A modified Particle Swarm Optimization algorithm with enhanced search quality and population using Hummingbird Flight patterns

Mohsen Zare, Mohammad Amin Akbari, Rasoul Azizipanah-Abarghooee, Mostafa Malekpour, Seyedali Mirjalili, Laith Abualigah

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This study proposes a modified Particle Swarm Optimization (PSO) algorithm based on Hummingbird Flight (HBF) patterns to enhance the search quality and population diversity. The HBF has five concepts: (1) Smaller steps toward position updating are more likely than larger ones, (2) Position changes are made step by step throughout the flight, (3) Flight energy is conserved during the nectar-searching process, (4) Hummingbirds do not fly in large groups in confined spaces, and (5) Simultaneous position changes in all directions are not realistic. A comprehensive study on two CEC-2010 and CEC-2013 benchmark suites is conducted to verify the effectiveness of the proposed PSO-HBF algorithm. The proposed algorithm is also evaluated and compared to other well-known PSO algorithms using shifted and rotated CEC 2005 and CEC 2014 benchmark functions. Four cases in economic dispatch, the 10-unit reserve constraint, and the 30-unit dynamic economic dispatch (DED) are further examined. The last two cases investigate how the proposed PSO-HBF deals with large-scale practical problems. The results demonstrated that the PSO-HBF algorithm is superior to seven other modified algorithms, improving eight and ten functions on the 2010 and 2013 benchmarks, respectively. Furthermore, achieving the third rank among the nineteen improved PSO algorithms based on the 2005 functions confirms the effectiveness of the proposed algorithm. Moreover, in two cases of the DED problem, the results of PSO-HBF show significant improvement over previously published papers. The PSO-HBF algorithm's source code can be accessed publicly at http://www.optim-app.com/projects/psohbf.

Original languageEnglish
Article number100251
JournalDecision Analytics Journal
Publication statusPublished - Jun 2023


  • Algorithm
  • Becnhmark
  • Dynamic economic dispatch
  • Economic dispatch
  • Evolutionary algorithm
  • Hummingbird flight
  • Large-scale optimization
  • Optimization
  • Particle swarm optimization


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