Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD

Multi-Tree Decomposition Methods for Large-Scale Mixed Integer Nonlinear Optimization

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. Decomposition methods solve a block-separable MINLP by alternately solving master problems and sub-problems. In practice, decomposition methods are sometimes the only possibility to compute high-quality solutions of large-scale optimization problems. However, efficient implementations may require expert knowledge and problem-specific features. Recently, there is renewed interest in making these methods accessible to general users by developing generic decomposition frameworks and modelling support. The focus of this chapter is on so-called multi-tree decomposition methods, which iteratively approximate the feasible area without using a single (global) branch-and-bound tree, i.e. branch-and-bound is only used for solving sub-problems. After an introduction, we describe first outer approximation (OA) decomposition methods, including the adaptive, multivariate partitioning (AMP) and the novel decomposition-based outer approximation (DECOA) algorithm . This is followed by a description of multi-tree methods using a reduced master problem for solving large-scale industrial optimization problems. The first method to be described applies parallel column generation (CG) and iterative fixing for solving nonconvex transport optimization problems with several hundred millions of variables and constraints. The second method is based on a novel approach combining CG and compact outer approximation. The last methodology to be discussed is the general Benders decomposition method for globally solving large nonconvex stochastic programs using a reduced mixed-integer programming (MIP) master problem

Beyond economics : understanding the decision-making of German small private landlords in terms of energy efficiency investment

The German government aims to achieve virtually climate-neutral building stock by 2050 to tackle climate change. To realise this goal, comprehensive policy packages based on neoclassical economic theory are in place to foster energy efficiency investment. However, in the building sector, there is increasingly a gap between this aspiration and the reality. It is claimed that one of the main reasons for this is that the existing policy framework fails to address the specific characteristics and needs of different groups of building owners. This is a particular challenge in Germany, where 80% of all dwellings are owned privately and 37% are rented out by small private landlords (SPL). Despite the significant numbers of SPL, they often follow black box decision-making processes when considering energy renovations. In this study, the author uses an explanatory model to understand the decision-making processes of SPL, combining theoretical aspects from different research disciplines. This model was applied to a low-demand housing market in a neighbourhood in the Ruhr area. Eighteen semi-structured interviews (each lasting between 37 and 115 min) were conducted, demonstrating that in addition to economic factors, the values, beliefs, norms and routines of SPL - as well as their personal capabilities and contextual factors - play an important role in their decision-making. Based on the findings, recommendations are made for enhancing the effectiveness of existing energy efficiency policies and other supporting instruments (e.g. tenancy law and social legislation), tailored to the specific needs of SPL