Abstract
Firefly algorithm is one of the most promising population-based meta-heuristic algorithms. It has been successfully applied in many optimization problems. Several modifications have been proposed to the original algorithm to boost the performance in terms of accuracy and speed of convergence. This work proposes a partition cum unification based genetic firefly algorithm to explore the benefits of both the algorithms in a novel way. With this, the initial population is partitioned into two compartments based on a weight factor. An improved firefly algorithm runs in the first compartment, whereas, the genetic operators like selection, crossover, and mutation are applied on the relatively inferior fireflies in the second compartment giving added exploration abilities to the weaker solutions. Finally, unification is applied on the subsets of fireflies of the two compartments before going to the next iterative cycle. The new algorithm in three variants of weightage factor have been compared with the two constituents i.e. standard firefly algorithm and genetic algorithm, additionally with some state-of-the-art meta-heuristics namely particle swarm optimization, cuckoo search, flower pollination algorithm, pathfinder algorithm and bio-geography based optimization on 19 benchmark objective functions covering different dimensionality of the problems viz. 2-D, 16-D, and 32-D. The new algorithm is also tested on two classical engineering optimization problems namely tension-compression spring and three bar truss problem and the results are compared with all the other algorithms. Non-parametric statistical tests, namely Wilcoxon rank-sum tests are conducted to check any significant deviations in the repeated independent trials with each algorithm. Multi criteria decision making tool is applied to statistically determine the best performing algorithm given the different test scenarios. The results show that the new algorithm produces the best objective function value for almost all the functions including the engineering problems and it is way much faster than the standard firefly algorithm.
Similar content being viewed by others
References
Xin-She Yang. Nature-inspired metaheuristic algorithms. Luniver press, 2010
Ilhem Boussaïd, Julien Lepagnot, and Patrick Siarry. A survey on optimization metaheuristics. Information sciences, 237:82, 2013
John H Holland. Genetic algorithms and adaptation. In Adaptive Control of Ill-Defined Systems, pp 317. Springer, 1984
Kalyanmoy Deb. An introduction to genetic algorithms. Sādhanā, 24(4-5):293, 1999
Tansel Dokeroglu, Ender Sevinc, Tayfun Kucukyilmaz, and Ahmet Cosar. A survey on new generation metaheuristic algorithms. Computers & Industrial Engineering, 137:106040, 2019
Kashif Hussain, Mohd Najib Mohd Salleh, Shi Cheng, and Yuhui Shi. Metaheuristic research: a comprehensive survey. Artificial Intelligence Review, 52(4):2191, 2019
Xin-She Yang. Firefly algorithms for multimodal optimization. In International symposium on stochastic algorithms, p 169. Springer, 2009
Waqar A Khan, Nawaf N Hamadneh, Surafel L Tilahun, and Ngnotchouye J M. A review and comparative study of firefly algorithm and its modified versions. Optimization Algorithms-Methods and Applications, p 281, 2016
Iztok Fister, Iztok Fister Jr, Xin-She Yang, and Janez Brest 2013. A comprehensive review of firefly algorithms. Swarm and Evolutionary Computation, 13:34, 2013
Nilanjan Dey. Applications of firefly algorithm and its variants. Springer, Berlin, 2020
Mahmood Reza Shakarami and Reza Sedaghati. A new approach for network reconfiguration problem in order to deviation bus voltage minimization with regard to probabilistic load model and dgs. Int. J. Electr. Comput. Energ. Electr. Commun. Eng., 8(2):430, 2014
Abdollah Kavousi-Fard, Haidar Samet, and Fatemeh Marzbani. A new hybrid modified firefly algorithm and support vector regression model for accurate short term load forecasting. Expert systems with applications, 41(13):6047, 2014
Xiaoyu Lin, Yiwen Zhong, and Hui Zhang. An enhanced firefly algorithm for function optimisation problems. International Journal of Modelling, Identification and Control, 18(2):166, 2013
Amir Hossein Gandomi, X-S Yang, S Talatahari, and Amir Hossein Alavi. Firefly algorithm with chaos. Communications in Nonlinear Science and Numerical Simulation, 18(1):89, 2013
