Skip to main content
SpringerLink
Log in

A memetic animal migration optimizer for multimodal optimization

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

Unimodal optimization algorithms can find only one global optimum solution, while multimodal ones have the ability to detect all/most existing local/global optima in the problem space. Many practical scientific and engineering optimization problems have multiple optima to be located. There are a considerable number of optimization approaches in the literature to address the unimodal problems. Although multimodal optimization methods have not been studied as much as the unimodal ones, they have attracted an enormous amount of attention recently. However, most of them suffer from a common niching parameter problem. The main difficulty faced by existing approaches is determining the proper niching radius. Determining the appropriate radius of the niche requires prior knowledge of the problem space. This paper proposes a novel multimodal optimization scheme that does not face the dilemma of having prior knowledge of the problem space as it does not require the niching parameter to be determined in advance. This scheme is the extended version of the unimodal animal migration optimization (AMO) algorithm that has the capability of taking advantage of finding multiple solutions. Like other multimodal optimization approaches, the proposed MAMO requires specific modifications to make it possible to locate multiple optima. The local neighborhood policy is modified to adapt the multimodal search by utilizing Coulomb's law. Also, Coulomb's law is also applied to decide the movement direction of the individuals. Hence, instead of moving an individual toward the two randomly chosen individuals, it moves toward the near and good enough two neighborhoods. Additionally, a further local search step is performed to improve the exploitation. To investigate the performance of the MAMO, the comparisons are conducted with five existing multi-modal optimization algorithms on nine benchmarks of the CEC 2013 competition. The experimental results reveal that the MAMO performs success in locating all or most of the local/global optima and outperforms other compared methods. Note that the source codes of the proposed MAMO algorithm are publicly available at www.taymaz.dev.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Abed-alguni BH (2019) Island-based cuckoo search with highly disruptive polynomial mutation. Int J Artif Intell 17:57–82

    Google Scholar 

  • Alami J, Imrani AE, Bouroumi A (2007) A multipopulation cultural algorithm using fuzzy clustering. Appl Soft Comput 7:506–519. https://doi.org/10.1016/j.asoc.2006.10.010

    Article  Google Scholar 

  • Barrera J, Coello CAC (2009a) A particle swarm optimization method for multimodal optimization based on electrostatic interaction. In: MICAI. Springer, pp 622–632

  • Barrera J, Coello CAC (2009b) A particle swarm optimization method for multimodal optimization based on electrostatic interaction. In: Mexican international conference on artificial intelligence. Springer, pp 622–632

  • Cioppa AD, Stefano CD, Marcelli A (2007) Where are the niches? Dynamic fitness sharing. IEEE Trans Evolut Comput 11:453–465. https://doi.org/10.1109/TEVC.2006.882433

    Article  Google Scholar 

  • De Jong KA (1975) Analysis of the behavior of a class of genetic adaptive systems. University of Michigan, Ann Arbor

    Google Scholar 

  • El Imrani A, Bouroumi A, El Abidine HZ, Limouri M, Essaı̈d A (2000) A fuzzy clustering-based niching approach to multimodal function optimization. Cogn Syst Res 1:119–133. https://doi.org/10.1016/S1389-0417(99)00013-3

    Article  Google Scholar 

  • Engelbrecht AP (2006) Fundamentals of computational swarm intelligence. Wiley, New York

    Google Scholar 

  • Farshi TR, 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

    Article  Google Scholar 

  • Gan J, Warwick K (2001) Dynamic Niche clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No.01TH8546), 27–30 May 2001, vol 211, pp 215–222. https://doi.org/10.1109/CEC.2001.934392

  • 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, pp 41–49

  • Goldberg DE, Wang L (1997) Adaptive niching via coevolutionary sharing. Genet Algorithms Evolut Strategy Eng Comput Sci 97007:21–38

    Google Scholar 

  • Gu X, Angelov P, Rong H-J (2019) Local optimality of self-organising neuro-fuzzy inference systems. Inf Sci 503:351–380

    Article  Google Scholar 

  • Jha K, Saha S (2021) Incorporation of multimodal multiobjective optimization in designing a filter based feature selection technique. Appl Soft Comput 98:106823. https://doi.org/10.1016/j.asoc.2020.106823

    Article  Google Scholar 

  • Kamyab S, Eftekhari M (2016) Feature selection using multimodal optimization techniques. Neurocomputing 171:586–597. https://doi.org/10.1016/j.neucom.2015.06.068

    Article  Google Scholar 

  • Lazar A, Reynolds R (2003) Heuristic knowledge discovery for archaeological data using cultural algorithms and rough sets. Citeseer

  • 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 (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14:150–169

    Article  Google Scholar 

  • Li J-P, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evolut Comput 10:207–234

    Article  Google Scholar 

  • 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

  • Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24:1867–1877. https://doi.org/10.1007/s00521-013-1433-8

    Article  Google Scholar 

  • Li Y, Chen Y, Zhong J, Huang Z (2019) Niching particle swarm optimization with equilibrium factor for multi-modal optimization. Inf Sci 494:233–246. https://doi.org/10.1016/j.ins.2019.01.084

