Journal of Korea Society of Industrial Information Systems (한국산업정보학회논문지)

Korea Society of Industrial Information Systems (한국산업정보학회)
권호 표지
DOI QR코드

DOI QR Code

Approximation Algorithm for Multi Agents-Multi Tasks Assignment with Completion Probability

작업 완료 확률을 고려한 다수 에이전트-다수 작업 할당의 근사 알고리즘

  • 김광 (조선대학교 경영학부)
  • Received : 2022.01.03
  • Accepted : 2022.02.28
  • Published : 2022.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

A multi-agent system is a system that aims at achieving the best-coordinated decision based on each agent's local decision. In this paper, we consider a multi agent-multi task assignment problem. Each agent is assigned to only one task and there is a completion probability for performing. The objective is to determine an assignment that maximizes the sum of the completion probabilities for all tasks. The problem, expressed as a non-linear objective function and combinatorial optimization, is NP-hard. It is necessary to design an effective and efficient solution methodology. This paper presents an approximation algorithm using submodularity, which means a marginal gain diminishing, and demonstrates the scalability and robustness of the algorithm in theoretical and experimental ways.

다수 에이전트 시스템(Multi-agent system)은 에이전트 각자의 결정으로 최상의 조직화 된 결정을 달성하는 것을 목표로 하는 시스템으로 본 논문에서는 다수 에이전트-다수 작업의 할당 문제를 제시한다. 본 문제는 각 에이전트가 하나의 작업에 할당이 되어 수행하고, 작업 수행에 대한 작업 완료 확률(completion probability)이 있으며 모든 작업의 수행 확률을 최대화하는 할당을 결정한다. 비선형(non-linearity)의 목적함수와 조합 최적화(combinatorial optimization)로 표현되는 본 문제는 NP-hard로, 효과적이면서 효율적인 문제 해결 방법론 제시가 필요하다. 본 연구에서는 한계 이익(marginal gain)의 감소를 의미하는 하위모듈성(submodularity)을 활용한 근사 알고리즘(approximation algorithm)을 제안하고, 확장성(scalability)과 강건성(robustness) 측면에서 우수한 알고리즘임을 이론 및 실험적으로 제시한다.

Keywords

Acknowledgement

이 논문은 2021학년도 조선대학교 학술연구비의 지원을 받아 연구되었음.

References

  1. Bai, X., Yan, W., Ge, S. S., & Cao, M. (2018). An integrated multi-population genetic algorithm for multi-vehicle task assignment in a drift field. Information Sciences, 453, 227-238. https://doi.org/10.1016/j.ins.2018.04.044
  2. Conforti, M., & Cornuejols, G. (1984). Submodular set functions, matroids and the greedy algorithm: tight worst-case bounds and some generalizations of the Rado-Edmonds theorem. Discrete applied mathematics, 7(3), 251-274. https://doi.org/10.1016/0166-218X(84)90003-9
  3. Degas, A., Kaddoum, E., Gleizes, M. P., Adreit, F., & Rantrua, A. (2021). Cooperative multi-agent model for collision avoidance applied to air traffic management. Engineering Applications of Artificial Intelligence, 102, 104286. https://doi.org/10.1016/j.engappai.2021.104286
  4. Douma, A. M., van Hillegersberg, J., & Schuur, P. C. (2012). Design and evaluation of a simulation game to introduce a multi-agent system for barge handling in a seaport. Decision support systems, 53(3), 465-472. https://doi.org/10.1016/j.dss.2012.02.013
  5. Fisher, M. L., Nemhauser, G. L., & Wolsey, L. A. (1978). An analysis of approximations for maximizing submodular set functions-II. Berlin, Heidelberg. Polyhedral combinatorics, pp. 73-87.
  6. Jung, J.J. (2007). Applying CSP techniques to automated scheduling with agents in distributed environment. Journal of the Korea Industrial Information Systems Research, 12(1), 87-94.
  7. Heilig, L., Lalla-Ruiz, E., & Voss, S. (2017). port-IO: an integrative mobile cloud platform for real-time inter-terminal truck routing optimization. Flexible Services and Manufacturing Journal, 29(3), 504-534. https://doi.org/10.1007/s10696-017-9280-z
  8. Isler, V., & Bajcsy, R. (2005, April). The sensor selection problem for bounded uncertainty sensing models. In IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005. pp. 151-158.
  9. Jeong, H. Y., David, J. Y., Min, B. C., & Lee, S. (2020). The humanitarian flying warehouse. Transportation research part E: logistics and transportation review, 136, 101901. https://doi.org/10.1016/j.tre.2020.101901
  10. Le Thi, H. A., Nguyen, D. M., & Dinh, T. P. (2012). Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches. Optimization Letters, 6(2), 315-329. https://doi.org/10.1007/s11590-010-0259-x
  11. Lee, J.H. & Shin M.I (2016), Stochastic Weapon Target Assignment Problem under Uncertainty in Targeting Accuracy, The Korean Operations Research and Management Science Society, 41(3), 23-36.
  12. Li, J. J., Zhang, R. B., & Yang, Y. (2015). Meta-heuristic ant colony algorithm for multi-tasking assignment on collaborative AUVs. International Journal of Grid and Distributed Computing, 8(3), 135-144. https://doi.org/10.14257/ijgdc.2015.8.3.14
  13. Nemhauser, G. L., Wolsey, L. A., & Fisher, M. L. (1978). An analysis of approximations for maximizing submodular set functions-I. Mathematical programming, 14(1), 265-294. https://doi.org/10.1007/BF01588971
  14. Pollanen, R., Toivonen, H., Perajarvi, K., Karhunen, T., Ilander, T., Lehtinen, J., … & Juusela, M. (2009). Radiation surveillance using an unmanned aerial vehicle. Applied radiation and isotopes, 67(2), 340-344. https://doi.org/10.1016/j.apradiso.2008.10.008
  15. Qu, G., Brown, D., & Li, N. (2019). Distributed greedy algorithm for multi-agent task assignment problem with submodular utility functions. Automatica, 105, 206-215. https://doi.org/10.1016/j.automatica.2019.03.007
  16. Sun, X., Cassandras, C. G., & Meng, X. (2017, December). A submodularity-based approach for multi-agent optimal coverage problems. 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 4082-4087.
  17. Terelius, H., Topcu, U., & Murray, R. M. (2011). Decentralized multi-agent optimization via dual decomposition. IFAC proceedings volumes, 44(1), 11245-11251. https://doi.org/10.3182/20110828-6-it-1002.01959
  18. Wu, J., Yuan, S., Ji, S., Zhou, G., Wang, Y., & Wang, Z. (2010). Multi-agent system design and evaluation for collaborative wireless sensor network in large structure health monitoring. Expert Systems with Applications, 37(3), 2028-2036. https://doi.org/10.1016/j.eswa.2009.06.098
  19. Yuan, D., Xu, S., & Zhao, H. (2011). Distributed primal-dual subgradient method for multiagent optimization via consensus algorithms. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 41(6), 1715-1724. https://doi.org/10.1109/TSMCB.2011.2160394
  20. Yun, Y.S. & Chuluunsukh, A. (2019). Green Supply Chain Network Model: Genetic Algorithm Approach. Journal of the Korea Industrial Information Systems Research, 24(3), 31-38. https://doi.org/10.9723/JKSIIS.2019.24.3.031