An orthogonal parallel symbiotic organism search algorithm embodied with augmented Lagrange multiplier for solving constrained optimization problems
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.
KeywordsSymbiotic organism search Constrained nonlinear problem Augmented Lagrange multiplier method Orthogonal array Parallel implementation
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.
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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.
- 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
- 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
- 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
- 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
- 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
- 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
- MATLAB Box plot, available at Mathworks online: http://in.mathworks.com/help/stats/boxplot.html?refresh=true (2016)
- 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
- 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
- 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
- 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
- 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
- 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