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Bee colony optimization for scheduling independent tasks to identical processors

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Abstract

The static scheduling of independent tasks on homogeneous multiprocessor systems is studied in this paper. This problem is treated by the Bee Colony Optimization (BCO) meta-heuristic. The BCO algorithm belongs to the class of stochastic swarm optimization methods inspired by the foraging habits of bees in nature. To investigate the performance of the proposed method extensive numerical experiments are performed. Our BCO algorithm is able to obtain the optimal value of the objective function in the majority of test examples known from literature. The deviation of non-optimal solutions from the optimal ones in our test examples is at most 2%. The CPU times required to find the best solutions by BCO are significantly smaller than the corresponding times required by the CPLEX optimization solver. Moreover, our BCO is competitive with state-of-the-art methods for similar problems, with respect to both solution quality and running time. The stability of BCO is examined through multiple executions and it is shown that solution deviation is less than 1%.

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References

  • Abbass, H.A.: MBO: marriage in honey bees optimization-a haplometrosis polygynous swarming approach. In: Proceedings of the Congress on Evolutionary Computation, Seoul, South Korea, pp. 207–214 (2001)

    Google Scholar 

  • Afshar, A., Bozorg Haddad, O., Mariño, A.M., Adams, B.J.: Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation. J. Franklin Inst. 344(5), 452–462 (2007)

    Article  Google Scholar 

  • Camazine, S., Sneyd, J.: A model of collective nectar source by honey bees: self-organization through simple rules. J. Theor. Biol. 149, 547–571 (1991)

    Article  Google Scholar 

  • Chong, C.S., Low, M.Y.H., Sivakumar, A.I., Gay, K.L.: A bee colony optimization algorithm to job shop scheduling. In: Proceedings of the Winter Simulation Conference, Washington, DC, pp. 1954–1961 (2006)

    Chapter  Google Scholar 

  • Coffman, E.G. Jr, Garey, M.R., Johnson, D.S.: An application of bin-packing to multiprocessor scheduling. SIAM J. Comput. 7, 1–17 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Coffman, E.G. Jr, Garey, M.R., Johnson, D.S.: Approximation algorithm for bin-packing: A survey. In: Hockbaum, D. (ed.) Approximation Algorithms for NP-Hard Problems, pp. 46–93. PSW, Boston (1996)

    Google Scholar 

  • Davidović, T., Crainic, T.G.: Benchmark problem instances for static task scheduling of task graphs with communication delays on homogeneous multiprocessor systems. Comput. Oper. Res. 33(8), 2155–2177 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Davidović, T., Hansen, P., Mladenović, N.: Permutation based genetic, tabu and variable neighborhood search heuristics for multiprocessor scheduling with communication delays. Asia-Pac. J. Oper. Res. 22(3), 297–326 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Davidović, T., Šelmić, M., Teodorović, D.: Scheduling independent tasks: Bee colony optimization approach. In: Proc. 17th Mediterranean Conference on Control and Automation, Makedonia Palace, Thessaloniki, Greece, pp. 1020–1025 (2009)

    Chapter  Google Scholar 

  • Davidović, T., Ramljak, D., Šelmić, M., Teodorović, D.: Bee colony optimization for the p-center problem. Comput. Oper. Res. 38(10), 1367–1376 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Dell’Amico, M., Martello, S.: Optimal scheduling of tasks on identical parallel processors. ORSA J. Comput. 7, 191–200 (1995)

    Article  MATH  Google Scholar 

  • Drias, H., Sadeg, S., Yahi, S.: Cooperative bees swarm for solving the maximum weighted satisfiability problem. In: Computational Intelligence and Bioinspired Systems. LNCS, vol. 3512, pp. 318–325 (2005)

    Chapter  Google Scholar 

  • Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. J. Heuristics 2, 5–30 (1996)

    Article  Google Scholar 

  • Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completness. Freeman, New York (1979)

    Google Scholar 

  • Graham, R.L.: Bounds on multiprocessor timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  • Haouari, M., Gharbi, A., Jemmali, M.: Tight bounds for the identical parallel machine scheduling problem. Int. Trans. Oper. Res. 13, 529–548 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • ILOG CPLEX 11.2 Reference Manual (2008)

  • Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Tech. rep., Erciyes University, Engineering Faculty Computer Engineering Department Kayseri/Turkiye (2005)

  • Karaboga, D., Basturk Akay, B., Ozturk, C.: Artificial bee colony (ABC) optimization algorithm for training feed-forward neural networks. In: Modeling Decisions for Artificial Intelligence. LNCS, vol. 4617, pp. 318–319 (2007)

    Chapter  Google Scholar 

  • Levine, J., Ducatelle, F.: Ant colony optimization and local search for bin packing and cutting stock problems. J. Oper. Res. Soc. 55, 705–716 (2004)

    Article  MATH  Google Scholar 

  • Lučić, P., Teodorović, D.: Bee system: modeling combinatorial optimization transportation engineering problems by swarm intelligence. In: Preprints of the TRISTAN IV Triennial Symposium on Transportation Analysis, Sao Miguel, Azores Islands, pp. 441–445 (2001)

    Google Scholar 

  • Lučić, P., Teodorović, D.: Transportation modeling: an artificial life approach. In: Proceedings of the 14th IEEE International Conference on Tools with Artificial Intelligence, Washington, DC, pp. 216–223 (2002)

