, Volume 46, Issue 1, pp 3–24 | Cite as

Hybridization of particle swarm optimization with quadratic approximation

  • Kusum DeepEmail author
  • Jagdish Chand Bansal
Theory and Methodology


Particle swarm optimization (PSO) has been extensively used in recent years for the optimization of nonlinear optimization problems. Two of the most popular variants of PSO are PSO-W (PSO with inertia weight) and PSO-C (PSO with constriction factor). Efforts have also been made to hybridize PSO with other methodologies to improve its performance. In this paper we present the hybridization of PSO with quadratic approximation operator (QA). The hybridization is performed by splitting the whole swarm into two subswarms in such a way that the PSO operators are applied on one subswarm, whereas the QA operator is applied on the other subswarm, ensuring that both subswarms are updated using the global best particle of the entire swarm. Based on this concept, two algorithms, namely qPSO-W and qPSO-C have been developed and their performance is evaluated with respect to PSO-W and PSO-C on the basis of 15 benchmark test problems and 3 real life problems taken from literature. The numerical and graphical results are a proof that the hybridized approach is a definite improvement in terms of efficiency, reliability and robustness.


Particle swarm optimization Quadratic approximation Nonlinear optimization Hybridization 


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Copyright information

© Operational Research Society of India 2009

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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