Abstract
Belief propagation (BP) approaches, such as Max-sum and its variants, are important methods to solve large-scale Distributed Constraint Optimization Problems. However, these algorithms face a huge challenge since their computational complexity scales exponentially with the arity of each constraint function. Current accelerating techniques for BP use sorting or branch-and-bound (BnB) strategy to reduce the search space. However, the existing BnB-based methods are mainly designed for specific problems, which limits their applicability. On the other hand, though several generic sorting-based methods have been proposed, they require significantly high preprocessing as well as memory overhead, which prohibits their adoption in some realistic scenarios. In this paper, we aim to propose a series of generic and memory-efficient heuristic search techniques to accelerate belief propagation. Specifically, by leveraging dynamic programming, we efficiently build function estimations for every partial assignment scoped in a constraint function in the preprocessing phase. Then, by using these estimations to build upper bounds and employing a branch-and-bound in a depth-first fashion to reduce the search space, we propose our first method called FDSP. Next, we enhance FDSP by adapting a concurrent-search strategy and leveraging the upper bounds as guiding information and propose its first heuristic variant framework called CONC-FDSP. Finally, by choosing to expand the partial assignment with the highest upper bound in each step of exploration, we propose the second heuristic variant of FDSP, called BFS-FDSP. We prove the correctness of our methods theoretically, and our empirical evaluations indicate their superiority for accelerating Max-sum in terms of both time and memory, compared with the state-of-the-art.
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Data availability
The implementation of the compared baselines and our proposed algorithms are available and can be found in https://github.com/czy920/FDSP.
Notes
Current work all finds the optimal assignments to guarantee the optimality when solving tree-structure problems with Max-sum.
The main difference between Fast Max-Sum and Max-Sum is that the domain size of each variable in Fast Max-Sum is reduced to 2.
One can easily prove that the pre-stored full assignments in bestEntryView are solutions to the corresponding problems according to the way we construct.
References
Aji, S., & McEliece, R. (2000). The generalized distributive law. IEEE Transactions on Information Theory, 46, 325–343.
Cerquides, J., Rodríguez-Aguilar, J. A., Emonet, R., & Picard, G. (2021). Solving highly cyclic distributed optimization problems without busting the bank: A decimation-based approach. Logic Journal of the IGPL, 29(1), 72–95.
Chen, D., Deng, Y., Chen, Z., Zhang, W., & He, Z. (2020). Hs-cai: A hybrid dcop algorithm via combining search with context-based inference. In Proceedings of the 34th AAAI conference on artificial intelligence (pp. 7087–7094).
Chen, Z., Deng, Y., Wu, T., & He, Z. (2018). A class of iterative refined max-sum algorithms via non-consecutive value propagation strategies. Autonomous Agents and Multi-Agent Systems, 32(6), 822–860.
Chen, Z., Jiang, X., Deng, Y., Chen, D., & He, Z. (2019). A generic approach to accelerating belief propagation based incomplete algorithms for dcops via a branch-and-bound technique. In Proceedings of the 33rd AAAI conference on artificial intelligence (pp. 6038–6045).
Chen, Z., Zhang, W., Deng, Y., Chen, D., & Li, Q. (2020). Rmb-dpop: Refining mb-dpop by reducing redundant inference. In Proceedings of the 19th international conference on autonomous agents and multiagent Systems (pp. 249–257).
Cohen, L., Galiki, R., & Zivan, R. (2020). Governing convergence of max-sum on dcops through damping and splitting. Artificial Intelligence, 279, 103212.
Delle Fave, F.M., Rogers, A., Xu, Z., Sukkarieh, S., & Jennings, N. R. (2012). Deploying the max-sum algorithm for decentralised coordination and task allocation of unmanned aerial vehicles for live aerial imagery collection. In Proceedings of the 2012 IEEE international conference on robotics and automation (pp. 469–476).
Deng, Y., & An, B. (2021). Utility distribution matters: enabling fast belief propagation for multi-agent optimization with dense local utility function. Autonomous Agents and Multi-Agent Systems, 35(2), 1–40.
Farinelli, A., Rogers, A., & Jennings, N. R. (2014). Agent-based decentralised coordination for sensor networks using the max-sum algorithm. Autonomous Agents and Multi-Agent Systems, 28(3), 337–380.
Farinelli, A., Rogers, A., Petcu, A., & Jennings, N. R. (2008). Decentralised coordination of low-power embedded devices using the Max-sum algorithm. In Proceedings of the 7th international joint conference on autonomous agents and multiagent systems (pp. 639–646).
Fioretto, F., Pontelli, E., & Yeoh, W. (2018). Distributed constraint optimization problems and applications: A survey. Journal of Artificial Intelligence Research, 61, 623–698.
