A core firework updating information guided dynamic fireworks algorithm for global optimization

  • Haitong Zhao
  • Changsheng ZhangEmail author
  • Jiaxu Ning
Methodologies and Application


As a new variant of swarm intelligence algorithm, fireworks algorithm (FWA) exhibits promising performance on a wide set of optimization problems, for which the fireworks algorithm has been concentrated on and investigated by researchers recently. This paper aims to improve the performance of the FWA by exploiting updating information of the core firework to guide the algorithm’s searching process. Based on this mentality, this paper ameliorated the explosion strategy of core firework of dynamic fireworks algorithm (dynFWA). The proposed algorithm, named dynPgFWA in this paper, improved FWA from two aspects: amplifying the explosion amplitude on the direction on which core firework is updated, and making more sparks which are generated by core firework distributed on this direction to enhance the algorithm’s searching ability on updating direction. A numerical experiment on CEC2015 and CEC2017 test suite was implemented to verify the performance of the proposed algorithm. Results of the experiment indicated that dynPgFWA outperformed the compared evolutionary algorithms in the quality of solutions.


Fireworks algorithm Updating information Core firework Swarm intelligence algorithm Evolutionary computing 



This study was funded by the National Natural Science Foundation Program of China (61572116, 61572117, 61502089), the National key Technology R&D Program of the Ministry of Science and Technology (2015BAH09F02), the Provincial Scientific and Technological Project (2015302002) and the Special Fund for Fundamental Research of Central Universities of Northeastern University (N150408001, N150404009).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Barraza J et al (2017) Iterative fireworks algorithm with fuzzy coefficients. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEEGoogle Scholar
  2. Barraza J et al (2017) Fuzzy fireworks algorithm based on a sparks dispersion measure. Algorithms 10(3):83CrossRefzbMATHGoogle Scholar
  3. Barraza J et al (2018) A new hybridization approach between the fireworks algorithm and grey wolf optimizer algorithm. J Optim 2018:1–18MathSciNetCrossRefzbMATHGoogle Scholar
  4. Beni G, Wang J (1993) Swarm intelligence in cellular robotic systems. In: Dario P, Sandini G, Aebischer P (eds) Robots and biological systems: towards a new bionics. Springer, pp 703–712Google Scholar
  5. Bolaji AL, Ahmad AA, Shola PB (2018) Training of neural network for pattern classification using fireworks algorithm. Int J Syst Assur Eng Manag 9(1):208–215CrossRefGoogle Scholar
  6. Chen J, Yang Q, Ni J et al (2015) An improved fireworks algorithm with landscape information for balancing exploration and exploitation. In: 2015 IEEE congress on evolutionary computation (CEC). IEEE, pp 1272–1279Google Scholar
  7. Chen S et al (2018) PS-FW: a hybrid algorithm based on particle swarm and fireworks for global optimization. Comput Intell Neurosci 2018:1–27Google Scholar
  8. Cheng R et al (2019) Improved fireworks algorithm with information exchange for function optimization. Knowl Based Syst 163:82–90CrossRefGoogle Scholar
  9. Ding K, Zheng S, Tan Y (2013) A gpu-based parallel fireworks algorithm for optimization. In: Proceedings of the 15th annual conference on genetic and evolutionary computation. ACM, pp 9–16Google Scholar
  10. Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66CrossRefGoogle Scholar
  11. Gao H, Diao M (2011) Cultural firework algorithm and its application for digital filters design. Int J Model Ident Control 14(4):324–331CrossRefGoogle Scholar
  12. Gao KZ, Suganthan PN, Pan QK et al (2016) Artificial bee colony algorithm for scheduling and rescheduling fuzzy flexible job shop problem with new job insertion. Knowl Based Syst 109:1–16CrossRefGoogle Scholar
  13. Han MF, Lin CT, Chang JY (2013) Differential evolution with local information for neuro-fuzzy systems optimisation. Knowl Based Syst 44(1):78–89CrossRefGoogle Scholar
  14. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):24–32CrossRefGoogle Scholar
  15. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol 4, pp 1942–1948Google Scholar
  16. Knowles J, Thiele L, Zitzler E (2006) A tutorial on the performance assessment of stochastic multiobjective optimizers. Tik Rep 214:327–332Google Scholar
  17. Lana I, Del Ser J, Vélez M (2017) A novel fireworks algorithm with wind inertia dynamics and its application to traffic forecasting. In: 2017 IEEE congress on evolutionary computation (CEC). IEEEGoogle Scholar
  18. Lee Y, Filliben JJ, Micheals RJ et al (2013) Sensitivity analysis for biometric systems: a methodology based on orthogonal experiment designs. Comput Vis Image Underst 117(5):532–550CrossRefGoogle Scholar
