Skip to main content

Advertisement

SpringerLink
Log in

Virtual machine consolidation using constraint-based multi-objective optimization

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

With the blooming of cloud computing, the demand for data centers has been rising greatly in recent years. Their energy consumption and environmental impact has become much more significant due to the continuous growth of data center supply. It is possible to reduce the amount of energy consumed by a data center by shutting down unnecessary servers and maintaining only a subset running, such that it is enough to fulfill the resource demand. With recent advances in virtualization technology, it even became possible to consolidate the workload of multiple under-utilized servers into a single server. However, too aggressive consolidation may lead to significant degradation of data center performance. Therefore, the problem of simultaneously minimizing energy consumption and performance degradation in a data center is a complex and challenging problem. In this paper, a novel multi-objective Boolean optimization encoding for virtual machine consolidation is proposed and several approaches to solve it are described and compared. Moreover, this encoding is extended to consider anti-collocation constraints and the migration of virtual machines that are initially placed. This work is in part motivated by the great improvements in the performance of Boolean optimization solvers, thus increasing their applicability and effectiveness for a wider spectrum of complex problems. In this case, specific techniques are applied to further boost the performance, namely search space reduction by symmetry breaking and heuristic reduction of the instance size. An extensive experimental evaluation shows the suitability of the proposed solution in comparison to the state-of-the-art approaches based on stochastic methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. A Pseudo-Boolean Satisfaction (PBS) solver is used to check the satisfiability of \(\phi _W\).

  2. Note that the migration cost objective function is not a PB expression either, but is easily converted to one by replacing \((1 - x_{i, k})\) with \(\lnot x_{i,k}\).

  3. Extraction of the \(A_P\) subset can be performed using nondominated sorting like in the NSGAII genetic Algorithm (Deb et al. 2000).

  4. http://code.google.com/p/googleclusterdata/.

  5. http://sat.inesc-id.pt/dome.

  6. http://moeaframework.org/.

References

  • Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient symmetry breaking for Boolean satisfiability. IEEE Trans. Comput. 55(5), 549–558 (2006)

    Article  Google Scholar 

  • Bartók D., Mann ZÁ.: A branch-and-bound approach to virtual machine placement. In: HPI Cloud Symposium Operating the Cloud, pp. 49–63 (2015)

  • Beloglazov, A., Buyya, R.: Optimal online deterministic algorithms and adaptive heuristics for energy and performance efficient dynamic consolidation of virtual machines in cloud data centers. Concurr. Comput. Pract. Exp. 24(13), 1397–1420 (2012)

    Article  Google Scholar 

  • Beloglazov, A., Abawajy, J.H., Buyya, R.: Energy-aware resource allocation heuristics for efficient management of data centers for cloud computing. Future Gener. Comput. Syst. 28(5), 755–768 (2012)

    Article  Google Scholar 

  • Bjørner N., Phan A., Fleckenstein L.: \(\nu \)z: an optimizing SMT solver. In: 21st International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS, London, pp. 194–199 (2015)

  • Bobroff, N., Kochut, A., Beaty, K.A.: Dynamic placement of virtual machines for managing SLA violations. In: 10th IFIP/IEEE International Symposium on Integrated Network Management, Munich, pp. 119–128 (2007)

  • Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discrete Appl. Math. 123(1), 155–225 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Cambazard, H., Mehta, D., O’Sullivan, B., Simonis, H.: Constraint programming based large neighbourhood search for energy minimisation in data centres. In: 10th International Conference on Economics of Grids, Clouds, Systems, and Services GECON, Zaragoza, pp. 44–59 (2013)

  • Carter, L., Wegman, M.N.: Universal classes of hash functions (extended abstract). In: 9th Annual ACM Symposium on Theory of Computing, Boulder, pp. 106–112 (1977)

  • Chakraborty, S., Meel, K.S., Vardi, M.Y.: A scalable and nearly uniform generator of SAT witnesses. In: 25th International Conference on Computer Aided Verification CAV, Saint Petersburg, pp. 608–623 (2013)

  • Chakraborty, S., Meel, K.S., Vardi, M.Y.: Algorithmic improvements in approximate counting for probabilistic inference: From linear to logarithmic SAT calls. In: 25th International Joint Conference on Artificial Intelligence, IJCAI, New York, pp. 3569–3576 (2016)

  • Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evolut. Comput. 18(4), 577–601 (2014)

    Article  Google Scholar 

  • Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimisation: NSGA-II. In: 6th International Conference on Parallel Problem Solving from Nature PPSN, Paris, pp. 849–858 (2000)

  • Eén, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. J. Satisf. Boolean Model. Comput. 2(1–4), 1–26 (2006)

    MATH  Google Scholar 

  • Fan, X., Weber, W., Barroso, L.A.: Power provisioning for a warehouse-sized computer. In: 34th International Symposium on Computer Architecture, ISCA, San Diego, pp. 13–23 (2007)

  • Ferreto, T.C., Netto, M.A.S., Calheiros, R.N., Rose, C.A.F.D.: Server consolidation with migration control for virtualized data centers. Future Gener. Comput. Syst. 27(8), 1027–1034 (2011)

    Article  Google Scholar 

  • Fox, A., Griffith, R., Joseph, A., Katz, R., Konwinski, A., Lee, G., Patterson, D., Rabkin, A., Stoica, I.: Above the clouds: a berkeley view of cloud computing. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Rep UCB/EECS, vol. 28, p. 13 (2009)

  • Gao, Y., Guan, H., Qi, Z., Hou, Y., Liu, L.: A multi-objective ant colony system algorithm for virtual machine placement in cloud computing. J. Comput. Syst. Sci. 79(8), 1230–1242 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Gomes, C.P., Sabharwal, A., Selman, B.: Near-uniform sampling of combinatorial spaces using XOR constraints. In: 20th Annual Conference on Neural Information Processing Systems on Advances in Neural Information Processing Systems, vol. 19, Vancouver, pp. 481–488 (2006)

  • Graça, A., Lynce, I., Marques-Silva, J., Oliveira, A.: Efficient and accurate haplotype inference by combining parsimony and pedigree information. In: Algebraic and Numeric Biology. Springer, LNCS, vol. 6479, pp. 38–56 (2010)

  • Guazzone, M., Anglano, C., Canonico, M.: Exploiting VM migration for the automated power and performance management of green cloud computing systems. In: 1st International Workshop on Energy Efficient Data Centers E2DC, Revised Selected Papers, Madrid, pp. 81–92 (2012)

  • Guenter B., Jain N., Williams, C.: Managing cost, performance, and reliability tradeoffs for energy-aware server provisioning. In: INFOCOM 2011, 30th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, Shanghai, pp. 1332–1340 (2011)

  • Hermenier, F., Lorca, X., Menaud, J., Muller, G., Lawall, J.L.: Entropy: a consolidation manager for clusters. In: 5th ACM SIGPLAN/SIGOPS International Conference on Virtual Execution Environments VEE, Washington, pp. 41–50 (2009)

  • Ignatiev, A., Janota, M., Marques-Silva, J.: Towards efficient optimization in package management systems. In: International Conference on Software Engineering, ACM, pp. 745–755 (2014)

  • Jackson, D., Estler, H., Rayside, D., et al: The guided improvement algorithm for exact, general-purpose, many-objective combinatorial optimization. Technical Report MIT-CSAIL-TR-2009-033, MIT Massachusetts Institute of Technology (2009)

  • Jo, C., Gustafsson, E., Son, J., Egger, B.: Efficient live migration of virtual machines using shared storage. In: ACM SIGPLAN/SIGOPS International Conference on Virtual Execution Environments (co-located with ASPLOS) VEE, Houston, pp. 41–50 (2013)

  • Jung, G., Hiltunen, M.A., Joshi, K.R., Schlichting, R.D., Pu, C.: Mistral: Dynamically managing power, performance, and adaptation cost in cloud infrastructures. In: International Conference on Distributed Computing Systems ICDCS, Genova, pp. 62–73 (2010)

  • Le Berre, D., Parrain, A.: The sat4j library, release 2.2. J. Satisf. Boolean Model. Comput. 7(2–3), 59–60 (2010)

    Google Scholar 

  • Leavitt, N.: Is cloud computing really ready for prime time? Computer 1, 15–20 (2009)

    Google Scholar 

  • Li, R., Zheng, Q., Li, X., Wu, J.: A novel multi-objective optimization scheme for rebalancing virtual machine placement. In: IEEE International Conference on Cloud Computing CLOUD, pp. 710–717 (2016)

