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Soft Computing

, Volume 23, Issue 24, pp 13339–13349 | Cite as

Distributed minimum spanning tree differential evolution for multimodal optimization problems

  • Zi-Jia Wang
  • Zhi-Hui ZhanEmail author
  • Jun Zhang
Methodologies and Application
  • 131 Downloads

Abstract

Multimodal optimization problem (MMOP) requires to find optima as many as possible for a single problem. Recently, many niching techniques have been proposed to tackle MMOPs. However, most of the niching techniques are either sensitive to the niching parameters or causing a waste of fitness evaluations. In this paper, we proposed a novel niching technique based on minimum spanning tree (MST) and applied it into differential evolution (DE), termed as MSTDE, to solve MMOPs. In every generation, an MST is built based on the distance information among the individuals. After that, we cut the M largest weighted edges of the MST to form some subtrees, so-called subpopulations. The DE operators are executed within the subpopulations. Besides, a dynamic pruning ratio (DPR) strategy is proposed to determine M with an attempt to reduce its sensitivity, so as to enhance the niching performance. Meanwhile, the DPR strategy can achieve a good balance between diversity and convergence. Besides, taking the advantage of fast availability in time from virtual machines (VMs), a distributed model is applied in MSTDE, where different subpopulations run concurrently on distributed VMs. Experiments have been conducted on the CEC2013 multimodal benchmark functions to test the performance of MSTDE, and the experimental results show that MSTDE can outperform many existed multimodal optimization algorithms.

Keywords

Differential evolution Minimum spanning tree Multimodal optimization problems Distributed model 

