Enhancing Firefly Algorithm with Best Neighbor Guided Search Strategy
WU Shuangke, WU Zhijian, PENG Hu1. School of Computer Science, Wuhan University, Wuhan 430072, Hubei, China; 2. School of Information Science and Technology, Jiujiang University, Jiujiang 332005, Jiangxi, China
Firefly algorithm (FA) is a recently-proposed swarm intelligence technique. It has shown good performance in solving various optimization problems. According to the standard firefly algorithm and most of its variants, a firefly migrates to every other brighter firefly in each iteration. However, this method leads to defects of oscillations of positions, which hampers the convergence to the optimum. To address these problems and enhance the performance of FA, we propose a new firefly algorithm, which is called the Best Neighbor Firefly Algorithm (BNFA). It employs the best neighbor guided strategy, where each firefly is attracted to the best firefly among some randomly chosen neighbors, thus reducing the firefly oscillations in every attraction-induced migration stage, while increasing the probability of the guidance a new better direction. Moreover, it selects neighbors randomly to prevent the firefly form being trapped into a local optimum. Extensive experiments are conducted to find out the optimal parameter settings. To verify the performance of BNFA, 13 classical benchmark functions are tested. Results show that BNFA outperforms the standard FA and other recently proposed modified FAs.
Key words:firefly algorithm (FA); global optimization; random neighbour; exploration and exploitation
 Kennedy J. Particle swarm optimization [C]// Encyclopedia of Machine Learning. New York: Springer-Verlag, 2010: 760- 766.
 Peng H, Guo Z, Deng C, et al. Enhancing differential evolu-tion with random neighbors based strategy[J]. Journal of Computational Science, 2018, 26: 501-511.
 Peng H, Wu Z. Heterozygous differential evolution with Taguchi local search[J]. Soft Computing, 2015, 19(11): 3273-3291.
 Karaboga D. An Idea Based on Honey Bee Swarm for Nu-merical Optimization [R]. Kayseri: Erciyes University, 2005.
 Yang X S. Nature-Inspired Metaheuristic Algorithms [M]. United Kingdom: Luniver Press, 2010.
 Jaradat A S, Hamad S B. Community structure detection using firefly algorithm[J]. International Journal of Applied Metaheuristic Computing (IJAMC), 2018, 9(4): 52-70.
 Moazenzadeh R, Mohammadi B, Shamshirband S, et al. Coupling a firefly algorithm with support vector regression to predict evaporation in northern Iran[J]. Engineering Ap-plications of Computational Fluid Mechanics, 2018, 12(1): 584-597.
 Spea S R. Economic-emission dispatch problem using firefly algorithm[C]//2017 Nineteenth International Middle East Power Systems Conference (MEPCON). Washington D C: IEEE, 2017: 671-676.
 Yu S, Su S, Lu Q, et al. A novel wise step strategy for firefly algorithm[J]. International Journal of Computer Mathematics, 2014, 91(12): 2507-2513.
 Yu S, Zhu S, Ma Y, et al. A variable step size firefly algo-rithm for numerical optimization[J]. Applied Mathematics and Computation, 2015, 263: 214-220.
 Fister Jr I, Yang X S, Fister I, et al. Memetic firefly algorithm for combinatorial optimization [EB/OL]. [2012-05-10]. https://arxiv.org/abs/1204.5165.
 Gandomi A H, Yang X S, Talatahari S, et al. Firefly algo-rithm with chaos[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(1): 89-98.
 Wang H, Wang W, Sun H, et al. Firefly algorithm with ran-dom attraction[J]. International Journal of Bio-Inspired Computation, 2016, 8(1): 33-41.
 Yang X S. Engineering Optimization: An Introduction with Metaheuristic Applications[M]. New York: John Wiley & Sons, 2010.
 Farahani S M, Abshouri A A, Nasiri B, et al. A Gaussian firefly algorithm[J]. International Journal of Machine Learning and Computing, 2011, 1(5): 448-453.
 Surafel L T, Hong C. Modified firefly algorithm[J]. J Appl Math, 2012, 39: 1-12.
 Fister I, Yang X S, Brest J, et al. Modified firefly algorithm using quaternion representation[J]. Expert Systems with Ap-plications, 2013, 40(18): 7220-7230.
 Poursalehi N, Zolfaghari A, Minuchehr A. Multi-objective loading pattern enhancement of PWR based on the discrete firefly algorithm[J]. Annals of Nuclear Energy, 2013, 57: 151-163.
 Sayadi M K, Hafezalkotob A, Naini S G J. Firefly-inspired algorithm for discrete optimization problems: An application to manufacturing cell formation[J]. Journal of Manufacturing Systems, 2013, 32(1): 78-84.
 Chandrasekaran K, Simon S P. Network and reliability con-strained unit commitment problem using binary real coded firefly algorithm[J]. International Journal of Electrical Power & Energy Systems, 2012, 43(1): 921-932.
 Marichelvam M K, Prabaharan T, Yang X S. A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems[J]. IEEE Transactions on Evolutionary Computation, 2014, 18(2): 301-305.
 Rahmani A, Mirhassani S A. A hybrid firefly-genetic algo-rithm for the capacitated facility location problem [J]. In-formation Sciences, 2014, 283: 70-78.
 Baykasoğlu A, Ozsoydan F B. An improved firefly algorithm for solving dynamic multidimensional knapsack problems [J]. Expert Systems with Applications, 2014, 41(8): 3712-3725.
 Xu M, Liu G. A multipopulation firefly algorithm for corre-lated data routing in underwater wireless sensor networks [J]. International Journal of Distributed Sensor Networks, 2013, 9(3): 865154.
 Hassanzadeh T, Kanan H R. Fuzzy FA: A modified firefly algorithm [J]. Applied Artificial Intelligence, 2014, 28(1): 47-65.
 Verma O P, Aggarwal D, Patodi T. Opposition and dimen-sional based modified firefly algorithm [J]. Expert Systems with Applications, 2016, 44: 168-176.
 Wang B, Li D X, Jiang J P, et al. A modified firefly algorithm based on light intensity difference [J]. Journal of Combinatorial Optimization, 2016, 31(3): 1045-1060.
 Wang H, Wang W, Zhou X, et al. Firefly algorithm with neighborhood attraction [J]. Information Sciences, 2017, 382: 374-387.
 Yao X, Liu Y, Lin G. Evolutionary programming made faster [J]. IEEE Transactions on Evolutionary computation, 1999, 3(2): 82-102.
 García S, Fernández A, Luengo J, et al. Advanced nonpara-metric tests for multiple comparisons in the design of ex-periments in computational intelligence and data mining: Experimental analysis of power [J]. Information Sciences, 2010, 180(10): 2044-2064.
 García S, Molina D, Lozano M, et al. A study on the use of non-parametric tests for analyzing the evolutionary algo-rithms’ behaviour: A case study on the CEC’2005 special session on real parameter optimization [J]. Journal of Heu-ristics, 2009, 15(6): 617-644.
 Alcalá-Fdez J, Sánchez L, Garcia S, et al. KEEL: A software tool to assess evolutionary algorithms for data mining prob-lems [J]. Soft Computing, 2009, 13(3): 307-318.