Solution Quality Improvements for Massively Multi-Agent Pathfinding

In multi-agent pathfinding, MAPP (Wang and Botea 2009; 2010) has previously been shown to be state-of-the-art in terms of scalability and success ratio (i.e., percentage of solved units), on problems involving significantly larger numbers of mobile units than can be tractably handled using optimal algorithms. MAPP further provides a formal characterization of problems it can solve, and low-polynomial upper bounds on the resources required. However, until now, MAPP’s solution quality had not been extensively analyzed. In this work we empirically analyze the quality of MAPP’s solutions using multiple quality criteria, such as total travel distance, makespan, and sum of actions (including move and wait actions). We introduce enhancements that have shown significant improvements. On average, the sum of actions is cut to half. We maintain MAPP’s advantages on different performance criteria, such as scalability, success ratio, complexity upper bounds, and ability to tell apriori if it will succeed in the instance at hand. The improved MAPP becomes state-of-the-art in terms of solution quality, being competitive with FAR (Wang and Botea 2008) and WHCA* (Silver 2005), two successful algorithms from the literature. On the other hand, FAR and WHCA* lack the ability to a priori decide whether they can solve an instance, and their upper bounds on resources required are not known. Since finding optimal solutions is NP-complete (Surynek 2010; Ratner and Warmuth 1986), optimal algorithms have limited scalability. To evaluate the quality of the solutions provided by suboptimal algorithms, we compare their solutions to lower bounds of optimal values, which are cheap to compute. These lower bounds are obtained from counting moves only, ignoring wait actions. In the cases of total travel distance and sum of actions, we sum the shortest path from each start to target. For makespan, we take the number of moves in the longest path. Results show that MAPP’s solutions have a reasonable quality. For instance, MAPP’s total travel distance is on average 19% longer than an A* lower bound on the optimal value.