Abstract
In recent years, multi-modal optimization algorithms have attracted considerable attention, largely because many real-world problems have more than one solution. Multi-modal optimization algorithms are able to find multiple local/global optima (solutions), while unimodal optimization algorithms only find a single global optimum (solution) among the set of the solutions. Niche-based multi-modal optimization approaches have been widely used for solving multi-modal problems. These methods require a predefined niching parameter but estimating the proper value of the niching parameter is challenging without having prior knowledge of the problem space. In this paper, a novel multi-modal optimization algorithm is proposed by extending the unimodal bacterial foraging optimization algorithm. The proposed multi-odal bacterial foraging optimization (MBFO) scheme does not require any additional parameter, including the niching parameter, to be determined in advance. Furthermore, the complexity of this new algorithm is less than its unimodal form because the elimination-dispersal step is excluded, as is any other phase, like a clustering or local search algorithm. The algorithm is compared with six multi-modal optimization algorithms on nine commonly used multi-modal benchmark functions. The experimental results demonstrate that the MBFO algorithm is useful in solving multi-modal optimization problems and outperforms other methods.
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References
Barrera J, Coello CAC (2009) A particle swarm optimization method for multimodal optimization based on electrostatic interaction. In: Mexican international conference on artificial intelligence, Springer, pp 622–632
Bian Q, Nener B, Wang X (2019a) A modified bacterial-foraging tuning algorithm for multimodal optimization of the flight control system. Aerosp Sci Technol 93:105274. https://doi.org/10.1016/j.ast.2019.07.007
Bian Q, Nener B, Wang X (2019b) A quantum inspired genetic algorithm for multimodal optimization of wind disturbance alleviation flight control system. Chin J Aeronaut 32:2480–2488. https://doi.org/10.1016/j.cja.2019.04.013
Chen H, Zhang Q, Luo J, Xu Y, Zhang X (2020) An enhanced bacterial foraging optimization and its application for training kernel extreme learning machine. Appl Soft Comput 86:105884. https://doi.org/10.1016/j.asoc.2019.105884
Črepinšek M, Liu S-H, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45:35. https://doi.org/10.1145/2480741.2480752
De Jong KA (1975) Analysis of the behavior of a class of genetic adaptive systems. PhD Dissertation, University of Michigan, USA
Gálvez J, Cuevas E, Avalos O, Oliva D, Hinojosa S (2018) Electromagnetism-like mechanism with collective animal behavior for multimodal optimization. Appl Intell 48:2580–2612
Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multimodal function optimization. In: Genetic algorithms and their applications: proceedings of the second international conference on genetic algorithms, Lawrence Erlbaum, Hillsdale, NJ, pp 41–49
Goldberg DE, Wang L (1997) Adaptive niching via coevolutionary sharing. In: Genetic algorithms and evolution strategy in engineering and computer science, vol 97007, pp 21–38
Jorge G, Erik C, Omar A (2017) Flower pollination algorithm for multimodal optimization. Int J Comput Intell Syst 10:627–646. https://doi.org/10.2991/ijcis.2017.10.1.42
Jun Y, Takagi H, Ying T (2019) Fireworks algorithm for multimodal optimization using a distance-based exclusive strategy. In: 2019 IEEE congress on evolutionary computation (CEC), IEEE, pp 2215–2220
Kim DH, Cho JH (2005) Adaptive tuning of PID controller for multivariable system using bacterial foraging based optimization. In: International atlantic web intelligence conference, Springer, pp 231–235
Li X (2007) A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio. In: Proceedings of the 9th annual conference on genetic and evolutionary computation, pp 78–85
Li X (2009) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14:150–169
Li JP, Wood AS (2009) An adaptive species conservation genetic algorithm for multimodal optimization. Int J Numer Methods Eng 79:1633–1661
Li J-P, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evol Comput 10:207–234
Li M, Tang W, Tang W, Wu Q, Saunders J (2007) Bacterial foraging algorithm with varying population for optimal power flow. In: Workshops on applications of evolutionary computation, Springer, pp 32–41