Notes

Acknowledgements

This work was partially supported by the Outstanding Youth Science Foundation with No. 61822602, the National Natural Science Foundations of China (NSFC) with Nos. 61772207 and 61332002, the Natural Science Foundations of Guangdong Province for Distinguished Young Scholars with No. 2014A030306038, the Project for Pearl River New Star in Science and Technology with No. 201506010047, the GDUPS (2016), and the Fundamental Research Funds for the Central Universities.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Agrawal S, Silakari S (2014) FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization. Soft Comput 18(11):2227–2243CrossRefGoogle Scholar
  2. Ahrari A, Deb K, Preuss M (2017) Multimodal optimization by covariance matrix self-adaptation evolution strategy with repelling subpopulations. Evol Comput 25(3):439–471CrossRefGoogle Scholar
  3. Arellano-Verdejo J, Alba E, Godoy-Calderon S (2016) Efficiently finding the optimum number of clusters in a dataset with a new hybrid differential evolution algorithm: DELA. Soft Comput 20(3):895–905CrossRefGoogle Scholar
  4. Arora P, Bhargava S, Srivastava S, Hanmandlu M (2017) Multimodal biometric system based on information set theory and refined scores. Soft Comput 21(17):5133–5144CrossRefGoogle Scholar
  5. Biswas S, Kundu S, Das S (2014) An improved parent-centric mutation with normalized neighborhoods for inducing niching behavior in differential evolution. IEEE Trans Cybern 44(10):1726–1737CrossRefGoogle Scholar
  6. Biswas S, Kundu S, Das S (2015) Inducing niching behavior in differential evolution through local information sharing. IEEE Trans Evol Comput 19(2):246–263CrossRefGoogle Scholar
  7. Chen CH, Yang SY (2013) A knowledge-based cooperative differential evolution for neural fuzzy inference systems. Soft Comput 17(5):883–895CrossRefGoogle Scholar
  8. Chen N, Chen WN, Gong YJ, Zhan ZH, Zhang J, Li Y, Tan YS (2015) An evolutionary algorithm with double-level archives for multiobjective optimization. IEEE Trans Cybern 45(9):1851–1863CrossRefGoogle Scholar
  9. Cuevas E, González M (2013) An optimization algorithm for multimodal functions inspired by collective animal behavior. Soft Comput 17(3):489–502CrossRefGoogle Scholar
  10. Cuevas E, González M, Zaldívar D, Pérez-Cisneros M (2014) Multi-ellipses detection on images inspired by collective animal behavior. Neural Comput Appl 24(5):1019–1033CrossRefGoogle Scholar
  11. Datta D, Figueira JR (2011) Graph partitioning by multi-objective real-valued metaheuristics: a comparative study. Appl Soft Comput 11(5):3976–3987CrossRefGoogle Scholar
  12. Derrac J, Garcıa S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18CrossRefGoogle Scholar
  13. Dick G, Whigham PA (2011) Weighted local sharing and local clearing for multimodal optimization. Soft Comput 15(9):1707–1721CrossRefGoogle Scholar
  14. Gao W, Yen GG, Liu S (2014) A cluster-based differential evolution with self-adaptive strategy for multimodal optimization. IEEE Trans Cybern 44(8):1314–1327CrossRefGoogle Scholar
  15. Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the international conference on genetic algorithms, Cambridge, pp 41–49Google Scholar
  16. Hui S, Suganthan PN (2016) Ensemble and arithmetic recombination-based speciation differential evolution for multimodal optimization. IEEE Trans Cybern 46(1):64–74CrossRefGoogle Scholar
  17. Jeyakumar G, Velayutham CS (2014) Distributed heterogeneous mixing of differential and dynamic differential evolution variants for unconstrained global optimization. Soft Comput 18(10):1949–1965CrossRefGoogle Scholar
  18. Li X (2005) Efficient differential evolution using speciation for multimodal function optimization. In: Proceeding of the conference on genetic and evolutionary computation, Washington, DC, pp 873–880Google Scholar
  19. Li X, Engelbrecht A, Epitropakis MG (2013) Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimization. Evol Comput Mach Learn Group RMIT University, Melbourne, Technical report (Online). http://goanna.cs.rmit.edu.au/~xiaodong/cec13-lsgo/competition/
  20. Li YL, Zhan ZH, Gong YJ, Chen WN, Zhang J, Li Y (2015) Differential evolution with an evolution path: a DEEP evolutionary algorithm. IEEE Trans Cybern 45(9):1798–1810CrossRefGoogle Scholar
  21. Lin Y, Jiang YS, Gong YJ, Zhan ZH, Zhang J (2018) A discrete multiobjective particle swarm optimizer for automated assembly of parallel cognitive diagnosis tests. IEEE Trans Cybern.  https://doi.org/10.1109/tcyb.2018.2836388 CrossRefGoogle Scholar
  22. Liu XF, Zhan ZH, Zhang J (2018a) Neural network for change direction prediction in dynamic optimization. IEEE Access 6:72649–72662CrossRefGoogle Scholar
  23. Liu XF, Zhan ZH, Gao Y, Zhang J, Kwong S, Zhang J (2018b) Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization. IEEE Trans Evol Comput.  https://doi.org/10.1109/tevc.2018.2875430 CrossRefGoogle Scholar