    Google Scholar 

  • Lučić, P., Teodorović, D.: Computing with bees: attacking complex transportation engineering problems. Int. J. Artif. Intell. Tools 12, 375–394 (2003a)

    Article  Google Scholar 

  • Lučić, P., Teodorović, D.: Vehicle routing problem with uncertain demand at nodes: the bee system and fuzzy logic approach. In: Verdegay, J.L. (ed.) Fuzzy Sets based Heuristics for Optimization, pp. 67–82. Physica, Berlin (2003b)

    Google Scholar 

  • Marković, G., Teodorović, D., Aćimović-Raspopović, V.: Routing and wavelength assignment in all-optical networks based on the bee colony optimization. AI Commun. 20, 273–285 (2007)

    MathSciNet  MATH  Google Scholar 

  • Mokotoff, E.: An exact algorithm for the identical parallel machine scheduling problem. Eur. J. Oper. Res. 152, 758–769 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Navrat, P.: Bee hive metaphor for web search. In: Rachev, B., Smrikarov, A. (eds.) Proceedings of the International Conference on Computer Systems and Technologies—CompSysTech 2006, Veliko Turnovo, Bulgaria, p. IIIA.12 (2006)

    Google Scholar 

  • Pham, D.T., Ghanbarzadeh, A., Koc, E., Otri, S., Zaidi, M.: The bees algorithm—a novel tool for complex optimisation problems. In: Proceedings of the 2nd Virtual International Conference on Intelligent Production Machines and Systems (IPROMS 2006), pp. 454–459. Elsevier, Cardiff (2006)

    Google Scholar 

  • Quijano, N., Passino, K.M.: Honey bee social foraging algorithms for resource allocation, Part I: Algorithm and theory. In: Proceedings of the American Control Conference, New York, pp. 3383–3388 (2007a)

    Chapter  Google Scholar 

  • Quijano, N., Passino, K.M.: Honey bee social foraging algorithms for resource allocation, Part II: Application. In: Proceedings of the American Control Conference, New York, pp. 3389–3394 (2007b)

    Chapter  Google Scholar 

  • Shakeri, S., Logendran, R.: A mathematical programming-based scheduling framework for multitasking environments. Eur. J. Oper. Res. 176, 193–209 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Teodorović, D., Dell’Orco, M.: Bee colony optimization—a cooperative learning approach to complex transportation problems. In: Advanced OR and AI Methods in Transportation. Proceedings of the 10th Meeting of the EURO Working Group on Transportation, Poznan, Poland, pp. 51–60 (2005)

    Google Scholar 

  • Teodorović, D., Dell’Orco, M.: Mitigating traffic congestion: solving the ride-matching problem by bee colony optimization. Transport Plan Tech. 31, 135–152 (2008)

    Article  Google Scholar 

  • Thesen, A.: Design and evaluation of a tabu search algorithm for multiprocessor scheduling. J. Heuristics 4(2), 141–160 (1998)

    Article  MATH  Google Scholar 

  • Tobita, T., Kasahara, H.: A standard task graph set for fair evaluation of multiprocessor scheduling algorithms. J. Sched. 5(5), 379–394 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Šelmić, M., Teodorović, D., Vukadinović, K.: Locating inspection facilities in traffic networks: an artificial intelligence approach. Transport Plan Tech. 33, 481–493 (2010)

    Article  Google Scholar 

  • Wedde, H.F., Farooq, M., Zhang, Y.: BeeHive: an efficient fault-tolerant routing algorithm inspired by honey bee behavior. In: Ant Colony Optimization and Swarm Intelligence. LNCS, vol. 3172, pp. 83–94 (2004)

    Chapter  Google Scholar 

  • Wedde, H.F., Sebastian, L., van Bernhard, B., Zeynep, B.: A novel class of multi-agent algorithms for highly dynamic transport planning inspired by honey bee behavior. In: Proceedings of the 12th IEEE International Conference on Factory Automation, Patras, Greece, pp. 1157–1164 (2007)

    Google Scholar 

  • Yang, X.: Engineering optimizations via nature-inspired virtual bee algorithms. In: Mira, J., Alvarez, J.R. (eds.) IWINAC 2005. LNCS, vol. 3562, pp. 317–323 (2005)

    Google Scholar 

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Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their useful comments and suggestions that yielded a significant improvement to this work. The gratefulness also goes to Mr. Milos Rancic for his dedicated approach to proofreading.

This work has been supported by Serbian Ministry of Science and Technological Development, grants No. 144007 and 144033.

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Authors and Affiliations

  1. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, P.O. Box 367, 11001, Belgrade, Serbia

    Tatjana Davidović

  2. Faculty of Transport and Traffic Engineering, University of Belgrade, Vojvode Stepe 305, 11010, Belgrade, Serbia

    Milica Šelmić & Dušan Teodorović

  3. Center for Data Analytics and Biomedical Informatics, Temple University, 322 Wachman Hall, 1805 N. Broad St., Philadelphia, PA, 19122, USA

    Dušan Ramljak

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  1. Tatjana Davidović
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  2. Milica Šelmić
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  3. Dušan Teodorović
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  4. Dušan Ramljak
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Correspondence to Tatjana Davidović.

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Davidović, T., Šelmić, M., Teodorović, D. et al. Bee colony optimization for scheduling independent tasks to identical processors. J Heuristics 18, 549–569 (2012). https://doi.org/10.1007/s10732-012-9197-3

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