We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding (MAPF) problem. By analyzing the second smallest eigenvalue (commonly known as lambda2) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller lambda2 tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity (QD) that is capable of producing maps with specified lambda2 ranges, offering a possible way for generating challenging MAPF instances. Despite the absence of a strict monotonic correlation with lambda2 and the empirical hardness of MAPF, this study serves as a valuable initial investigation for gaining a deeper understanding of what makes a MAPF instance hard to solve.

Solving Multi-Agent Path Finding (MAPF) problems optimally is known to be NP-Hard for both make-span and total arrival time minimization. Many algorithms have been developed to solve MAPF problems optimally and they all have different strengths and weaknesses. There is no dominating MAPF algorithm that works well in all types of problems and no standard guidelines for when to use which algorithm. Therefore, there is a need for developing an automatic algorithm selector that suggests the best optimal algorithm to use given a MAPF problem instance. We propose a model based on convolutions and inception modules by treating the input MAPF instance as an image. We further show that techniques such as single-agent shortest path annotation and graph embedding are very effective for improving training quality. We evaluate our model and show that it outperforms all individual algorithms in its portfolio, as well as an existing state-of-the-art MAPF algorithm selector.