A fresh perspective on the classic Traveling Salesperson problem could boost the efficiency of space missions, especially to moving objects like asteroids. Researchers Isaac Rudich from Polytechnique Montréal and Michael Römer from Universität Bielefeld have devised a new method that aims to help space agencies plan better missions.
The Traveling Salesperson problem looks for the shortest route for visiting multiple locations. This is straightforward if the destinations are fixed, like a salesperson visiting towns. However, it gets trickier when the objects in question, such as asteroids, are constantly in motion.
Space missions often need to navigate these moving targets. While some missions use gravity from nearby planets for slingshot maneuvers—like the famous Voyager missions—others must directly travel between asteroids that change position continuously.
Rudich and Römer introduced the “Asteroid Routing Problem” (ARP). This focuses on optimizing both travel time and fuel consumption as spacecraft visit these celestial objects. Their approach requires calculating the best time and path to travel between asteroids.
“The ARP is particularly tough because it involves another complex problem—Lambert’s problem,” they explained. Lambert’s problem, dating back to the 1700s, addresses how to find the best trajectory between two moving objects. Solving this for one pair is challenging, let alone for multiple asteroids.
To simplify their calculations, the researchers used Decision Diagrams. This technique allows certain decisions to be grouped together, which reduces the number of calculations needed for Lambert’s problem. “Our method often delivers solutions that are around 20% more efficient in terms of travel time and fuel compared to traditional methods,” they noted.
While there aren’t many missions visiting multiple asteroids, a few notable ones exist. NASA’s Dawn mission explored Ceres and Vesta, while the ongoing Lucy mission is en route to several Trojan asteroids near Jupiter. Rudich and Römer suggest that examining Lucy’s mission plan with their approach could yield worthwhile insights, but they stress that ARP is a simplified version of real-world astrodynamics.
Even a small improvement—like 1% efficiency—could lead to significant savings in time, money, and fuel. Beyond space missions, this research could help optimize earthly routes, such as those for public transport, supply chains, and shipping—where factors like weather and traffic also create dynamic challenges.
Rudich and Römer published their findings in the INFORMS Journal on Computing on April 2, highlighting that their innovative mathematical approach could pioneer new efficiencies not just in space travel, but in various aspects of optimization challenges.