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Liu X, Liu H, Duan H (2007) Particle swarm optimization based on dynamic niche technology with applications to conceptual design. Adv Eng Softw 38:668–676. https://doi.org/10.1016/j.advengsoft.2006.10.009

    Article  Google Scholar 

  • 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 1–19

  • Miller BL, Shaw MJ (1996) Genetic algorithms with dynamic niche sharing for multimodal function optimization. Proc IEEE Int Conf Evolut Comput 20–22(1996):786–791. https://doi.org/10.1109/ICEC.1996.542701

    Article  Google Scholar 

  • Orujpour M, Feizi-Derakhshi M-R, Rahkar-Farshi T (2019) Multi-modal forest optimization algorithm. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04113-z

    Article  Google Scholar 

  • Petrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation, 20–22 May 1996, pp 798–803. https://doi.org/10.1109/ICEC.1996.542703

  • Precup R-E, David R-C (2019) Nature-inspired optimization algorithms for fuzzy controlled servo systems. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Precup R-E, David R-C, Petriu EM, Szedlak-Stinean A-I, Bojan-Dragos C-A (2016) Grey wolf optimizer-based approach to the tuning of pi-fuzzy controllers with a reduced process parametric sensitivity. IFAC-PapersOnLine 49:55–60

    Article  Google Scholar 

  • Qu B-Y, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inf Sci 197:131–143

    Article  Google Scholar 

  • Qu BY, Suganthan PN, Liang JJ (2012) Differential evolution with neighborhood mutation for multimodal optimization. IEEE Trans Evol Comput 16:601–614. https://doi.org/10.1109/TEVC.2011.2161873

    Article  Google Scholar 

  • Rahkar Farshi T, Demirci R (2021) Multilevel image thresholding with multimodal optimization. Multimed Tools Appl. https://doi.org/10.1007/s11042-020-10432-4

    Article  Google Scholar 

  • Rahkar Farshi T, Orujpour M (2021) A multi-modal bacterial foraging optimization algorithm. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02755-9

    Article  Google Scholar 

  • Rahkar Farshi T (2020) Battle royale optimization algorithm. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05004-4

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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: Proceedings of the 22nd Signal Processing and Communications Applications Conference (SIU), Trabzon, 2014, pp 894–898. https://doi.org/10.1109/SIU.2014.6830374

  • Rim C, Piao S, Li G, Pak U (2018) A niching chaos optimization algorithm for multimodal optimization. Soft Comput 22:621–633

    Article  Google Scholar 

  • 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. https://doi.org/10.1016/j.pnucene.2013.12.011

    Article  Google Scholar 

  • Sareni B, Krahenbuhl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2:97–106. https://doi.org/10.1109/4235.735432

    Article  Google Scholar 

  • Shir OM, Emmerich M, Bäck T (2010) Adaptive Niche Radii and Niche Shapes Approaches for Niching with the CMA-ES. Evolut Comput 18:97–126. https://doi.org/10.1162/evco.2010.18.1.18104

    Article  Google Scholar 

  • Stoean C, Preuss M, Stoean R, Dumitrescu D (2010) Multimodal optimization by means of a topological species conservation algorithm. IEEE Trans Evol Comput 14:842–864

    Article  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization KanGAL report 2005005

  • 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

    Article  Google Scholar 

  • Wong K-C, Leung K-S, Wong M-H (2010) Protein structure prediction on a lattice model via multimodal optimization techniques. In: Proceedings of the 12th annual conference on genetic and evolutionary computation, pp 155–162

  • Woo D, Choi J, Ali M, Jung H (2011) A novel multimodal optimization algorithm applied to electromagnetic optimization. IEEE Trans Magn 47:1667–1673. https://doi.org/10.1109/TMAG.2011.2106218

    Article  Google Scholar 

  • Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evolut Comput 14:1–14

    Article  Google Scholar 

  • 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

  • Yue CT, Liang JJ, Qu BY, Yu KJ, Song H (2019) Multimodal multiobjective optimization in feature selection. In: 2019 IEEE congress on evolutionary computation (CEC), 10–13 June 2019, pp 302–309.:https://doi.org/10.1109/CEC.2019.8790329

  • Zapata H, Perozo N, Angulo W, Contreras J (2020) A hybrid swarm algorithm for collective construction of 3D structures

  • Zhang J, Huang D-S, Lok T-M, Lyu MR (2006) A novel adaptive sequential niche technique for multimodal function optimization. Neurocomputing 69:2396–2401. https://doi.org/10.1016/j.neucom.2006.02.016

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Zou J, Deng Q, Zheng J, Yang S (2020) A close neighbor mobility method using particle swarm optimizer for solving multimodal optimization problems. Inf Sci 519:332–347. https://doi.org/10.1016/j.ins.2020.01.049

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Software Engineering Department, Ayvansaray University, Istanbul, Turkey

    Taymaz Rahkar Farshi

Authors
  1. Taymaz Rahkar Farshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Taymaz Rahkar Farshi.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Farshi, T.R. A memetic animal migration optimizer for multimodal optimization. Evolving Systems 13, 133–144 (2022). https://doi.org/10.1007/s12530-021-09368-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-021-09368-3

Keywords

Search

Navigation