Mohd Herwan Sulaiman, Hamdan Daniyal, and Mohd Wazir Mustafa. Modified firefly algorithm in solving economic dispatch problems with practical constraints. In 2012 IEEE International Conference on Power and Energy (PECon), pp 157. IEEE, 2012
Bin Wang, Dong-Xu Li, Jian-Ping Jiang, and Yi-Huan Liao. A modified firefly algorithm based on light intensity difference. Journal of Combinatorial Optimization, 31(3):1045, 2016
Shuhao Yu, Shoubao Su, Qingping Lu, and Li Huang. A novel wise step strategy for firefly algorithm. International Journal of Computer Mathematics, 91(12):2507, 2014
Amit Kumar Ball, Shibendu Shekhar Roy, Dakshina Ranjan Kisku, Naresh Chandra Murmu, and Leandro dos Santos Coelho. Optimization of drop ejection frequency in ehd inkjet printing system using an improved firefly algorithm. Applied Soft Computing, 94:106438, 2020
Abhishek Ghosh Roy, Pratyusha Rakshit, Amit Konar, Samar Bhattacharya, Eunjin Kim, and Atulya K Nagar. Adaptive firefly algorithm for nonholonomic motion planning of car-like system. In 2013 IEEE Congress on Evolutionary Computation, pp 2162. IEEE, 2013
Shuhao Yu, Shenglong Zhu, Yan Ma, and Demei Mao. Enhancing firefly algorithm using generalized opposition- based learning. Computing, 97(7):741, 2015
MJ Kazemzadeh-Parsi. A modified firefly algorithm for engineering design optimization problems. Iranian Journal of Science and Technology. Transactions of Mechanical Engineering, 38(M2):403, 2014
Mohammad Javad Kazemzadeh-Parsi, Farhang Daneshmand, Mohammad Amin Ahmadfard, and Jan Adamowski. Optimal remediation design of unconfined contaminated aquifers based on the finite element method and a modified firefly algorithm. Water Resources Management, 29(8):2895, 2015
Sirus Mohammadi, Babak Mozafari, Soodabeh Solimani, and Taher Niknam. An adaptive modified firefly optimisation algorithm based on hong’s point estimate method to optimal operation management in a microgrid with consideration of uncertainties. Energy, 51:339, 2013
Tahereh Hassanzadeh and Hamidreza Rashidy Kanan. Fuzzy fa: a modified firefly algorithm. Applied Artificial Intelligence, 28(1):47, 2014
Sankalap Arora, Sarbjeet Singh, Satvir Singh, and Bhanu Sharma. Mutated firefly algorithm. In 2014 International Conference on Parallel, Distributed and Grid Computing, p 33. IEEE, 2014
Sankalap Arora and Satvir Singh. Performance research on firefly optimization algorithm with mutation. In International conference, computing & systems, 2014
Wen-chuan Wang, Lei Xu, Kwok-wing Chau, and Dong-mei Xu. Yin-yang firefly algorithm based on dimensionally cauchy mutation. Expert Systems with Applications, 150:113216, 2020
Hu Peng, Wenhua Zhu, Changshou Deng, and Zhijian Wu. Enhancing firefly algorithm with courtship learning. Information Sciences, 543:18, 2021
Nan Tong, Qiang Fu, Caiming Zhong, and Pengjun Wang. A multi-group firefly algorithm for numerical optimization. In Journal of Physics: Conference Series, vol 887, p 012060. IOP Publishing, 2017
Lingyun Zhou, Lixin Ding, Maode Ma, and Wan Tang. An accurate partially attracted firefly algorithm. Computing, 101(5):477, 2019
Adil Baykasoğlu and Fehmi Burcin Ozsoydan. An improved firefly algorithm for solving dynamic multidimensional knapsack problems. Expert Systems with Applications, 41(8):3712, 2014
Jingsen Liu, Yinan Mao, Xiaozhen Liu, and Yu Li. A dynamic adaptive firefly algorithm with globally orientation. Mathematics and Computers in Simulation, 2020
Iztok Fister, Xin-She Yang, Janez Brest, and Iztok Fister Jr. Modified firefly algorithm using quaternion representation. Expert Systems with Applications, 40(18):7220, 2013
Hui Wang, Wenjun Wang, Xinyu Zhou, Hui Sun, Jia Zhao, Xiang Yu, and Zhihua Cui. Firefly algorithm with neighborhood attraction. Information Sciences, 382:374, 2017
Sh M Farahani, AA Abshouri, B Nasiri, and MR2011 Meybodi. A gaussian firefly algorithm. International Journal of Machine Learning and Computing, 1(5):448, 2011
Xin-She Yang. Firefly algorithm, levy flights and global optimization. In Research and development in intelligent systems XXVI, p 209. Springer, 2010
Lyes Tighzert, Cyril Fonlupt, and Boubekeur Mendil. A set of new compact firefly algorithms. Swarm and Evolutionary Computation, 40:92, 2018
