Abstract
In this work, first, we model the non-overlapping Multi-Agent Pathfinding (MAPF) to an NP-complete traditional puzzle called Numberlink puzzle owing to its features. Interestingly, this puzzle is reasonably shown to be analogous to the Flow Free game. Hence an approach that solves the puzzle can be considered as the AI for solving Flow Free game. Then, we investigate various promising approaches such as SAT, Heuristics, and Monte-Carlo Tree Search (MCTS) based methods to find a fast and accurate solution and provide a fair comparison. We implement and evaluate two SAT and MCTS-based approaches. Finally, we propose an enhanced MCTS with three optimizations to solve the problem faster with lower memory consumption, particularly in significant test sizes with many agents. All the methods are compared and analyzed on the same test cases in different grid sizes and various agents. The optimized MCTS-based method solves the most extensive test case with a size of 40 \(\times \) 40 with 100 agents in 988.5 s, respectively, indicating 22.8% and 63.6% improvements in time and memory consumption compared to the state-of-the-art MCTS-based method. It also shows 72% and 39.2% improvement in performance with lower memory consumption than the best results of investigated SAT and heuristic-based methods, sequentially.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adcock, A., et al.: Zig-Zag numberlink is NP-complete. J. Inf. Process. 23(3), 239–245 (2015)
Ahle, T.D.: Program for generating and solving numberlink (2012)
Almagor, S., Lahijanian, M.: Explainable multi agent path finding. In: To Appear in International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS) (2020)
Björnsson, Y., Halldórsson, K.: Improved heuristics for optimal path-finding on game maps. AIIDE 6, 9–14 (2006)
Botea, A., Bouzy, B., Buro, M., Bauckhage, C., Nau, D.: Pathfinding in games. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2013)
Browne, C.B., et al.: A survey of Monte Carlo tree search methods. IEEE Trans. Comput. Int. AI Games 4(1), 1–43 (2012)
Chu, C.Y., Hashizume, H., Guo, Z., Harada, T., Thawonmas, R.: Combining pathfinding algorithm with knowledge-based Monte-Carlo tree search in general video game playing. In: 2015 IEEE CIG, pp. 523–529. IEEE (2015)
Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)
Daneshvaramoli, M., et al.: Decentralized communication-less multi-agent task assignment with cooperative Monte-Carlo tree search. In: 2020 6th International Conference on Control, Automation and Robotics (ICCAR), pp. 612–616. IEEE (2020)
De Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: International Conference on Tools and Algorithms for the Construction and Analysis of Systems, pp. 337–340. Springer (2008). https://doi.org/10.1007/978-3-540-78800-3_24
Dudeney, H.E.: 536 Puzzles and Curious Problems. Courier Dover Publications (2016)
Dutertre, B.: Yices 2.2. In: International Conference on Computer Aided Verification, pp. 737–744. Springer (2014)
Galler, B.A., Fisher, M.J.: An improved equivalence algorithm. Commun. ACM 7(5), 301–303 (1964)
Gomes, C.P., Selman, B., McAloon, K., Tretkoff, C.: Randomization in backtrack search: exploiting heavy-tailed profiles for solving hard scheduling problems. In: AIPS, pp. 208–213 (1998)
Graham, R., McCabe, H., Sheridan, S.: Pathfinding in computer games. ITB J. 4(2), 6 (2003)
Kaduri, O., Boyarski, E., Stern, R.: Algorithm selection for optimal multi-agent pathfinding. In: Proceedings of the 30th International Conference on Automated Planning and Scheduling, pp. 161–165. AAAI Press (2020)
Kautz, H., Selman, B.: Pushing the envelope: planning, propositional logic, and stochastic search. In: Proceedings of the National Conference on Artificial Intelligence, pp. 1194–1201 (1996)
