eesti teaduste
akadeemia kirjastus
SINCE 1952
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of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
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Modified particle swarm optimization algorithm based on gravitational field interactions; pp. 15–27

Full article in PDF format | doi: 10.3176/proc.2016.1.01

Margarita Spichakova


In this paper we present the modified particle swarm optimization algorithm, where gravitational interactions between particles are used for computing learning coefficients. The behaviour of the algorithm is demonstrated by solving the twodimensional Diophantine equation problem. This allows us to observe the search space and workflow of the algorithm directly on the two-dimensional plane.


  1. Abraham, S., Sanya, S., and Sanglikar, M. A. Particle swarm optimization based diophantine equation solver. CoRR, abs/1003.2724, 2010.

  2. Formato, R. A. Central force optimization: a new metaheuristic with applications in applied electromagnetics. PIER, 2007, 77, 425–491.

  3. Hsiao, Y.-T., Chuang, C.-L., Jiang, J.-A., and Chien, C.-C. A novel optimization algorithm: space gravitational optimization. In Systems, Man and Cybernetics, 2005 IEEE International Conference, Vol. 3. 2005, 2323–2328.

  4. Hsiung, S. and Mattews, J. Genetic algorithm example: Diophantine equation, 1999. [accessed 23 May 2015].

  5. Kennedy, J. and Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Vol. 4. 1995, 1942–1948.

  6. Luke, S. Essentials of Metaheuristics. Lulu, second edition, 2013. Available at$\sim$sean/book/metaheuristics/ [accessed 23 May 2015].

  7. Mirjalili, S. and Hashim, S. Z. M. A new hybrid PSOGSA algorithm for function optimization. In Proceedings of International Conference on Computer and Information Application (ICCIA). 2010, 374–377.

  8. Mo, S., Zeng, J., and Xu, W. An extended particle swarm optimization algorithm based on self-organization topology driven by fitness. J. Comput. Inform. Syst., 2011, 7(12), 4441–4454.

  9. Qi, K., Lei, W., and Qidi, W. A novel self-organizing particle swarm optimization based on gravitation field model. In American Control Conference, 2007, ACC '07, 2007, 528–533.

10. Rashedi, E., Nezamabadi-pour, H., Saryazdi, S., and Farsangi, M. M. Allocation of static var compensator using gravitational search algorithm. In First Joint Congress on Fuzzy and Intelligent Systems Ferdowsi University of Mashhad, Iran, August, 29–31. 2007, 29–31.

11. Rashedi, E., Nezamabadi-pour, H., and Saryazdi, S. GSA: a gravitational search algorithm. Inform. Sci., 2009, 179(13), 2232–2248.

12. Rashedi, E., Nezamabadi-pour, H., and Saryazdi, S. Filter modeling using gravitational search algorithm. Eng. Appl. Artif. Intell., 2011, 24, 117–122.

13. Tsai, H.-C., Tyan, Y.-Y., Wu, Y.-W., and Lin, Y.-H. Gravitational particle swarm. Appl. Math. Comput., 2013, 219(17), 9106–9117.

14. Webster, B. Solving Combinatorial Optimization Problems Using a New Algorithm Based on Gravitational Attraction. PhD thesis, Florida Institute of Technology, Melbourne, FL, USA, 2004.

15. Webster, B. and Bernhard, P. J. A Local Search Optimization Algorithm Based on Natural Principles of Gravitation. Technical Report CS-2003-10, Florida Institute of Technology, 2003.

16. Zibanezhad, B., Zamanifar, K., Nematbakhsh, N., and Mardukhi, F. An approach for web services composition based on QoS and gravitational search algorithm. In Proceedings of the 6th International Conference on Innovations in Information Technology, IIT'09. IEEE Press, Piscataway, NJ, USA, 2009, 121–125.

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