Which Objective Function is Solved Faster in Multi-Agent Pathfinding? It Depends

Multi-agent pathfinding (MAPF) is the problem of finding safe paths for multiple mobile agents within a shared environment. This problem finds practical applications in real-world scenarios like navigation, warehousing, video games, and autonomous intersections. Finding the optimal solution to MAPF is known to be computationally hard. In the literature, two commonly used cost functions are makespan and the sum of costs. To tackle this complex problem, various algorithms have been developed, falling into two main categories: search-based approaches (e.g., Conflict Based Search) and reduction-based approaches, including reduction to SAT or ASP. In this study, we empirically compare these two approaches in the context of both makespan and the sum of costs, aiming to identify situations where one cost function presents more challenges than the other. We compare our results with older studies and improve upon their findings. Despite these solving approaches initially being designed for different cost functions, we observe similarities in their behavior. Furthermore, we identify a tipping point related to the size of the environment. On smaller maps, the sum of costs is more challenging, while makespan poses greater difficulties on larger maps for both solving paradigms, defying intuitive expectations. Our study also offers insights into the reasons behind this behavior.