Abstract
Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. This paper investigates the potential of using decomposition and a novel multiobjective-based column and cut generation approach for solving nonconvex block-separable MINLPs, based on the so-called resource-constrained reformulation. Based on this approach, two decomposition-based inner- and outer-refinement algorithms are presented and preliminary numerical results with nonconvex MINLP instances are reported.
Highlights
Most real-world Mixed Integer Nonlinear Programming (MINLP) models are sparse, e.g. instances of the MINLPLib (Vigerske 2018)
We investigate the potential of this approach combining them with Decomposition-based Inner- and Outer-Refinement (DIOR), see Nowak et al (2018)
MINLP is a strong paradigm for modelling practical optimization problems
Summary
Most real-world Mixed Integer Nonlinear Programming (MINLP) models are sparse, e.g. instances of the MINLPLib (Vigerske 2018). These models can be reformulated as block-separable problems, defined by low-dimensional sub-problems, which are coupled by a moderate number of linear global constraints. We investigate the potential of solving block-separable MINLPs using a decomposition multi-tree approach
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