Li M, Lin D, Kou J (2012) A hybrid niching PSO enhanced with recombination-replacement crowding strategy for multimodal function optimization. Appl Soft Comput 12:975–987
Li X, Engelbrecht A, Epitropakis MG (2013) Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimization. RMIT University, Evolutionary Computation and Machine Learning Group, Australia, Tech Rep
Liang J, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CC, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. J Appl Mech 41:8–31
Lin C-Y, Wu W-H (2002) Niche identification techniques in multimodal genetic search with sharing scheme. Adv Eng Softw 33:779–791
Liu Q, Du S, van Wyk BJ, Sun Y (2019) Niching particle swarm optimization based on Euclidean distance and hierarchical clustering for multimodal optimization. Nonlinear Dyn. https://doi.org/10.1007/s11071-019-05414-7
Mahfoud SW (1992) Crowding and preselection revisited. In: PPSN, pp 27–36
Miller BL, Shaw MJ (1996) Genetic algorithms with dynamic niche sharing for multimodal function optimization. In: Proceedings of IEEE international conference on evolutionary computation, IEEE, pp 786–791
Orujpour M, Feizi-Derakhshi M-R, Rahkar-Farshi T (2019) Multi-modal forest optimization algorithm. Neural Comput Appl 32:6159–6173. https://doi.org/10.1007/s00521-019-04113-z
Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22:52–67. https://doi.org/10.1109/MCS.2002.1004010
Pétrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation, IEEE, pp 798–803
Qu B-Y, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inf Sci 197:131–143
Rahkar Farshi T (2020) Battle royale optimization algorithm. Neural Comput App. https://doi.org/10.1007/s00521-020-05004-4
Rahkar-Farshi T, Behjat-Jamal S (2016) A multimodal firefly optimization algorithm based on Coulomb’s law. Int J Adv Comput Sci Appl 7:134–141
Rahkar-Farshi T, Kesemen O, Behjat-Jamal S (2014) Multi hyperbole detection on images using modified artificial bee colony (ABC) for multimodal function optimization. In: 22nd signal processing and communications applications conference (SIU). IEEE, pp 894–898. https://doi.org/10.1109/SIU.2014.6830374
Rahkar Farshi T, Drake JH, Özcan E (2020) A multimodal particle swarm optimization-based approach for image segmentation. Expert Syst Appl 149:113233. https://doi.org/10.1016/j.eswa.2020.113233
Sacco WF, Henderson N, Rios-Coelho AC (2014) Topographical clearing differential evolution: a new method to solve multimodal optimization problems. Prog Nucl Energy 71:269–278
Sareni B, Krahenbuhl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2:97–106
Sathya PD, Kayalvizhi R (2011) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl 38:15549–15564. https://doi.org/10.1016/j.eswa.2011.06.004
Shir OM, Emmerich M, Bäck T (2010) Adaptive niche radii and niche shapes approaches for niching with the CMA-ES. Evol Comput 18:97–126
Streichert F, Stein G, Ulmer H, Zell A (2003) A clustering based niching ea for multimodal search spaces. In: International conference on artificial evolution (evolution artificielle), Springer, pp 293–304
Tang K, Xiao X, Wu J, Yang J, Luo L (2017) An improved multilevel thresholding approach based modified bacterial foraging optimization. Appl Intell 46:214–226
Wang X, Sheng M, Ye K, Lin J, Mao J, Chen S, Sheng W (2019) A multilevel sampling strategy based memetic differential evolution for multimodal optimization. Neurocomputing 334:79–88
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893
Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14
Yin X, Germay N (1993) A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization. In: Artificial neural nets and genetic algorithms, Springer, pp 450–457
Yu E, Suganthan PN (2010) Ensemble of niching algorithms. Inf Sci 180:2815–2833
Zhang Q, Wang R, Yang J, Ding K, Li Y, Hu J (2017) Collective decision optimization algorithm: a new heuristic optimization method. Neurocomputing 221:123–137. https://doi.org/10.1016/j.neucom.2016.09.068
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Rahkar Farshi, T., Orujpour, M. A multi-modal bacterial foraging optimization algorithm. J Ambient Intell Human Comput 12, 10035–10049 (2021). https://doi.org/10.1007/s12652-020-02755-9
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DOI: https://doi.org/10.1007/s12652-020-02755-9