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

  • Arnapurna Panda
  • Sabyasachi Pani


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.


Symbiotic 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.

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.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

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

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