg, A. Mitsos and Matthias Wessling, Rational design of ion separation membranes, Journal of Membrane Science 569 (2019) 209-219.
- P. Schäfer, A.M. Schweidtmann, P.H.A. Lenz, H.M.C. Markgraf, A. Mitsos, Wavelet-based grid-adaptation for nonlinear scheduling subject to time-variable electricity prices, Computers and Chemical Engineering (2019) in press.
- A.M. Schweidtmann, D. Bongartz, W.R. Huster, A. Mitsos, Deterministic Global Process Optimization: Flash Calculations via Artificial Neural Networks, Computer Aided Chemical Engineering 46 (2019) 937-942.
- A.M. Schweidtmann and A. Mitsos, Deterministic Global Optimization with Artificial Neural Networks Embedded, Journal of Optimization Theory and Applications 180 (2019) 925-948.
- A.M. Schweidtmann, W.R. Huster, J.T. Lüthje and A. Mitsos, Deterministic global process optimization: Accurate (single-species) properties via artificial neural networks, Computers & Chemical Engineering 121 (2019) 67-74.