Abstract
Approximation methods are employed to remedy the significant computational time required by exact methods. They provide an approximate solution, close to the optimum, for complex problems (NP-hard problems). The performance guarantees of these methods vary depending on the chosen parameter values. However, selecting parameter values that yield good performance is a challenging task. Since the 1950s, Genichi Taguchi, a Japanese engineer, has developed robust design techniques to improve the quality of manufactured goods. Recently, these techniques have found applications in various domains, including engineering and biotechnology. In this paper, we investigate the application of the Taguchi design for the first time to simplify the process of selecting suitable parameter values for Elephant Herding Optimization (EHO) variants. These later are recent and known by their simplicity and ease implementation. A study case of using EHO variants is the segmentation of Brain Magnetic Resonance (MR) images using Hidden Markov Random Fields (HMRF) to help physician get the right decision. HMRF is a powerful model widely used for segmenting brain MR images which can be formulated as a problem of minimization an objective function. Subsequently, we compare the obtained results with those of well-known brain images’ segmentation tools such as FSL (the Functional Magnetic Resonance Imaging of the Brain Software Library) to demonstrate the usefulness of the Taguchi design. The quality of the segmentation is measured and tested using the Dice coefficient criterion and established on BrainWeb and IBSR images. Our findings indicate that the Taguchi design is effective, and Sine Cosine EHO (SCEHO) and Enhanced EHO (EEHO) methods yield excellent results based on the conducted tests.
Similar content being viewed by others
Data availability
The BrainWeb and IBSR images are available at the following links: BrainWeb: https://brainweb.bic.mni.mcgill.ca/brainweb/, IBSR: https://www.nitrc.org/projects/ibsr.
References
Marti R, Reinelt G. Exact and heuristic methods in combinatorial optimization, vol 175. Springer; 2022.
Hochba DS. Approximation algorithms for np-hard problems. ACM SIGACT News. 1997;28(2):40–52.
Williamson DP, Shmoys DB. The design of approximation algorithms. Cambridge University Press; 2011.
Taguchi G. Introduction to quality engineering. American Supplier Institute; 1989.
Taguchi G, Chowdhury S, Wu Y. Taguchi’s quality engineering handbook. New York: Wiley; 2004.
Zhang JZ, Chen JC, Kirby ED. Surface roughness optimization in an end-milling operation using the Taguchi design method. J Mater Process Technol. 2007;184(1–3):233–9.
Sarıkaya M, Güllü A. Taguchi design and response surface methodology based analysis of machining parameters in cnc turning under mql. J Clean Prod. 2014;65:604–16.
Qattawi A, et al. Investigating the effect of fused deposition modeling processing parameters using Taguchi design of experiment method. J Manuf Process. 2018;36:164–74.
Karmakar B, Dhawane SH, Halder G. Optimization of biodiesel production from castor oil by Taguchi design. J Environ Chem Eng. 2018;6(2):2684–95.
Moralı U, Demiral H, Şensöz S. Optimization of activated carbon production from sunflower seed extracted meal: Taguchi design of experiment approach and analysis of variance. J Clean Prod. 2018;189:602–11.
Wang GG, Deb S, Coelho LdS. Elephant herding optimization, 1–5 (IEEE, 2015).
Ismaeel AA, Elshaarawy IA, Houssein EH, Ismail FH, Hassanien AE. Enhanced elephant herding optimization for global optimization. IEEE Access. 2019;7:34738–52. https://doi.org/10.1109/ACCESS.2019.2904679.
Li W, Wang GG, Alavi AH. Learning-based elephant herding optimization algorithm for solving numerical optimization problems. Knowl-Based Syst. 2020;195: 105675. https://doi.org/10.1016/j.knosys.2020.105675.
Singh H, Singh B, Kaur M. An improved elephant herding optimization for global optimization problems. London: Springer; 2021. (0123456789).
Singh P, Meena NK, Bishnoi SK, Singh B, Bhadu M. Hybrid elephant herding and particle swarm optimizations for optimal dg integration in distribution networks. Electric Power Components Syst. 2020;48(6–7):727–41. https://doi.org/10.1080/15325008.2020.1797931.
Sambariya D. K., Fagna R. A novel elephant herding optimization based pid controller design for load frequency control in power system. In: 2017 International Conference on Computer, Communications and Electronics, COMPTELIX 2017, 2017; p. 595–600. https://doi.org/10.1109/COMPTELIX.2017.8004039.
Guerrout E-H, Ait-Aoudia S, Michelucci D, Mahiou R. Hidden Markov random field model and Broyden-Fletcher-Goldfarb-Shanno algorithm for brain image segmentation. J Exp Theoret Artif Intell. 2018;30(3):415–27.
Guerrout E-H, Ait-Aoudia S, Michelucci D, Mahiou R. Conjugate gradient method for brain magnetic resonance images segmentation. Springer; 2018. p. 561–72.
Guerrout E, Mahiou R, Ait-Aoudia S. Hidden Markov random fields and particle swarm combination for brain image segmentation. Int Arab J Inf Technol. 2018;15(3):462–8.
Dice LR. Measures of the amount of ecologic association between species. Ecology. 1945;26(3):297–302.
Norton BJ, Strube MJ. Guide for the interpretation of two-way analysis of variance. Phys Ther. 1986;66(3):402–12.
Rao S, Samant P, Kadampatta A, Shenoy R. An overview of Taguchi method: evolution, concept and interdisciplinary applications. Int J Sci Eng Res. 2013;4(10):621–6.
Li J, Lei H, Alavi AH, Wang GG. Elephant herding optimization: variants, hybrids, and applications. Mathematics. 2020. https://doi.org/10.3390/MATH8091415.
Mirjalili S. Sca: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst. 2016;96:120–33. https://doi.org/10.1016/j.knosys.2015.12.022.
Tizhoosh HR. Opposition-based learning: a new scheme for machine intelligence. In: Proceedings -International Conference on computational intelligence for modelling, control and automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet. 2005;1: 695–701. https://doi.org/10.1109/cimca.2005.1631345 .
Lee CY, Yao X. Evolutionary algorithms with adaptive lévy mutations. In: Proceedings of the IEEE Conference on Evolutionary Computation, ICEC. 2001;1:568–75. https://doi.org/10.1109/cec.2001.934442.
Ait-Aoudia S, Mahiou R, Guerrout E. Evaluation of volumetric medical images segmentation using hidden Markov random field model, pp. 513–518, IEEE, 2011.
Guerrout E.-H, Mahiou R, Michelucci D, Randa B, Assia, O. Hidden markov random fields and cuckoo search method for medical image segmentation 2–6. 2020. arXiv:2005.09377 .
Boyd S, Vandenberghe L. Convex optimization. Cambridge University Press; 2004.
Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell. 1984;6:721–41.
Boykov Y, Veksler O, Zabih R. Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell. 2001;23(11):1222–39.
Dice LR. Measures of the Amount of Ecologic Association Between Species Author ( s ): Lee R . Dice Published by: Ecological Society of America Stable. Ecology. 1945;26(3): 297–302. http://www.jstor.org/stable/1932409.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the topical collection “Recent Trends on AI for Health Care” guest edited by Lydia Bouzar-Benlabiod.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Mahiou, R., Guerrout, EH. & Sannef, M.E. Taguchi Design for Setting EHO Variants Parameters: Application in Brain Image Segmentation Using HMRF. SN COMPUT. SCI. 4, 794 (2023). https://doi.org/10.1007/s42979-023-02197-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s42979-023-02197-y