The project, carried out from 1 May 2020 to 30 April 2023, addressed the integration of neighbourhood‑scale power networks into larger transmission and distribution grids. The main scientific challenge was to minimise the adverse effects of fluctuating renewable injections while respecting the multiple, often conflicting, objectives that arise in network operation. This required the development of a robust multi‑objective optimisation framework that can handle uncertainty in the parameters that influence the objective functions.

A key contribution of the work was the introduction of a vectorisation scheme for non‑convex set‑valued optimisation problems. By reformulating a set‑valued objective into a multi‑objective vector problem, the scheme allows the use of standard multi‑objective solvers while preserving the original problem’s structure. The authors demonstrated that this approach can be applied to a broad class of non‑convex problems that arise in power system optimisation, including those with uncertain parameters. In parallel, an epigraphical reformulation was developed for uncertain multi‑objective problems. This reformulation transforms the robust counterpart of a multi‑objective problem into a deterministic semi‑infinite optimisation problem, which can be tackled with existing algorithms. The combination of vectorisation and epigraphical reformulation provides a systematic way to solve robust set‑valued optimisation problems that were previously intractable.

The methodology was applied to the specific context of integrating neighbourhood networks into the German grid. The robust optimisation model explicitly accounts for the variability of renewable injections and the resulting uncertainty in network constraints. By treating each neighbourhood’s flexibility as an individual objective, the model achieves a higher optimisation potential compared with aggregated approaches. The authors reported that the robust solutions obtained through the new framework maintain acceptable performance even under worst‑case scenarios, thereby reducing the risk of network violations. Although the report does not list numerical performance figures, the results were published in the SIAM Journal on Optimization (2022) and presented at several international conferences, where they received positive feedback from the optimisation community.

In addition to the set‑valued optimisation work, the project explored multi‑objective bilevel optimisation, which naturally arises when the network operation problem is nested within a higher‑level planning problem. The authors leveraged their expertise in bilevel optimisation to model the hierarchical decision structure and to propose solution strategies that respect the multiple objectives at both levels. A dissertation project scheduled for 2024 will implement the proposed algorithms and make the implementation publicly available, further extending the impact of the research.

Collaboration was central to the project’s success. The consortium comprised the Technical University of Ilmenau, the University of Bremen, OFFIS e.V., and IAV GmbH. Each partner contributed complementary expertise: Ilmenau provided the mathematical theory and algorithm development; Bremen supplied application knowledge and data from real‑world networks; OFFIS contributed computational resources and software engineering; and IAV offered industry perspective and validation. The project was funded by the German Research Foundation (DFG) under grant number 528525668, titled “Zur Stützeigenschaft in der multikriteriellen Optimierung.” The consortium’s joint effort enabled the translation of advanced mathematical concepts into tools that can be applied to the design and operation of future energy systems.