Jinran Wu, You-Gan Wang, Kevin Burrage, Yu-Chu Tian, Brodie Lawson, and Zhe Ding. An improved firefly algorithm for global continuous optimization problems. Expert Systems with Applications, 149:113340, 2020
Jitin Luthra and Saibal K Pal. A hybrid firefly algorithm using genetic operators for the cryptanalysis of a monoalphabetic substitution cipher. In 2011 World congress on information and communication technologies, p 202. IEEE, 2011
A Rahmani and SA MirHassani. A hybrid firefly-genetic algorithm for the capacitated facility location problem. Information Sciences, 283:70, 2014
Shubhendu Kumar Sarangi, Rutuparna Panda, Sabnam Priyadarshini, and Archana Sarangi. A new modified firefly algorithm for function optimization. In 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), p 2944. IEEE, 2016
İbrahim Berkan Aydilek, İzzettin Hakan Karaçizmeli, Mehmet Emin Tenekeci, Serkan Kaya, and Abdülkadir Gümüşçü. Using chaos enhanced hybrid firefly particle swarm optimization algorithm for solving continuous optimization problems. Sādhanā, 46(2):1, 2021
Aref Yelghi and Cemal Köse. A modified firefly algorithm for global minimum optimization. Applied Soft Computing, 62:29, 2018
Kadavy Tomas, Pluhacek Michal, Viktorin Adam, and Senkerik Roman. Firefly algorithm enhanced by orthogonal learning. In Computer Science On-line Conference, p 477. Springer, 2018
Yu-Pei Huang, Xiang Chen, and Cheng-En Ye. A hybrid maximum power point tracking approach for photovoltaic systems under partial shading conditions using a modified genetic algorithm and the firefly algorithm. International Journal of Photoenergy, 2018, 2018
Russell Eberhart and James Kennedy. Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks, volume 4, pages 1942–1948. Citeseer, 1995
Xin-She Yang and Suash Deb. Cuckoo search via lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC), p 210. IEEE, 2009
R Indumathy, S Uma Maheswari, and G Subashini. Nature-inspired novel cuckoo search algorithm for genome sequence assembly. Sādhanā, 40(1):1, 2015
Xin-She Yang. Flower pollination algorithm for global optimization. In International conference on unconventional computing and natural computation, p 240. Springer, 2012
Hamza Yapici and Nurettin Cetinkaya. A new meta-heuristic optimizer: pathfinder algorithm. Applied soft computing, 78:545, 2019
Dan Simon. Biogeography-based optimization. IEEE transactions on evolutionary computation, 12(6):702, 2008
Singiresu S Rao. Engineering optimization: theory and practice. John Wiley & Sons, 2019
Amir Parnianifard, Ratchatin Chancharoen, Gridsada Phanomchoeng, and Lunchakorn Wuttisittikulkij. A new approach for low-dimensional constrained engineering design optimization using design and analysis of simulation experiments. International Journal of Computational Intelligence Systems, 13(1):1663, 2020
Jasbir Singh Arora. Introduction to optimum design. Elsevier, 2004
Young-Jou Lai, Ting-Yun Liu, and Ching-Lai Hwang. Topsis for modm. European journal of operational research, 76(3):486, 1994
Momin Jamil and Xin-She Yang. A literature survey of benchmark functions for global optimization problems. arXiv preprintarXiv:1308.4008, 2013
Sudhanshu K Mishra. Some new test functions for global optimization and performance of repulsive particle swarm method. Available at SSRN 926132, 2006
Carlos A Coello Coello. Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry, 41(2):113, 2000
Joaquín Derrac, Salvador García, Daniel Molina, and Francisco Herrera. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1):3, 2011
Author information
Authors and Affiliations
Corresponding author
Supplementary Information
Below is the link to the electronic supplementary material.
Abbreviations
Abbreviations
- GA:
-
Genetic algorithm
- FA:
-
Firefly algorithm
- PUBG-FA:
-
Partition cum unification based genetic - FA
- PSO:
-
Particle swarm optimization
- CS:
-
Cuckoo search
- FPA:
-
Flower pollination algorithm
- PFA:
-
Pathfinder algorithm
- BBO:
-
Bio-geography based optimization
- MCDM:
-
Multi-criteria decision making
- TOPSIS:
-
Technique for order of preference by similarity to ideal solution
Rights and permissions
About this article
Cite this article
Gupta, D., Dhar, A.R. & Roy, S.S. A partition cum unification based genetic- firefly algorithm for single objective optimization. Sādhanā 46, 121 (2021). https://doi.org/10.1007/s12046-021-01641-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12046-021-01641-0