How does one plan a space mission that involves visiting multiple celestial bodies which are constantly moving? Researchers at Bielefeld University have, for the first time, developed a precise mathematical approach to this problem. The publication in a leading international journal demonstrates that decision-support methods at the interface between economics and mathematics can advance space travel and transport planning – with implications extending far beyond space missions.
Key facts at a glance:
• An international team, including researchers from Bielefeld University, has developed the first precise solution to a highly complex problem in space logistics.
• The results were published in INFORMS Journal on Computing, a leading international journal.
• The method could help make not only space missions, but also transportation and logistics systems on Earth more efficient in the future.
A new scientific publication from Bielefeld University sets a benchmark in optimization research. Together with an international team, Professor Michael Römer from the Faculty of Business Administration and Economics has developed a mathematical framework that solves a complex problem from space logistics exactly for the first time: the optimal planning of a route to visit several asteroids under conditions that are as close to reality as possible.
At the center of the research is the so-called Asteroid Routing Problem. It addresses the question: In what order should a spacecraft visit multiple asteroids if both travel time and fuel consumption are to be minimized? The challenge is that, unlike in classical routing problems, the travel time between destinations is constantly changing because all celestial bodies are in continuous motion.
From an ESA idea to a top-tier publication
The idea for the study originated in Bielefeld, sparked by a success in a competition organized by the European Space Agency (ESA). During a research stay in Bielefeld, lead author Isaac Rudich revisited the topic and, together with the team, developed a new solution approach.
The researchers used so-called Decision Diagrams—graphical optimization models that systematically structure very large sets of possible solutions. Combined with a specialized search method that narrows down promising solutions efficiently, the team was able to compute exact solutions to this problem for the first time.
A particularly challenging component involved a subproblem from celestial mechanics known as the Lambert problem. It describes how to calculate an optimal trajectory between two moving objects. Because this calculation must be repeated for every possible route, the overall problem had previously been considered extremely difficult to solve.
Relevance far beyond space exploration
The social significance extends far beyond the space industry, as many real-world planning problems operate in a similar way: in the case of bus routes, supply chains or shipping routes, too, journey times often depend on the departure time, because factors such as weather or traffic volumes change dynamically. The calculations involved are often very complex. The new approach could help make such systems more efficient and robust in the future. This has implications for mobility, supply systems, and sustainability. In tests, the method delivered not only multiple provably optimal solutions, but also new benchmark values that can guide future research.
Statement by Professor Michael Römer
“This work is special because it combines a scientific breakthrough with strong future potential. We have not only solved a long-standing open problem exactly for the first time, but also shown that our methods can generate impulses for space exploration, logistics, and public transport. It is precisely this connection between fundamental research and societal application that makes this publication so relevant.”