Fioretto, F., Yeoh, W., & Pontelli, E. (2017). A multiagent system approach to scheduling devices in smart homes. In Proceedings of the 16th international conference on autonomous agents and multiagent systems (pp. 981–989).
Hirayama, K., Miyake, K., Shiota, T., & Okimoto, T. (2019). DSSA+: Distributed collision avoidance algorithm in an environment where both course and speed changes are allowed. TransNav, International Journal on Marine Navigation and Safety of Sea Transportation, 13(1).
Hirayama, K., & Yokoo, M. (1997). Distributed partial constraint satisfaction problem. In Proceedings of the international conference on principles and practice of constraint programming (pp. 222–236).
Hirayama, K., & Yokoo, M. (2005). The distributed breakout algorithms. Artificial Intelligence, 161(1–2), 89–115.
Katagishi, H., & Pearce, J. P. (2007). Kopt: Distributed dcop algorithm for arbitrary k-optima with monotonically increasing utility. DCR-07.
Khan, M., Tran-Thanh, L., & Jennings, N. R. (2018). A generic domain pruning technique for gdl-based dcop algorithms in cooperative multi-agent systems. In Proceedings of the 17th international conference on autonomous agents and multiagent systems (pp. 1595–1603).
Kiekintveld, C., Yin, Z., Kumar, A., & Tambe, M. (2010). Asynchronous algorithms for approximate distributed constraint optimization with quality bounds. In Proceedings of the 9th international conference on autonomous agents and multi-agent systems (pp. 133–140).
Kim, Y., Krainin, M., & Lesser, V. (2011). Effective variants of the max-sum algorithm for radar coordination and scheduling. In Proceedings of the 2011 IEEE/WIC/ACM international conferences on web intelligence and intelligent agent technology (pp. 357–364).
Kim, Y., & Lesser, V. (2013). Improved max-sum algorithm for DCOP with n-ary constraints. In Proceedings of the 12th international conference on autonomous agents and multiagent systems (pp. 191–198).
Litov, O., & Meisels, A. (2017). Forward bounding on pseudo-trees for DCOPs and ADCOPs. Artificial Intelligence, 252, 83–99.
Macarthur, K., Stranders, R., Ramchurn, S., & Jennings, N. (2011). A distributed anytime algorithm for dynamic task allocation in multi-agent systems. In Proceedings of 25th the AAAI conference on artificial intelligence (pp. 701–706).
Maheswaran, R. T., Pearce, J. P., Tambe, M., et al. (2004). Distributed algorithms for dcop: A graphical-game-based approach. In ISCA PDCS (pp. 432–439). Citeseer.
Modi, P. J., Shen, W. M., Tambe, M., & Yokoo, M. (2005). ADOPT: Asynchronous distributed constraint optimization with quality guarantees. Artificial Intelligence, 161(1–2), 149–180.
Monteiro, T. L., Pujolle, G., Pellenz, M. E., Penna, M. C., & Souza, R. D. (2012). A multi-agent approach to optimal channel assignment in wlans. In Proceedings of the 2012 IEEE wireless communications and networking conference (WCNC) (pp. 2637–2642).
Netzer, A., Grubshtein, A., & Meisels, A. (2012). Concurrent forward bounding for distributed constraint optimization problems. Artificial Intelligence, 193, 186–216.
Nguyen, D. T., Yeoh, W., Lau, H. C., & Zivan, R. (2019). Distributed Gibbs: A linear-space sampling-based DCOP algorithm. Journal of Artificial Intelligence Research, 64, 705–748.
Okimoto, T., Joe, Y., Iwasaki, A., Yokoo, M., & Faltings, B. (2011). Pseudo-tree-based incomplete algorithm for distributed constraint optimization with quality bounds. In Proceedings of the 17th international conference on principles and practice of constraint programming (pp. 660–674). Springer.
Ottens, B., Dimitrakakis, C., & Faltings, B. (2017). DUCT: An upper confidence bound approach to distributed constraint optimization problems. ACM Transactions on Intelligent Systems and Technology (TIST), 8(5), 69.
Pearce, J. P., & Tambe., M. (2007). Quality guarantees on k-optimal solutions for distributed constraint optimization problems. In Proceedings of the 20th international joint conference on artifical intelligence (pp. 1446–1451).
Pepyne, D., Westbrook, D., Philips, B., Lyons, E., Zink, M., & Kurose, J. (2007). A design for distributed collaborative adaptive sensing of the atmosphere. Tech. rep., Technical Report CMPSCI-2007-018, University of Massachusetts.
Petcu, A., & Faltings, B. (2005). Approximations in distributed optimization. In Proceedings of the 11st international conference on principles and practice of constraint programming (pp. 802–806). Springer.