  • Lin, W., Xu, S., Li, J., Xu, L., Peng, Z.: Design and theoretical analysis of virtual machine placement algorithm based on peak workload characteristics. Soft Comput. 21(5), 1301–1314 (2017)

    Article  MATH  Google Scholar 

  • Manquinho, V.M., Marques-Silva, J.P.: On using cutting planes in pseudo-Boolean optimization. J. Satisf. Boolean Model. Comput. 2(1–4), 209–219 (2006)

    MATH  Google Scholar 

  • Marques-Silva, J., Lynce, I., Manquinho, V.M.: Symmetry breaking for maximum satisfiability. In: 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning LPAR, Doha, pp. 1–15 (2008)

  • Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere, A., Heule, M., Van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, pp. 131–153 (2009)

  • McMillan, K.L.: Applying SAT methods in unbounded symbolic model checking. In: 14th International Conference on Computer Aided Verification CAV, Copenhagen, pp. 250–264 (2002)

  • Mills M.P.: The cloud begins with coal. Digital Power Group (2013). http://www.tech-pundit.com/wp-content/uploads/2013/07/Cloud_Begins_With_Coal.pdf. Accessed 31 Oct 2018

  • Miranda, M., Lynce, I., Manquinho, V.: Inferring phylogenetic trees using pseudo-Boolean optimization. AI Commun. 27(3), 229–243 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Mishra, M., Sahoo, A.: On theory of VM placement: anomalies in existing methodologies and their mitigation using a novel vector based approach. In: IEEE International Conference on Cloud Computing CLOUD, Washington, pp. 275–282 (2011)

  • Morgado, A., Marques-Silva, J.: Good learning and implicit model enumeration. In: 17th IEEE International Conference on Tools with Artificial Intelligence ICTAI, pp. 131–136 (2005)

  • Nejad, M.M., Mashayekhy, L., Grosu, D.: Truthful greedy mechanisms for dynamic virtual machine provisioning and allocation in clouds. IEEE Trans. Parallel Distrib. Syst. 26(2), 594–603 (2015)

    Article  Google Scholar 

  • Pareto, V.: Manuale di economia politica, vol. 13. Societa Editrice (1906)

  • Portaluri, G., Giordano, S.: Multi objective virtual machine allocation in cloud data centers. In: IEEE International Conference on Cloud Networking Cloudnet, pp. 107–112 (2016)

  • Prestwich, S., Quirke, C.: Boolean and pseudo-Boolean models for scheduling. In: International Workshop on Modelling and Reformulating Constraint Satisfaction Problems (2003)

  • Ravi, K., Somenzi, F.: Minimal satisfying assignments for conjunctive normal formulae. In: International Conference on Tools and Algorithms for the Construction and Analysis of Systems (2004)

  • Ribas, B.C., Suguimoto, R.M., Montaño, R.A.N.R., Silva, F., Castilho, M.A.: PBFVMC: A new pseudo-Boolean formulation to virtual-machine consolidation. In: Brazilian Conference on Intelligent Systems BRACIS, Fortaleza, pp. 201–206 (2013)

  • Ruan, X., Chen, H.: Performance-to-power ratio aware virtual machine (VM) allocation in energy-efficient clouds. In: IEEE International Conference on Cluster Computing, CLUSTER, pp. 264–273 (2015)

  • Saber, T., Ventresque, A., Gandibleux, X., Murphy, L.: Genepi: A multi-objective machine reassignment algorithm for data centres. In: 9th International Workshop on Hybrid Metaheuristics, pp. 115–129 (2014)

  • Saber, T., Ventresque, A., Marques-Silva, J., Thorburn, J., Murphy, L.: MILP for the multi-objective VM reassignment problem. In: 27th International Conference on Tools with Artificial Intelligence, pp. 41–48 (2015)

  • Saber, T., Marques-Silva, J., Thorburn, J., Ventresque, A.: Exact and hybrid solutions for the multi-objective VM reassignment problem. Int. J. Artif. Intell. Tools 26(1), 1–36 (2017)

    Article  Google Scholar 

  • Sakallah, K.A.: Symmetry and satisfiability. Handb Satisf 185, 289–338 (2009)

    Google Scholar 

  • Salfner, F., Tröger, P., Polze, A.: Downtime analysis of virtual machine live migration. In: 4th International Conference on Dependability (DEPEND), IARIA, pp. 100–105 (2011)

