Soft Computing

, Volume 22, Issue 8, pp 2429–2447 | Cite as

An orthogonal parallel symbiotic organism search algorithm embodied with augmented Lagrange multiplier for solving constrained optimization problems

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Abstract

Many practical engineering design problems need constrained optimization. The literature reports several meta-heuristic algorithms have been applied to solve constrained optimization problems. In many cases, the algorithms fail due to violation of constraints. Recently in 2014, a new meta-heuristic algorithm known as symbiotic organism search (SOS) is reported by Cheng and Prayogo. It is inspired by the natural phenomenon of interaction between organisms in an ecosystem which help them to survive and grow. In this paper, the SOS algorithm is combined with augmented Lagrange multiplier (ALM) method to solve the constrained optimization problems. The ALM is accurate and effective as the constraints in this case do not have the power to restrict the search space or search direction. The orthogonal array strategies have gained popularity among the meta-heuristic researchers due to its potentiality to enhance the exploitation process of the algorithms. Simultaneously, researchers are also looking at designing parallel version of the meta-heuristics to reduce the computational burden. In order to enhance the performance, an Orthogonal Parallel SOS (OPSOS) is developed. The OPSOS along with ALM method is a suitable combination which is used here to solve twelve benchmark nonlinear constrained problems and four engineering design problems. Simulation study reveals that the proposed approach has almost similar accuracy with lower run time than ALM with Orthogonal SOS. Comparative analysis also establish superior performance over ALM with orthogonal colliding bodies optimization, modified artificial bee colony, augmented Lagrangian-based particle swarm optimization and Penalty function-based genetic algorithm.

Keywords

Symbiotic organism search Constrained nonlinear problem Augmented Lagrange multiplier method Orthogonal array Parallel implementation 

Notes

Acknowledgements

Ms. Arnapurna Panda received research grants in from of institute research scholar fellowship from Ministry of HRD, Govt. of India to to carry out her Ph.D work at Indian Institute of Technology Bhubaneswar.

Compliance with ethical standards

Conflict of interest

There is no conflict of interest.

Animals or humans

This article does not contain any studies with animals or humans performed by any of the authors.

