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Chaotic Simulator for Bilevel Optimization of Virtual Machine Placements in Cloud Computing

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Abstract

The drastic increase in engineering system complexity has spurred the development of highly efficient optimization techniques. Many real-world optimization problems have been identified as bilevel/multilevel as well as multiobjective. The primary aim of this work is to present a framework to tackle the bilevel virtual machine (VM) placement problem in cloud systems. This is done using the coupled map lattice (CML) approach in conjunction with the Stackelberg game theory and weighted-sum frameworks. The VM placement problem was modified from the original multiobjective (MO) problem to an MO bilevel formulation to make it more realistic albeit more complicated. Additionally comparative analysis on the performance of the CML approach was carried out against the particle swarm optimization method. A new bilevel metric called the cascaded hypervolume indicator is introduced and applied to measure the dominance of the solutions produced by both methods. Detailed analysis on the computational results is presented.

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Abbreviations

P j :

Power consumption of the jth server

y j :

Indicates whether server j is in use or not

x ij :

Indicates if VM i is assigned to server j

R pi :

CPU demand of each VM

T pj :

Threshold of CPU utilization associated with each server

T mj :

Threshold of memory utilization associated with each server

R mi :

Memory demand of each VM

W j :

Resource wastage of the jth server

ɛ o :

Positive real constant parameter

F 1 :

Total power consumption

F 2 :

Total resource wastage

f o :

Total VM utilization

P idle j :

Power consumption of the jth server when it is idle

P busy j :

Power consumption of the jth server when it is busy

cHVI:

Cumulative hypervolume indicator

(x *1 , x *2 , x *o ) :

Optimal candidate solution

(z 1 , z 2 , z o):

Nadir point

w 1, w 2 :

Weights for the weighted-sum approach

V ref :

Normalized hypervolume

K :

Scaling factor

I :

Total number of VMs

J :

Total number of servers

w, c 1 , c 2 , r 1 , r 2 :

Constant Parameters

v i (t):

Velocity of each particle

x i (t):

Position of each particle

T max :

Maximum limit of function evaluations

s i :

Initial social influence

p i :

Initial individual influence

ɛ :

Coupling parameter

j :

Iteration index

θ :

Logistic function constant

m :

Maximum number of iteration

s :

Index for the vertices on the lattice

y :

Mapping variable

References

  1. Bard, J.F.: Some properties of the bilevel programming problem. J. Optim. Theory Appl. 68(2), 371–378 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Vicente, L., Savard, G., Júdice, J.: Descent approaches for quadratic bilevel programming. J. Optim. Theory Appl. 81(2), 379–399 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Deng, X.: Complexity issues in bilevel linear programming. In: Multilevel Optimization: Algorithms and Applications, pp. 149–164. Springer, Boston (1998)

  4. Chowdhury, A., Zomorrodi, A.R., Maranas, C.D.: Bilevel optimization techniques in computational strain design. Comput. Chem. Eng. 72, 363–372 (2015)

    Article  Google Scholar 

  5. Chu, Y., You, F.: Integrated scheduling and dynamic optimization by stackelberg game: bilevel model formulation and efficient solution algorithm. Ind. Eng. Chem. Res. 53(13), 5564–5581 (2014)

    Article  Google Scholar 

  6. Gutjahr, W.J., Dzubur, N.: Bi-objective bilevel optimization of distribution center locations considering user equilibria. Transp. Res. Part E: Logist. Transp. Rev. 85, 1–22 (2016)

    Article  Google Scholar 

  7. Camacho-Vallejo, J.F., González-Rodríguez, E., Almaguer, F.J., González-Ramírez, R.G.: A bi-level optimization model for aid distribution after the occurrence of a disaster. J. Clean. Prod. 105, 134–145 (2015)

    Article  Google Scholar 

  8. Ding, T., Li, C., Yan, C., Li, F., Bie, Z.: A bilevel optimization model for risk assessment and contingency ranking in transmission system reliability evaluation. IEEE Trans. Power Syst. 32(5), 3803–3813 (2016)

    Article  Google Scholar 

  9. Limleamthong, P., Guillén-Gosálbez, G.: Rigorous analysis of Pareto fronts in sustainability studies based on bilevel optimization: application to the redesign of the UK electricity mix. J. Clean. Prod. 164, 1602–1613 (2017)

    Article  Google Scholar 

  10. Li, G., Zhang, R., Jiang, T., Chen, H., Bai, L., Li, X.: Security-constrained bi-level economic dispatch model for integrated natural gas and electricity systems considering wind power and power-to-gas process. Appl. Energy 194, 696–704 (2017)