  • Sheini, H.M., Sakallah, K.A.: Pueblo: a hybrid pseudo-Boolean SAT solver. J. Satisf. Boolean Model. Comput. 2(1–4), 165–189 (2006)

    MATH  Google Scholar 

  • Shi, L., Furlong, J., Wang, R.: Empirical evaluation of vector bin packing algorithms for energy efficient data centers. In: IEEE Symposium on Computers and Communications. ISCC, Split, pp. 9–15 (2013)

  • Song, W., Xiao, Z., Chen, Q., Luo, H.: Adaptive resource provisioning for the cloud using online bin packing. IEEE Trans. Comput. 63(11), 2647–2660 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Srikantaiah, S., Kansal, A., Zhao, F.: Energy aware consolidation for cloud computing. In: Conference on Power Aware Computing and Systems, vol. 10, San Diego, pp. 1–5 (2008)

  • Strunk, A.: Costs of virtual machine live migration: a survey. In: 8th IEEE World Congress on Services SERVICES, Honolulu, pp. 323–329 (2012)

  • Terra-Neves, M., Lynce, I., Manquinho, VM.: Introducing pareto minimal correction subsets. In: 20th International Conference on Theory and Applications of Satisfiability Testing, pp. 195–211 (2017)

  • Vaquero, L.M., Rodero-Merino, L., Caceres, J., Lindner, M.: A break in the clouds: towards a cloud definition. ACM SIGCOMM Comput. Commun. Rev. 39(1), 50–55 (2008)

    Article  Google Scholar 

  • Verma, A., Ahuja, P., Neogi, A.: PMAPPER: power and migration cost aware application placement in virtualized systems. In: 9th ACM/IFIP/USENIX International Middleware Conference, Middleware, pp. 243–264 (2008)

  • Verma, M., Gangadharan, G.R., Narendra, N.C., Ravi, V., Inamdar, V., Ramachandran, L., Calheiros, R.N., Buyya, R.: Dynamic resource demand prediction and allocation in multi-tenant service clouds. Concurr. Comput. Pract. Exp. 28(17), 4429–4442 (2016)

    Article  Google Scholar 

  • Wang, J.V., Fok, K., Cheng, C., Tse, C.K.: A stable matching-based virtual machine allocation mechanism for cloud data centers. In: IEEE World Congress on Services, SERVICES, pp. 103–106 (2016)

  • Xu, B., Peng, Z., Xiao, F., Gates, A.M., Yu, J.: Dynamic deployment of virtual machines in cloud computing using multi-objective optimization. Soft Comput. 19(8), 2265–2273 (2015)

    Article  Google Scholar 

  • Xu, J., Fortes, J.A.B.: Multi-objective virtual machine placement in virtualized data center environments. In: IEEE/ACM International Conference on Green Computing and Communications, GreenCom, & International Conference on Cyber, Physical and Social Computing, CPSCom, Hangzhou, pp. 179–188 (2010)

  • Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evolut. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  • Zheng, Q., Li, R., Li, X., Shah, N., Zhang, J., Tian, F., Chao, K., Li, J.: Virtual machine consolidated placement based on multi-objective biogeography-based optimization. Future Gener. Comput. Syst. 54, 95–122 (2016)

    Article  Google Scholar 

  • Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evolut. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Professors Salvador Pinto Abreu and Pedro Salgueiro from Universidade de Évora for granting the authors permission to use their cluster. This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with references UID/CEC/50021/2013, SFRH/BD/111471/2015, CMU/AIR/0022/2017 and PTDC/CCI-COM/31198/2017.

Author information

Authors and Affiliations

  1. INESC-ID / Instituto Superior Técnico, Universidade de Lisboa, Rua Alves Redol, 9, 1000-029, Lisbon, Portugal

    Miguel Terra-Neves, Inês Lynce & Vasco Manquinho

Authors
  1. Miguel Terra-Neves
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inês Lynce
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vasco Manquinho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Terra-Neves.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Terra-Neves, M., Lynce, I. & Manquinho, V. Virtual machine consolidation using constraint-based multi-objective optimization. J Heuristics 25, 339–375 (2019). https://doi.org/10.1007/s10732-018-9400-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-018-9400-2

Keywords

Search

Navigation