Kiarostami, M.S., Daneshvaramoli, M.R., Monfared, S.K., Rahmati, D., Gorgin, S.: Multi-agent non-overlapping pathfinding with Monte-Carlo tree search. In: 2019 IEEE Conference on Games (CoG), pp. 1–4, August 2019
Kiarostami, M.S., et al.: On using Monte-Carlo tree search to solve puzzles. In: 2021 7th International Conference on Computer Technology Applications, ICCTA 2021, pp. 18–26, New York, NY, USA, 2021. Association for Computing Machinery (2021)
Kiarostami, M.S., et al.: Unlucky explorer: a complete non-overlapping map exploration. In: 2021 3rd World Symposium on Software Engineering (WSSE 2021) (2021)
Koenig, S., Likhachev, M., Furcy, D.: Lifelong planning a. Artif. Intell. 155(1–2), 93–146 (2004)
Kotsuma, K., Takenaga, Y.: NP-completeness and enumeration of number link puzzle. IEICE Tech Report COMP2009-49, IEICE (2010)
Kramer, P.P.G., Van Leeuwen, J.: Wire routing in NP-complete, vol. 82. Unknown Publisher (1982)
Ma, H., Tovey, C., Sharon, G., Kumar, T.K.S., Koenig, S.: Multi-agent path finding with payload transfers and the package-exchange robot-routing problem. In: Thirtieth AAAI Conference on AI (2016)
Powley, E.J., Whitehouse, D., Cowling, P.I.: Monte Carlo tree search with macro-actions and heuristic route planning for the physical travelling salesman problem. In: 2012 IEEE Conference on Computational Intelligence and Games (CIG), pp. 234–241. IEEE (2012)
Sharon, G., Stern, R., Felner, A., Sturtevant, N.R.: Conflict-based search for optimal multi-agent pathfinding. Artif. Intell. 219, 40–66 (2015)
Silver, D.: Cooperative pathfinding. AIIDE 1, 117–122 (2005)
Stephan, P., Brayton, R.K., Sangiovanni-Vincentelli, A.L.: Combinational test generation using satisfiability. IEEE Trans. Comput.-Aided Des. Integ. Circ. Syst. 15(9), 1167–1176 (1996)
Stern, R.: Multi-Agent Path Finding - An Overview, pp. 96–115. Springer International Publishing, Cham, 2019. https://doi.org/10.1007/978-3-030-33274-7_6
Stern, R., et al.: Multi-agent pathfinding: definitions, variants, and benchmarks. In: Twelfth Annual Symposium on Combinatorial Search (2019)
Surynek, P., Michalík, P.: The joint movement of pebbles in solving the (n\({\hat{}}\)2-1)-puzzle suboptimally and its applications in rule-based cooperative path-finding. AAMAS 31(3), 715–763 (2017)
Torvaneye, B.: Solving the “flow free” game (2019)
Velev, M.N., Bryant, R.E.: Effective use of Boolean satisfiability procedures in the formal verification of superscalar and VLIW microprocessors. J. Symbol. Compt. 35(2), 73–106 (2003)
Yoshinaka, R., Saitoh, T., Kawahara, J., Tsuruma, K., Iwashita, H., Minato, S.: Finding all solutions and instances of numberlink and slitherlink by zdds. Algorithms 5(2), 176–213 (2012)
Yu, J., LaValle, S.M.: Multi-agent path planning and network flow. In: Algorithmic Foundations of Robotics X, pp. 157–173. Springer (2013)
Yurichev, D.: SAT/SMT by Example (2019)
Acknowledgments
This research is connected to the GenZ strategic profiling project at the University of Oulu, supported by the Academy of Finland (project number 318930), and CRITICAL (Academy of Finland Strategic Research, 335729). Part of the work was also carried out with the support of Biocenter Oulu, spearhead project ICON.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Daneshvaramoli, M. et al. (2022). A Study on Non-overlapping Multi-agent Pathfinding. In: Arai, K. (eds) Advances in Information and Communication. FICC 2022. Lecture Notes in Networks and Systems, vol 439. Springer, Cham. https://doi.org/10.1007/978-3-030-98015-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-98015-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-98014-6
Online ISBN: 978-3-030-98015-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)