Natural Computing

, Volume 13, Issue 1, pp 17–37 | Cite as

Quadratic interpolation based orthogonal learning particle swarm optimization algorithm

  • Ruochen Liu
  • Lixia Wang
  • Wenping Ma
  • Caihong Mu
  • Licheng Jiao


Particle swarm optimization (PSO) is a population based algorithm for solving global optimization problems. Owing to its efficiency and simplicity, PSO has attracted many researchers’ attention and developed many variants. Orthogonal learning particle swarm optimization (OLPSO) is proposed as a new variant of PSO that relies on a new learning strategy called orthogonal learning strategy. The OLPSO differs in the utilization of the information of experience from the standard PSO, in which each particle utilizes its historical best experience and globally best experience through linear summation. In OLPSO, particles can fly in better directions by constructing an efficient exemplar through orthogonal experimental design. However, the global version based orthogonal learning PSO (OLPSO-G) still have some drawbacks in solving some complex multimodal function optimization. In this paper, we proposed a quadratic interpolation based OLPSO-G (QIOLPSO-G), in which, a quadratic interpolation based construction strategy for the personal historical best experience is applied. Meanwhile, opposition-based learning, and Gaussian mutation are also introduced into this paper to increase the diversity of the population and discourage the premature convergence. Experiments are conducted on 16 benchmark problems to validate the effectiveness of the QIOLPSO-G, and comparisons are made with four typical PSO algorithms. The results show that the introduction of the three strategies does enhance the effectiveness of the algorithm.


Gaussian mutation Opposition-based learning Orthogonal learning Particle swarm optimization Quadratic interpolation 



This work was supported by the National Natural Science Foundation of China (Nos. 61373111, 61272279, 61003199 and 61203303); the Fundamental Research Funds for the Central Universities (Nos. K50511020014, K5051302084, K50510020011, K5051302049, and K5051302023); the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048); and the Program for New Century Excellent Talents in University (No. NCET-12-0920).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ruochen Liu
    • 1
  • Lixia Wang
    • 1
  • Wenping Ma
    • 1
  • Caihong Mu
    • 1
  • Licheng Jiao
    • 1
  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of ChinaXidian UniversityXi’anChina

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