  24. Liu XF, Zhan ZH, Lin Y, Chen WN, Gong YJ, Gu TL, Yuan HQ, Zhang J (2018c) Historical and heuristic based adaptive differential evolution. IEEE Trans Syst Man Cybern Syst.  https://doi.org/10.1109/tsmc.2018.2855155 CrossRefGoogle Scholar
  25. Preuss M (2010) Niching the CMA-ES via nearest-better clustering. In: Proceeding of the genetic and evolutionary computation, pp 1711–1718Google Scholar
  26. Preuss M (2012) Improved topological niching for real-valued global optimization. In: Proceeding of the European conference on the applications of evolutionary computation, pp 386–395Google Scholar
  27. Qu BY, Suganthan PN, Liang JJ (2012) Differential evolution with neighborhood mutation for multimodal optimization. IEEE Trans Evol Comput 16(5):601–614CrossRefGoogle Scholar
  28. Qu BY, Suganthan PN, Das S (2013) A distance-based locally informed particle swarm model for multimodal optimization. IEEE Trans Evol Comput 17(3):387–402CrossRefGoogle Scholar
  29. Rim C, Piao S, Li G, Pak U (2018) A niching chaos optimization algorithm for multimodal optimization. Soft Comput 22(2):621–633CrossRefGoogle Scholar
  30. Rönkkönen J, Li X, Kyrki V, Lampinen J (2011) A framework for generating tunable test functions for multimodal optimization. Soft Comput 15(9):1689–1706CrossRefGoogle Scholar
  31. Sharifi-Noghabi H, Mashhadi HR, Shojaee K (2017) A novel mutation operator based on the union of fitness and design spaces information for differential evolution. Soft Comput 21(22):6555–6562CrossRefGoogle Scholar
  32. Son NN, Anh HPH, Chau TD (2018) Adaptive neural model optimized by modified differential evolution for identifying 5-DOF robot manipulator dynamic system. Soft Comput 22(3):979–988CrossRefGoogle Scholar
  33. Thomsen R (2004) Multimodal optimization using crowding-based differential evolution. In: Proceeding of the IEEE congress on evolutionary computation, vol 2. Portland, pp 1382–1389Google Scholar
  34. Ursem RK (1999) Multinational evolutionary algorithms. In: Proceeding of the IEEE congress on evolutionary computation, pp 1633–1640Google Scholar
  35. Wang Y, Li HX, Yen GG, Song W (2014) MOMMOP: multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems. IEEE Trans Cybern 45(4):830–843CrossRefGoogle Scholar
  36. Wang ZJ, Zhan ZH, Zhang J (2015) An improved method for comprehensive learning particle swarm optimization. In: Proceeding of the IEEE symposium series on computational intelligence, pp 218–225Google Scholar
  37. Wang ZJ, Zhan ZH, Zhang J (2016a) Orthogonal learning particle swarm optimization with variable relocation for dynamic optimization. In: Proceeding of the IEEE congress on evolutionary computation, pp 594–600Google Scholar
  38. Wang ZJ, Zhan ZH, Zhang J (2016b) Parallel multi-strategy evolutionary algorithm using message passing interface for many-objective optimization. In: Proceeding of the IEEE symposium series on computational intelligence, pp 1–8Google Scholar
  39. Wang ZJ, Zhan ZH, Lin Y, Yu WJ, Yuan HQ, Gu TL, Kwong S, Zhang J (2018) Dual-strategy differential evolution with affinity propagation clustering for multimodal optimization problems. IEEE Trans Evol Comput 22(6):894–908CrossRefGoogle Scholar
  40. Weber M, Tirronen V, Neri F (2010) Scale factor inheritance mechanism in distributed differential evolution. Soft Comput 14(11):1187–1207CrossRefGoogle Scholar
  41. Wong KC, Leung KS, Wong MH (2010) Protein structure prediction on a lattice model via multimodal optimization techniques. In: Proceedings conference on genetic and evolutionary computation, Portland, pp 155–162Google Scholar
  42. Woo DK, Choi JH, Ali M, Jung HK (2011) A novel multimodal optimization algorithm applied to electromagnetic optimization. IEEE Trans Magn 47(6):1667–1673CrossRefGoogle Scholar
  43. Yang Q, Chen WN, Li Y, Chen CLP, Hu XM, Zhang J (2017) Multimodal estimation of distribution algorithms. IEEE Trans Cybern 47(3):636–650CrossRefGoogle Scholar
  44. Zhan ZH, Liu XF, Gong YJ, Zhang J, Chung HSH, Li Y (2015) Cloud computing resource scheduling and a survey of its evolutionary approaches. ACM Comput Surv 47(4):1–33 (Article 63) CrossRefGoogle Scholar
  45. Zhan ZH, Liu X, Zhang H, Yu Z, Weng J, Li Y, Gu T, Zhang J (2017) Cloudde: a heterogeneous differential evolution algorithm and its distributed cloud version. IEEE Trans Parallel Distrib Syst 28(3):704–716CrossRefGoogle Scholar
  46. Zhang X, Zhang X (2017) Improving differential evolution by differential vector archive and hybrid repair method for global optimization. Soft Comput 21(23):7107–7116CrossRefGoogle Scholar
  47. Zhang YH, Gong YJ, Zhang HX, Gu TL, Zhang J (2017) Toward fast niching evolutionary algorithms: a locality sensitive hashing-based approach. IEEE Trans Evol Comput 21(3):347–362Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Data and Computer ScienceSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Computer Science and EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China
  3. 3.Guangdong Provincial Key Lab of Computational Intelligence and Cyberspace InformationGuangzhouPeople’s Republic of China

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