A Particle Swarm Optimizer for Solving the Set Partitioning Problem in the Presence of Partitioning Constraints

Gerrit Anders, Florian Siefert, Wolfgang Reif

Abstract

Solving the set partitioning problem (SPP) is at the heart of the formation of several organizational structures in multi-agent systems (MAS). In large-scale MAS, these structures can improve scalability and enable cooperation between agents with (different) limited resources and capabilities. In this paper, we present a discrete Particle Swarm Optimizer, i.e., a metaheuristic, that solves the NP-hard SPP in the context of partitioning constraints – which restrict the structure of valid partitionings in terms of acceptable ranges for the number and the size of partitions – in a general manner. It is applicable to a broad range of applications in which regional or global knowledge is available. For example, our algorithm can be used for coalition structure generation, strict partitioning clustering (with outliers), anticlustering, and, in combination with an additional control loop, even for the creation of hierarchical system structures. Our algorithm relies on basic set operations to come to a solution and, as our evaluation shows, finds high-quality solutions in different scenarios.

References

  1. Abdallah, S. and Lesser, V. (2004). Organization-Based Cooperative Coalition Formation. Int. Conference on Intelligent Agent Technology, pages 162-168.
  2. Al Faruque, M. A., Krist, R., and Henkel, J. (2008). ADAM: run-time agent-based distributed application mapping for on-chip communication. In Proc. of the 45th annual Design Automation Conf., pages 760-765. ACM.
  3. Alam, S., Dobbie, G., and Riddle, P. (2008). An Evolutionary Particle Swarm Optimization Algorithm for Data Clustering. In IEEE Swarm Intelligence Symposium, 2008, pages 1-6.
  4. Anders, G., Seebach, H., Nafz, F., Steghöfer, J.-P., and Reif, W. (2011). Decentralized Reconfiguration for SelfOrganizing Resource-Flow Systems Based on Local Knowledge. In 8th IEEE Int. Conference and Workshops on Engineering of Autonomic and Autonomous Systems (EASe), pages 20-31.
  5. Anders, G., Siefert, F., Steghöfer, J.-P., and Reif, W. (2012). A decentralized multi-agent algorithm for the set partitioning problem. In PRIMA 2012: Principles and Practice of Multi-Agent Systems, volume 7455 of Lecture Notes in Computer Science, pages 107-121. Springer Berlin / Heidelberg.
  6. Apt, K. R. and Witzel, A. (2007). A Generic Approach to Coalition Formation. Proc. of the Int. Workshop on Computational Social Choice COMSOC, 11(3).
  7. Äyrämö, S. and Kärkkäinen, T. (2006). Introduction to partitioning-based clustering methods with a robust example. Technical report, Reports of the Department of Mathematical Information Technology, Series C. Software and Computational Engineering of the University of Jyväskylä.
  8. Bender, C., Brody, D., and Meister, B. (1999). Quantum field theory of partitions. Journal of Mathematical Physics, 40:3239.
  9. Buccafurri, F., Rosaci, D., Sarnè, G., and Ursino, D. (2002). An Agent-Based Hierarchical Clustering Approach for E-commerce Environments. In E-Commerce and Web Technologies, volume 2455 of LNCS, pages 109- 118. Springer.
  10. Chu, P. and Beasley, J. (1998). Constraint handling in genetic algorithms: The set partitioning problem. Journal of Heuristics, 4(4):323-357.
  11. Consoli, S., Moreno-Pérez, J., Darby-Dowman, K., and Mladenovic, N. (2010). Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem. Natural Computing, 9(1):29-46.
  12. Di Marzo Serugendo, G., Gleizes, M.-P., and Karageorgos, A. (2005). Self-organization in multi-agent systems. The Knowledge Engineering Review, 20:165-189.
  13. Garcia, F. and Perez, J. (2008). Jumping frogs optimization: a new swarm method for discrete optimization. Technical Report 3, Documentos de Trabajo del DEIOC, Department of Statistics, O.R. and Computing, University of La Laguna, Tenerife, Spain.
  14. Horling, B. and Lesser, V. (2004). A survey of multi-agent organizational paradigms. The Knowledge Engineering Review, 19(04):281-316.
  15. Ishioka, T. (2005). An expansion of x-means for automatically determining the optimal number of clusters. In Proceedings of International Conference on Computational Intelligence, pages 91-96.
  16. Kennedy, J. and Eberhart, R. (1995). Particle Swarm Optimization. In Proc. of the IEEE Int. Conf. on Neural Networks, 1995, volume 4, pages 1942 -1948.
  17. Kennedy, J. and Eberhart, R. (1997). A Discrete Binary Version of the Particle Swarm Algorithm. In IEEE International Conference on Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation., volume 5, pages 4104-4108.
  18. Kudo, Y. and Murai, T. (2009). On a criterion of similarity between partitions based on rough set theory. In Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, volume 5908 of LNCS, pages 101-108. Springer Berlin / Heidelberg.
  19. MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations.
  20. Ogston, E., Overeinder, B., Steen, M. V., and Brazier, F. (2003). A Method for Decentralized Clustering in Large Multi-Agent Systems. In Proc. of the 2nd Int. Joint Conference on Autonomous Agents and Multiagent Systems, pages 789-796.
  21. Rahwan, T., Ramchurn, S. D., Jennings, N. R., and Giovannucci, A. (2009). An Anytime Algorithm for Optimal Coalition Structure Generation. Journal of Artificial Intelligence Research, 34:521-567.
  22. Seren, C. (2011). A Hybrid Jumping Particle Swarm Optimization Method for High Dimensional Unconstrained Discrete Problems. In 2011 IEEE Congress on Evolutionary Computation, pages 1649-1656.
  23. Shehory, O. and Kraus, S. (1998). Methods for task allocation via agent coalition formation. Artificial Intelligence, 101(1-2):165-200.
  24. Valev, V. (1998). Set partition principles revisited. In Advances in Pattern Recognition, volume 1451 of LNCS, pages 875-881. Springer.
  25. Van der Merwe, D. and Engelbrecht, A. P. (2003). Data clustering using particle swarm optimization. In The 2003 Congress on Evolutionary Computation, volume 1, pages 215-220. IEEE.
  26. Younis, O. and Fahmy, S. (2004). HEED: A Hybrid, Energy-Efficient, Distributed Clustering Approach for Ad Hoc Sensor Networks. IEEE Transactions on Mobile Computing, 3:366-379.
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Paper Citation


in Harvard Style

Anders G., Siefert F. and Reif W. (2015). A Particle Swarm Optimizer for Solving the Set Partitioning Problem in the Presence of Partitioning Constraints . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-074-1, pages 151-163. DOI: 10.5220/0005220501510163


in Bibtex Style

@conference{icaart15,
author={Gerrit Anders and Florian Siefert and Wolfgang Reif},
title={A Particle Swarm Optimizer for Solving the Set Partitioning Problem in the Presence of Partitioning Constraints},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2015},
pages={151-163},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005220501510163},
isbn={978-989-758-074-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - A Particle Swarm Optimizer for Solving the Set Partitioning Problem in the Presence of Partitioning Constraints
SN - 978-989-758-074-1
AU - Anders G.
AU - Siefert F.
AU - Reif W.
PY - 2015
SP - 151
EP - 163
DO - 10.5220/0005220501510163