Abstract
In this paper, we present a new multi-tree approach for solving large scale Global Optimization Problems (GOP), called DECOA (Decomposition-based Outer Approximation). DECOA is based on decomposing a GOP into sub-problems, which are coupled by linear constraints. It computes a solution by alternately solving sub- and master-problems using Branch-and-Bound (BB). Since DECOA does not use a single (global) BB-tree, it is called a multi-tree algorithm. After formulating a GOP as a block-separable MINLP, we describe how piecewise linear Outer Approximations (OA) can be computed by reformulating nonconvex functions as a Difference of Convex functions. This is followed by a description of the main- and sub-algorithms of DECOA, including a decomposition-based heuristic for finding solution candidates. Finally, we present preliminary results with MINLPs and conclusions.
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Gleixner, A., Eifler, L., Gally, T., Gamrath, G., Gemander, P., Gottwald, R.L., Hendel, G., Hojny, C., Koch, T., Miltenberger, M., Müller, B., Pfetsch, M.E., Puchert, C., Rehfeldt, D., Schlösser, F., Serrano, F., Shinano, Y., Viernickel, J.M., Vigerske, S., Weninger, D., Witt, J.T., Witzig, J.: The SCIP Optimization Suite 5.0. Technical report, www.optimization-online.org/DB_HTML/2017/12/6385.html (2017)
Hart, W.E., Laird, C.D., Watson, J.P., Woodruff, D.L., Hackebeil, G.A., Nicholson, B.L., Siirola., J.D.: Pyomo–optimization modeling in python, vol. 67, second edn. Springer Science & Business Media, Heidelberg (2017)
Lundell, A., Kronqvist, J., Westerlund, T.: The supporting hyperplane optimization toolkit. www.optimization-online.org/DB_HTML/2018/06/6680.html (2018)
Nagarajan, H., Lu, M., Wang, S., Bent, R., Sundar, K.: An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs. J. Global Optim. (2019)
Nowak, I.: Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming. Birkhäuser (2005)
Nowak, I., Breitfeld, N., Hendrix, E.M.T., Njacheun-Njanzoua, G.: Decomposition-based inner- and outer-refinement algorithms for global optimization. J. Global Optim. 72(2), 305–321 (2018)
Tawarmalani, M., Sahinidis, N.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 225–249 (2005)
Vigerske, S.: Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming. Ph.D. thesis, Humboldt-Universität zu Berlin (2012)
Vigerske, S.: MINLPLib. http://minlplib.org/index.html (2018)
Wächter, A., Lorenz, B.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)
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Muts, P., Nowak, I. (2020). Towards Multi-tree Methods for Large-Scale Global Optimization. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_50
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DOI: https://doi.org/10.1007/978-3-030-21803-4_50
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