Following the 25th International Conference on Multiple Criteria Decision Making (MCDM 2019) in Istanbul, Turkey, June 16–21, 2019, and the Dagstuhl Seminar on Scalability in Multiobjective Optimization in Dagstuhl, Germany, January 12–17, 2020, we decided to organise a special issue on theory, computation, and practice of multiobjective optimisation. Since at the two conferences many presentations addressed a variety of different multiobjective optimisation problems, we decided to focus this special issue distinctively on recent developments in multiobjective optimisation falling within the a posteriori paradigm of multiple criteria decision making (MCDM). Motivated by the prevalence of presentations on this topic, our goal was to give the international community an opportunity to publish papers proposing models, methods, and algorithms for multiobjective optimisation and their supporting mathematical theory. In addition, to make the future volume appealing to scientists, engineers, and practitioners, the final call for papers also asked for manuscripts describing important applications of multiobjective optimisation in practice.

In total, we received 38 submissions for this issue. Of these submissions, 15 papers were out of scope by addressing other topics in the MCDM area; 9 papers were rejected following reviews; 1 paper was withdrawn by the authors during the review process; and 13 papers were accepted. These 13 papers constitute this special issue.

The topics addressed in these papers follow the recent trends observed in the optimisation area in general. The type of optimisation problems addressed ranges from scheduling problems with two objectives to mixed integer linear optimisation problems and nonlinear optimization problems, both with only continuous and with continuous as well as binary variables. Some multiobjective models are specifically bi- or tri-objective while the methods include exact, heuristic, or hybrid algorithms to compute or approximate the Pareto set of these problems. Exact methods are typically used for small-size problems while heuristic or hybrid algorithms are designed for large-scale instances for which they prove to be competitive. The presented applications reflect the type of decision-making situations that are important but challenging and therefore of interest to researchers.

We observe that multiobjective optimisation under uncertainty and multiobjective optimisation in practical applications are the dominating research themes throughout this volume because a majority of studies address either one or both of them simultaneously. Multiobjective optimisation models carrying uncertainty are considered from a theoretical as well as an applied perspective. For the former, you will find a paper developing robust optimality conditions for quadratic problems under data uncertainty, another one presenting optimality conditions for robust multiobjective optimisation problems, and still another one proposing robustness measures for integer linear problems under decision uncertainty. In an applied context, bi-objective facility location in the presence of data uncertainty and a robust optimisation approach to a closed loop supply-chain model are presented in two other papers.

To demonstrate a new methodology, many of the papers also cover an application problem either directly or as a case study. In particular, these case studies include 3D printing; load balancing in aeronautical telecommunication networks; a location-allocation problem for unmanned aircraft systems; and several problems arising in logistics and supply chain modelling (disassembly line balancing, supplier selection, and facility location). Other applications relate to education (efficiency and fairness in assigning students to projects) and medicine (radiotherapy treatment planning).

In summary, we believe that the 13 papers in this special issue, cover a wide range of optimisation models, solution methods and applications, and provide evidence that the area of multiobjective optimisation is continuously developing. We are confident that readers will find some contributions of interest to them and will appreciate the evolution of multiobjective optimisation that for us, the co-editors of this volume, has been a source of professional energy and fulfilment.