Researchers have proposed a new approach to solving the Steiner Traveling Salesman Problem (Steiner-TSP) on Graphs of Convex Sets. The problem involves finding the shortest path that visits a set of required convex sets while allowing optional transit vertices and revisits. To tackle this infinite solution space, the authors developed a unified branch-and-bound search algorithm that uses two lower-bound methods to prune the search tree. They demonstrated the effectiveness of their approach on a benchmark instance, achieving certified optimality gaps of 28.1% and 29.7%. The authors also showed how their method can be applied to a real-world problem involving mobile-manipulator inspection. --- Why it matters: This work matters because it provides a new tool for solving complex optimization problems in AI, specifically the Steiner-TSP on Graphs of Convex Sets. This could have significant implications for applications such as robotics and autonomous systems, where efficient path planning is crucial. Source: https://arxiv.org/abs/2608.21319