Project Details
Projekt
GRK 2982: Mathematics of Interdisciplinary Multiobjective Optimization
Subject Area
Mathematics
Term
since 2025
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 516090167
In many optimization problems, several, often even conflicting objective functions, such as time, cost, quality or sustainability, have to be optimized simultaneously. Very often, a linear combination with positive weights is formed and the resulting single-objective optimization problem is solved. This approach excludes relevant solutions for important classes of problems, such as discrete and non-convex problems, from the outset. If instead one solves this problem as a multi-objective optimization problem and computes or approximates the Pareto optima, one obtains significantly more information about possible compromise solutions and can make more informed decisions. The advantages offered by multi-objective optimization are well-known in principle, yet it is still far too uncommon in the treatment of real-world problems. In research, there is a discrepancy between the relatively simple practical procedures with little theoretical support - such as the one described above - and the existing theory of multi-objective optimization, which hardly considers practical constraints. Consequently, the goal of this Research Training Group is to explore the mathematics of multi-objective optimization that can be successfully used in applications. In addition to suitable theoretical foundations, we also address the topic of data in multi-objective optimization and consider different fields of application of multi-objective optimization, such as in engineering, traffic planning, and radiation therapy for cancer treatment. We formulate specific, interrelated research and doctoral theses topics for these three research areas, thus demonstrating the potential of the guiding theme of this RTG. Within the framework of the Research Training Group, we are particularly interested in training excellent young scientists who can further develop the theory and successfully apply methods of multi-objective optimization in applications. Such experts are rare and in high demand both in academia and industry, so that our future graduates will have excellent opportunities. Our training concept is closely linked to our research program and promotes through selected measures those competences that are needed to combine theory and practice of multi-objective optimization in a meaningful way. The applicants of this interdisciplinary project come from mathematics, computer science, and engineering sciences at the University Kaiserslautern-Landau and the Fraunhofer Institute for Industrial Mathematics (ITWM) in Kaiserslautern. They all have substantial previous work in the field of multi-objective optimization and have already cooperated successfully in joint projects.
DFG Programme
Research Training Groups
Applicant Institution
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Participating Institution
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM)
Spokesperson
Professor Dr. Stefan Ruzika