Petcu, A., & Faltings, B. (2005). Dpop: A scalable method for multiagent constraint optimization. In Proceedings of the 19th international joint conference on artifical intelligence (pp. 266–271).
Petcu, A., & Faltings, B. (2006). ODPOP: An algorithm for open/distributed constraint optimization. In Proceedings of the 21st AAAI conference on artificial intelligence (pp. 703–708).
Petcu, A., & Faltings, B. (2007). Mb-dpop: A new memory-bounded algorithm for distributed optimization. In Proceedings of the 20th international joint conference on artificial intelligence (pp. 1452–1457).
Ramchurn, S. D., Farinelli, A., Macarthur, K. S., & Jennings, N. R. (2010). Decentralized coordination in robocup rescue. The Computer Journal, 53(9), 1447–1461.
Rogers, A., Corkill, D. D., & Jennings, N. R. (2009). Agent technologies for sensor networks. IEEE Intelligent Systems, 24(02), 13–17.
Rogers, A., Farinelli, A., Stranders, R., & Jennings, N. R. (2011). Bounded approximate decentralised coordination via the Max-sum algorithm. Artificial Intelligence, 175(2), 730–759.
Rollon, E., & Larrosa, J. (2012). Improved bounded max-sum for distributed constraint optimization. In Proceedings of the international conference on principles and practice of constraint programming (pp. 624–632). Springer.
Rollon, E., & Larrosa, J. (2014). Decomposing utility functions in bounded max-sum for distributed constraint optimization. In Proceedings of the International conference on principles and practice of constraint programming (pp. 646–654). Springer.
Stranders, R., Farinelli, A., Rogers, A., & Jennings, N. (2009). Decentralised coordination of mobile sensors using the max-sum algorithm. In Proceedings of the 21st international joint conference on artificial intelligence (pp. 299–304).
Sultanik, E. A., Lass, R. N., & Regli, W. C. (2008). Dcopolis: A framework for simulating and deploying distributed constraint reasoning algorithms. In Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems: demo papers (pp. 1667–1668).
Sultanik, E. A., Modi, P. J., & Regli, W. C. (2007). On modeling multiagent task scheduling as a distributed constraint optimization problem. In Proceedings of the 20th international joint conference on artificial intelligence (pp. 1531–1536).
Vinyals, M., Rodríguez-Aguilar, J., & Cerquides, J. (2009). Generalizing DPOP: Action-GDL, a new complete algorithm for DCOPs. In Proceedings of The 8th international conference on autonomous agents and multiagent systems (pp. 1239–1240).
Weiss, Y., & Freeman, W. T. (2001). On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. IEEE Transactions on Information Theory, 47(2), 736–736.
Yedidia, J. S., Freeman, W. T., Weiss, Y., et al. (2003). Understanding belief propagation and its generalizations. Exploring Artificial Intelligence in the New Millennium, 8(236–239), 0018–9448.
Yeoh, W., Felner, A., & Koenig, S. (2010). Bnb-adopt: An asynchronous branch-and-bound dcop algorithm. Journal of Artificial Intelligence Research, 38, 85–133.
Yeoh, W., & Yokoo, M. (2012). Distributed problem solving. AI Magazine, 33(3), 53.
Zivan, R., Okamoto, S., & Peled, H. (2014). Explorative anytime local search for distributed constraint optimization. Artificial Intelligence, 212, 1–26.
Zivan, R., Parash, T., Cohen, L., Peled, H., & Okamoto, S. (2017). Balancing exploration and exploitation in incomplete Min/Max-sum inference for distributed constraint optimization. Autonomous Agents and Multi-Agent Systems, 31(5), 1165–1207.
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The research leading to these results received funding from Fundamental Research Funds for the Central Universities (2018CDXYJSJ0026).
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ZC and WZ contributed to the conception of the study; JG performed the experiment; JG, ZC and DC contributed significantly to analysis and manuscript preparation; JG performed the data analyses and wrote the manuscript; ZC, DC and QL helped perform the analysis with constructive discussions.
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This paper is an extension to our AAAI paper [5]. Besides additional examples, experiments and proofs, we also present two heuristic variants including Concurrent-search based FDSP (CONC-FDSP) and Best-first search based FDSP (BFS-FDSP) which are not included in our AAAI paper.
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Gao, J., Chen, Z., Chen, D. et al. Toward fast belief propagation for distributed constraint optimization problems via heuristic search. Auton Agent Multi-Agent Syst 38, 15 (2024). https://doi.org/10.1007/s10458-024-09643-y
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DOI: https://doi.org/10.1007/s10458-024-09643-y