  19. Li J, Tan Y (2015) Orienting mutation based fireworks algorithm. In: IEEE Congress on evolutionary computation (CEC). IEEE, pp 1265–1271Google Scholar
  20. Li Junzhi, Tan Ying (2018) The bare bones fireworks algorithm: a minimalist global optimizer. Appl Soft Comput 62:454–462CrossRefGoogle Scholar
  21. Li J, Zheng S, Tan Y (2014) Adaptive fireworks algorithm. In: IEEE Congress on evolutionary computation (CEC). IEEE, pp 3214–3221Google Scholar
  22. Liang JJ, Qu BY, Suganthan PN et al (2014) Problem definitions and evaluation criteria for the CEC 2015 competition on learning-based real-parameter single objective optimization. Technical Report201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, SingaporeGoogle Scholar
  23. Mosa MA, Hamouda A, Marei M (2016) Ant colony heuristic for user-contributed comments summarization. Knowl Based Syst 118:105–114CrossRefGoogle Scholar
  24. Nowak K, Märtens M, Izzo D (2014) Empirical performance of the approximation of the least hypervolume contributor. In: Bartz-Beielstein T, Branke J, Filipič B, Smith J (eds) International conference on parallel problem solving from nature. Springer, Cham, pp 662–671Google Scholar
  25. Panwar L, Reddy S, Kumar R (2015) Binary fireworks algorithm based thermal unit commitment. Int J Swarm Intell Evol Comput 6(2):87–101CrossRefGoogle Scholar
  26. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417CrossRefGoogle Scholar
  27. Reddy KS, Panwar LK, Kumar R et al (2016) Binary fireworks algorithm for profit based unit commitment (PBUC) problem. Int J Electr Power Energy Syst 83:270–282CrossRefGoogle Scholar
  28. Rueda JL, Loor R, Erlich I (2015) MVMO for optimal reconfiguration in smart distribution systems. IFAC PapersOnline 48(30):276–281CrossRefGoogle Scholar
  29. Si T, Ghosh R (2015) Explosion sparks generation using adaptive transfer function in firework algorithm. In: IEEE third international conference on signal processing, communications and networking, pp 305–314Google Scholar
  30. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  31. Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. In: International conference on advances in swarm intelligence. Springer, Berlin, pp 355–364Google Scholar
  32. Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: IEEE congress on evolutionary computation. IEEE, pp 1658–1665Google Scholar
  33. Thong PH, Le HS (2016) A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality. Knowl Based Syst 109:48–60CrossRefGoogle Scholar
  34. Xia C et al (2018) A novel mixed-variable fireworks optimization algorithm for path and time sequence optimization in WRSNs. In: International conference on communicatins and networking in China. Springer, ChamGoogle Scholar
  35. Xue Y et al (2018) A self-adaptive fireworks algorithm for classification problems. IEEE Access 6:44406–44416CrossRefGoogle Scholar
  36. Ye W, Wen J (2017) Adaptive fireworks algorithm based on simulated annealing. In: 2017 13th International conference on computational intelligence and security (CIS). IEEEGoogle Scholar
  37. Yu C, Tan Y (2015) Fireworks algorithm with covariance mutation. In: IEEE Congress on Evolutionary computation (CEC). IEEE, pp 1250–1256Google Scholar
  38. Yu C, Li J, Tan Y (2014) Improve enhanced fireworks algorithm with differential mutation. In: IEEE international conference on systems, man and cybernetics. IEEE, pp 264–269Google Scholar
  39. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958Google Scholar
  40. Zhang B, Zhang MX, Zheng YJ (2014) A hybrid biogeography-based optimization and fireworks algorithm. In: IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 3200–3206Google Scholar
  41. Zhang B, Zheng YJ, Zhang MX, Chen SY (2017) Fireworks algorithm with enhanced fireworks interaction. IEEE/ACM Trans Comput Biol Bioinform (TCBB) 14(1):42–55CrossRefGoogle Scholar
  42. Zheng S, Janecek A, Tan Y (2013) Enhanced fireworks algorithm. In: IEEE Congress on evolutionary computation. IEEE, pp 2069–2077Google Scholar
  43. Zheng S, Janecek A, Li J et al (2014) Dynamic search in fireworks algorithm. In: IEEE Congress evolutionary computation (CEC). IEEE, pp 3222–3229Google Scholar
  44. Zheng YJ, Xu XL, Ling HF et al (2015a) A hybrid fireworks optimization method with differential evolution operators. Neurocomputing 148(148):75–82CrossRefGoogle Scholar
  45. Zheng S, Li J, Janecek A et al (2015b) A cooperative framework for fireworks algorithm. IEEE/ACM Trans Comput Biol Bioinform 14(1):27–41CrossRefGoogle Scholar
  46. Zheng S, Yu C, Li J et al (2015c) Exponentially decreased dimension number strategy-based dynamic search fireworks algorithm for solving CEC2015 competition problems. In: 2015 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1083–1090Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Computer Science and EngineeringNortheastern UniversityShenyangPeople’s Republic of China

Personalised recommendations