    Article  Google Scholar 

  11. Hashem, I.A.T., Yaqoob, I., Anuar, N.B., Mokhtar, S., Gani, A., Khan, S.U.: The rise of “big data” on cloud computing: review and open research issues. Inf. Syst. 47, 98–115 (2015)

    Article  Google Scholar 

  12. Senyo, P.K., Addae, E., Boateng, R.: Cloud computing research: a review of research themes, frameworks, methods and future research directions. Int. J. Inf. Manag. 38(1), 128–139 (2018)

    Article  Google Scholar 

  13. Stergiou, C., Psannis, K.E., Kim, B.G., Gupta, B.: Secure integration of IoT and cloud computing. Future Gener. Comput. Syst. 78, 964–975 (2018)

    Article  Google Scholar 

  14. Kumar, M.R.V., Raghunathan, S.: Heterogeneity and thermal aware adaptive heuristics for energy efficient consolidation of virtual machines in infrastructure clouds. J. Comput. Syst. Sci. 82(2), 191–212 (2016)

    Article  MathSciNet  Google Scholar 

  15. Lopez-Pires, F., Baran, B.: Virtual machine placement literature review. arXiv:1506.01509 (2015)

  16. Usmani, Z., Singh, S.: A survey of virtual machine placement techniques in a cloud data center. Procedia Comput. Sci. 78, 491–498 (2016)

    Article  Google Scholar 

  17. Liu, X.F., Zhan, Z.H., Deng, J.D., Li, Y., Gu, T., Zhang, J.: An energy efficient ant colony system for virtual machine placement in cloud computing. IEEE Trans. Evol. Comput. 22(1), 113–128 (2016)

    Article  Google Scholar 

  18. Abdel-Basset, M., Abdle-Fatah, L., Sangaiah, A.K.: An improved Lévy based whale optimization algorithm for bandwidth-efficient virtual machine placement in cloud computing environment. Cluster Computing, pp. 1–16 (2018)

  19. Shabeera, T.P., Kumar, S.M., Salam, S.M., Krishnan, K.M.: Optimizing VM allocation and data placement for data-intensive applications in cloud using ACO metaheuristic algorithm. Eng. Sci. Technol. Int. J. 20(2), 616–628 (2017)

    Google Scholar 

  20. Abdelaziz, A., Elhoseny, M., Salama, A.S., Riad, A.M., Hassanien, A.E.: Intelligent algorithms for optimal selection of virtual machine in cloud environment, towards enhance healthcare services. In: International Conference on Advanced Intelligent Systems and Informatics, pp. 289–298. Springer, Cham (2017)

  21. Ghobaei-Arani, M., Shamsi, M., Rahmanian, A.A.: An efficient approach for improving virtual machine placement in cloud computing environment. J. Exp. Theor. Artif. Intell. 29(6), 1149–1171 (2017)

    Article  Google Scholar 

  22. Saber, T., Thorburn, J., Murphy, L., Ventresque, A.: VM reassignment in hybrid clouds for large decentralised companies: a multi-objective challenge. Future Gener. Comput. Syst. 79, 751–764 (2018)

    Article  Google Scholar 

  23. Zelinka, I., Davendra, D., Roman, S., Roman, J.: Do evolutionary algorithms dynamics create complex network structures? Complex Syst. 20(2), 127 (2011)

    Article  Google Scholar 

  24. Richter, H.: Coupled map lattices as spatio-temporal fitness functions: landscape measures and evolutionary optimization. Physica D. 237(2), 167–186 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang, Y.Q., Wang, X.Y.: Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice. Phys. A. 402, 104–118 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Huang, A., Zhang, H.M., Guan, W., Yang, Y., Zong, G.: Cascading failures in weighted complex networks of transit systems based on coupled map lattices. In: Mathematical Problems in Engineering (2015)

  27. Nematzadeh, H., Enayatifar, R., Motameni, H., Guimarães, F.G., Coelho, V.N.: Medical image encryption using a hybrid model of modified genetic algorithm and coupled map lattices. Opt. Lasers Eng. 110, 24–32 (2018)

    Article  Google Scholar 

  28. Gao, D., Li, X., Chen, H.: Application of improved particle swarm optimization in vehicle crashworthiness. In: Mathematical Problems in Engineering (2019). https://doi.org/10.1155/2019/8164609

  29. Lu, R., Gao, W., Hu, X., Liu, W., Li, Y., Liu, X.: Crushing analysis and crashworthiness optimization of tailor rolled tubes with variation of thickness and material properties. Int. J. Mech. Sci. 136, 67–84 (2018)

    Article  Google Scholar 

  30. Khunkitti, S., Watson, N.R., Chatthaworn, R., Premrudeepreechacharn, S., Siritaratiwat, A.: An improved DA-PSO optimization approach for unit commitment problem. Energies 12(12), 2335 (2019)

