A novel hybrid firefly-whale optimization algorithm and its application to optimization of MPC parameters

Cimen M. E. , Yalçın Y.

SOFT COMPUTING, vol.26, no.4, pp.1845-1872, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1007/s00500-021-06441-6
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.1845-1872
  • Keywords: Firefly algorithm, Whale optimization algorithm, Hybrid metaheuristic algorithm, Model predictive control, MODEL-PREDICTIVE CONTROL, DESIGN, SYSTEM
  • Istanbul Technical University Affiliated: Yes


In this paper, a novel optimization algorithm is proposed by hybridizing firefly and whale optimization algorithms and it is applied to the problem of determining optimal design parameters of model predictive control. The developed hybrid algorithm is compared with firefly and whale optimization algorithms considering unimodal, multimodal, composite and CEC-C06 2019 benchmark optimization problems in terms of statistical analysis. Comparison results showed that hybrid algorithm has the best performance for approximately 67% of 39 benchmark functions in finding the minimum in an average of independent 100 experiments for each function. For the functions in which the proposed algorithm gives the best results, approximately 64% improvement is achieved compared to FA and 39% improvement compared to WOA. In terms of convergence speed, in average 2% of improvement is obtained. As an application to engineering problems, optimization of parameters of the model predictive control for inverted pendulum and distillation column is considered and the performance of the proposed algorithm is compared with the performances of firefly algorithm and whale optimization algorithm. For the considered applications, a novel objective function is selected. The selected objective function for hybrid firefly-whale optimization algorithm enables finding the optimal prediction horizon and control horizon as well as the Q and R matrices such that the system responses satisfy desired settling time and maximum overshoot criteria. Most of considered comparisons demonstrate that the proposed hybrid algorithm has better performance.