References

  1. Abdullahi M, Ngadi MA (2015) Symbiotic organism search optimization based task scheduling in cloud computing environment. Future Gener Comput Syst 56:640–650CrossRefGoogle Scholar
  2. Afonso MV, Bioucas-Dias JM, Figueiredo MA (2011) An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans Image Process 20(3):681–695MathSciNetCrossRefMATHGoogle Scholar
  3. Baghel V, Nanda SJ, Panda G (2011) New GOPSO and its application to robust identification. In: Proceedings of IEEE international conference on energy, automation, and signal, pp 1–6Google Scholar
  4. Cagnina LC, Esquivel SC, Coello CAC (2011) Solving constrained optimization problems with a hybrid particle swarm optimization algorithm. Eng Optim 43(8):843–866MathSciNetCrossRefGoogle Scholar
  5. Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112CrossRefGoogle Scholar
  6. Cheng MY, Prayogo D, Tran DH (2015) Optimizing multiple-resources leveling in multiple projects using discrete symbiotic organisms search. J Comput Civil Eng 30(3):04015036CrossRefGoogle Scholar
  7. Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11):1245–1287MathSciNetCrossRefMATHGoogle Scholar
  8. Cung VD, Martins SL, Ribeiro CC, Roucairol C (2002) Strategies for the parallel implementation of metaheuristics. Essays and surveys in metaheuristics. Springer, USMATHGoogle Scholar
  9. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338CrossRefMATHGoogle Scholar
  10. Fogarty TC, Huang R (1990) Implementing the genetic algorithm on transputer based parallel processing systems. In: International conference on parallel problem solving from nature, Springer, Berlin, pp 145–149Google Scholar
  11. Ghasemishabankareh B, Li X, Ozlen M (2016) Cooperative coevolutionary differential evolution with improved augmented Lagrangian to solve constrained optimisation problems. Inf Sci 369:441–456MathSciNetCrossRefGoogle Scholar
  12. Gong W, Cai Z, Ling CX (2006) ODE: a fast and robust differential evolution based on orthogonal design. In: Proceedings of 19th Australian joint conference on artificial intelligence. Advances in artificial intelligence, Springer, Berlin, pp 709–718Google Scholar
  13. Gong W, Cai Z, Jiang L (2008) Enhancing the performance of differential evolution using orthogonal design method. Appl Math Comput 206(1):56–69MATHGoogle Scholar
  14. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99MathSciNetCrossRefGoogle Scholar
  15. He Q, Wang L (2007) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186(2):1407–1422MathSciNetMATHGoogle Scholar
  16. Ho SY, Lin HS, Liauh WH, Ho SJ (2008) OPSO: orthogonal particle swarm optimization and its application to task assignment problems. IEEE Trans Syst Man Cybern A Syst Hum 38(2):288–298Google Scholar
  17. Huang F, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356MathSciNetMATHGoogle Scholar
  18. Jansen PW, Perez RE (2011) Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach. Comput Struct 89(13):1352–1366CrossRefGoogle Scholar
  19. Joines JA, Houck CR (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: IEEE congress on evolutionary computation, pp 579–584Google Scholar
  20. Kamankesh H, Agelidis VG, Kavousi-Fard A (2016) Optimal scheduling of renewable micro-grids considering plug-in hybrid electric vehicle charging demand. Energy 100:285–297CrossRefGoogle Scholar
  21. Karaboga D, Akay B (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031CrossRefGoogle Scholar
  22. Kong H, Li N, Shen Y (2015) Adaptive double chain quantum genetic algorithm for constrained optimization problems. Chin J Aeronaut 28(1):214–228CrossRefGoogle Scholar
  23. Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59:703–736CrossRefMATHGoogle Scholar
  24. Leung YW, Wang Y (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evol Comput 5(1):41–53CrossRefGoogle Scholar
  25. Lin CH (2013) A rough penalty genetic algorithm for constrained optimization. Inf Sci 241:119–137CrossRefGoogle Scholar
  26. Liu H, Li P, Wen Y (2006) Parallel ant colony optimization algorithm. In: 6th IEEE world congress on intelligent control and automation, vol 1, pp 3222–3226Google Scholar
  27. Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10(2):629–640CrossRefGoogle Scholar
  28. Long W, Liang X, Huang Y, Chen Y (2014) An effective hybrid cuckoo search algorithm for constrained global optimization. Neural Comput Appl 25(3–4):911–926CrossRefGoogle Scholar
  29. MATLAB Box plot, available at Mathworks online: http://in.mathworks.com/help/stats/boxplot.html?refresh=true (2016)
  30. Nanda SJ, Panda G (2013) Automatic clustering algorithm based on multi-objective immunized PSO to classify actions of 3D human models. Eng Appl Artif Intell 26(5):1429–1441CrossRefGoogle Scholar
  31. Panda A, Pani S (2016) A symbiotic organisms search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems. Appl Soft Comput 46:344–360CrossRefGoogle Scholar
  32. Panda A, Pani S (2016) A WNN model trained with orthogonal colliding bodies optimization for accurate identification of hammerstein plant. In: Proceedings of IEEE congress on evolutionary computation (CEC-2016), VancouverGoogle Scholar
  33. Panda A, Pani S (2016) Improved Identification of hammerstein plant using a non-linear model trained with symbiotic organisms search. In: Proceedings of IEEE region 10 conference (TENCON 2016), pp 247–250Google Scholar
  34. Pattnaik SS, Bakwad KM, Devi S, Panigrahi BK, Das S (2011) Parallel bacterial foraging optimization. In: Handbook of swarm intelligence. Springer, Berlin, pp 487–502Google Scholar
  35. Prayogo D (2015) An innovative parameter-free symbiotic organisms search (SOS) for solving construction-engineering problems. Ph.D. Thesis, Department of Construction Engineering, National Taiwan University of Science and TechnologyGoogle Scholar
  36. Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396CrossRefGoogle Scholar
  37. Rocha AMA, Martins TF, Fernandes EM (2011) An augmented Lagrangian fish swarm based method for global optimization. J Comput Appl Math 235(16):4611–4620MathSciNetCrossRefMATHGoogle Scholar
  38. Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4:284–294CrossRefGoogle Scholar
  39. Runarsson TP, Yao X (2005) Search biases in constrained evolutionary optimization. IEEE Trans Syst Man Cybern C Appl Rev 35:233–243CrossRefGoogle Scholar
  40. Schutte JF, Reinbolt JA, Fregly BJ, Haftka RT, George AD (2004) Parallel global optimization with the particle swarm algorithm. Int J Numer Methods Eng 61(13):2296–2315CrossRefMATHGoogle Scholar
  41. Sedlaczek K, Eberhard P (2006) Using augmented Lagrangian particle swarm optimization for constrained problems in engineering. Struct Multidiscip Optim 32(4):277–286CrossRefGoogle Scholar
  42. Shukla UP, Nanda SJ (2016) Parallel social spider clustering algorithm for high dimensional datasets. Eng Appl Artif Intell 56:75–90CrossRefGoogle Scholar
  43. Tahk MJ, Sun BC (2000) Coevolutionary augmented Lagrangian methods for constrained optimization. IEEE Trans Evol Comput 4(2):114–124CrossRefGoogle Scholar
  44. Tejani GG, Savsani VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3(3):226–249Google Scholar
  45. Tran DH, Cheng MY, Prayogo D (2016) A novel multiple objective symbiotic organisms search (MOSOS) for timecostlabor utilization tradeoff problem. Knowl Based Syst 94:132–145CrossRefGoogle Scholar
  46. Vincent FY, Redi AP, Yang CL, Ruskartina E, Santosa B (2017) Symbiotic organisms search and two solution representations for solving the capacitated vehicle routing problem. Appl Soft Comput 52:657–672CrossRefGoogle Scholar
  47. Yang J, Bouzerdoum A, Phung SL (2010) A particle swarm optimization algorithm based on orthogonal design. In: Proceedings of IEEE evolutionary computation (CEC 10), pp 1–7Google Scholar
  48. Yeniay O (2005) Penalty function methods for constrained optimization with genetic algorithms. Math Comput Appl 10(1):45–56MathSciNetGoogle Scholar
  49. Zahara E, Kao Y (2009) Hybrid NelderMead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36(2):3880–3886CrossRefGoogle Scholar
  50. Zhan ZH, Zhang J, Li Y, Shi YH (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evol Comput 15(6):832–847CrossRefGoogle Scholar
  51. Zhang C, Lin Q, Gao L, Li X (2015) Backtracking search algorithm with three constraint handling methods for constrained optimization problems. Expert Syst Appl 42(21):7831–7845CrossRefGoogle Scholar
  52. Zhang Q, Leung YW (1999) An orthogonal genetic algorithm for multimedia multicast routing. IEEE Trans Evol Comput 3: 53–62CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Basic SciencesIndian Institute of Technology BhubaneswarBhubaneswarIndia

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