    Article  Google Scholar 

  31. Kumar, N.: Parameters analysis for PSO based task scheduling in cloud computing. (2019). https://doi.org/10.2139/ssrn.3349577

  32. Tam, J.H., Ong, Z.C., Ismail, Z., Ang, B.C., Khoo, S.Y.: A new hybrid GA–ACO–PSO algorithm for solving various engineering design problems. Int. J. Comput. Math. 96(5), 883–919 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  33. 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 

  34. Ganesan, T., Elamvazuthi, I., Vasant, P.: Swarm intelligence for multiobjective optimization of extraction process. In: Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics, pp. 516–544 (2016). https://doi.org/10.4018/978-1-4666-9644-0.ch020

  35. Ganesan, T., Vasant, P., Elamvazuthi, I.: Advances in Metaheuristics: Applications in Engineering Systems. CRC Press, Amsterdam (2016)

  36. Sinha, A., Malo, P., Frantsev, A., Deb, K.: Finding optimal strategies in a multi-period multi-leader–follower Stackelberg game using an evolutionary algorithm. Comput. Oper. Res. 41, 374–385 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. Ganesan, T., Vasant, P., Elamvazuthi, I.: Multiobjective optimization of solar-powered irrigation system with fuzzy type-2 noise modelling. In: Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices, pp. 189–214. (2017). https://doi.org/10.4018/978-1-5225-0914-1.ch008

  38. Zhang, H., Wang, X., Wang, S., Guo, K., Lin, X.: Application of coupled map lattice with parameter q in image encryption. Opt. Lasers Eng. 88, 65–74 (2017)

    Article  Google Scholar 

  39. Pan, I., Das, S.: Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO. ISA Trans. 62, 19–29 (2016)

    Article  Google Scholar 

  40. Shi, J., Zhang, W., Zhang, Y., Xue, F., Yang, T.: MPPT for PV systems based on a dormant PSO algorithm. Electr. Power Syst. Res. 123, 100–107 (2015)

    Article  Google Scholar 

  41. Jiang, S., Zhang, J., Ong, Y.S., Zhang, A.N., Tan, P.S.: A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans. Cybern. 45(10), 2202–2213 (2014)

    Article  Google Scholar 

  42. Ganesan, T., Aris, M.S., Vasant, P.: Extreme value metaheuristics for optimizing a many-objective gas turbine system. Int. J. Energy Optim. Eng. 7(2), 76–96 (2018)

    Google Scholar 

  43. Ganesan, T., Elamvazuthi, I.: A multi-objective approach for resilience-based plant design optimization. Qual. Eng. 29(4), 656–671 (2017)

    Article  Google Scholar 

  44. Ganesan, T., Aris, M.S., Elamvazuthi, I.: Multiobjective strategy for an industrial gas turbine: absorption chiller system. In: Handbook of Research on Emergent Applications of Optimization Algorithms, pp. 531–556. IGI Global (2018)

  45. Vasant, P.: Intelligent Computing and Optimization, vol. 866. Springer, Berlin (2018)

  46. Vasant, P., Kose, U., Watada, J.: Metaheuristic techniques in enhancing the efficiency and performance of thermo-electric cooling devices. Energies 10(11), 1703 (2017)

    Article  Google Scholar 

  47. Vasant, P., Marmolejo, J.A., Litvinchev, I., Aguilar, R.R.: Nature-inspired meta-heuristics approaches for charging plug-in hybrid electric vehicle. Wireless Networks, pp. 1–14 (2019)

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Acknowledgements

The authors thank the organizers of ICO’2018, 4–5th October 2018, Hard Rock Hotel, Pattaya, Thailand, for the opportunity to present their research results.

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Authors and Affiliations

  1. Member of American Mathematical Society, Alberta, T2P 0X2, Canada

    Timothy Ganesan

  2. Universiti Teknologi Petronas, Seri Iskandar, 32610, Malaysia

    Pandian Vasant

  3. Nuevo Leon State University, San Nicolás de los Garza, Nuevo León, CP, 66450, Mexico

    Igor Litvinchev

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  1. Timothy Ganesan
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  2. Pandian Vasant
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  3. Igor Litvinchev
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Corresponding author

Correspondence to Timothy Ganesan.

Appendix

Appendix

A.1 xij for the best individual solution obtained using the CML approach

A.2 xij for the best individual solution obtained using the PSO approach

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Ganesan, T., Vasant, P. & Litvinchev, I. Chaotic Simulator for Bilevel Optimization of Virtual Machine Placements in Cloud Computing. J. Oper. Res. Soc. China 10, 703–723 (2022). https://doi.org/10.1007/s40305-020-00326-5

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