{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:21:06Z","timestamp":1777447266322,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Greek Ministry of National Education and Religious Affairs","award":["MIS 375233"],"award-info":[{"award-number":["MIS 375233"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>One of the most challenging problems that are still open in the field of materials science is the 3D reconstruction of porous media using information from a single 2D thin image of the original material. Such a reconstruction is only feasible subject to some important assumptions that need to be made as far as the statistical properties of the material are concerned. In this study, the aforementioned problem is investigated as an explicitly formulated optimization problem, with the phase of each porous material point being decided such that the resulting 3D material model shows the same statistical properties as its corresponding 2D version. Based on this problem formulation, herein for the first time, several traditional (genetic algorithms\u2014GAs, particle swarm optimization\u2014PSO, differential evolution\u2014DE), as well as recently proposed (firefly algorithm\u2014FA, artificial bee colony\u2014ABC, gravitational search algorithm\u2014GSA) nature-inspired optimization algorithms were applied to solve the 3D reconstruction problem. These algorithms utilized a newly proposed data representation scheme that decreased the number of unknowns searched by the optimization process. The advantages of addressing the 3D reconstruction of porous media through the application of a parallel heuristic optimization algorithm were clearly defined, while appropriate experiments demonstrating the greater performance of the GA algorithm in almost all the cases by a factor between 5%\u201384% (porosity accuracy) and 3%\u201315% (auto-correlation function accuracy) over the PSO, DE, FA, ABC, and GSA algorithms were undertaken. Moreover, this study revealed that statistical functions of a high order need to be incorporated into the reconstruction procedure to increase the reconstruction accuracy.<\/jats:p>","DOI":"10.3390\/a13030065","type":"journal-article","created":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T09:27:41Z","timestamp":1584437261000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Nature-Inspired Optimization Algorithms for the 3D Reconstruction of Porous Media"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5545-1499","authenticated-orcid":false,"given":"George","family":"Papakostas","sequence":"first","affiliation":[{"name":"HUMAIN-Lab, Department of Computer Science, International Hellenic University, GR-654 04 Kavala, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Nolan","sequence":"additional","affiliation":[{"name":"Hephaestus Advanced Laboratory, Department of Chemistry, International Hellenic University, GR-654 04 Kavala, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Athanasios","family":"Mitropoulos","sequence":"additional","affiliation":[{"name":"Hephaestus Advanced Laboratory, Department of Chemistry, International Hellenic University, GR-654 04 Kavala, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Guo, Y., Zhang, L., Zhu, G., Yao, J., Sun, H., Song, W., Yang, Y., and Zhao, J. (2019). A Pore-Scale Investigation of Residual Oil Distributions and Enhanced Oil Recovery Methods. Energies, 12.","DOI":"10.3390\/en12193732"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Poonoosamy, J., Haber-Pohlmeier, S., Deng, H., Deissmann, G., Klinkenberg, M., Gizatullin, B., Stapf, S., Brandt, F., Bosbach, D., and Pohlmeier, A. (2020). Combination of MRI and SEM to Assess Changes in the Chemical Properties and Permeability of Porous Media due to Barite Precipitation. Minerals, 10.","DOI":"10.3390\/min10030226"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Duan, R., Dong, Y., and Zhang, Q. (2018). Characteristics of Aggregate Size Distribution of Nanoscale Zero-Valent Iron in Aqueous Suspensions and Its Effect on Transport Process in Porous Media. Water, 10.","DOI":"10.3390\/w10060670"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhu, L., Zhang, C., Zhang, C., Zhou, X., Zhang, Z., Nie, X., Liu, W., and Zhu, B. (2019). Challenges and prospects of digital core-reconstruction research. Geofluids, 2019.","DOI":"10.1155\/2019\/7814180"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/0021-9797(84)90481-8","article-title":"A new three-dimensional modeling technique for studying porous media","volume":"98","author":"Quiblier","year":"1984","journal-title":"J. Coll. Interface Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/0301-9322(90)90025-E","article-title":"Flow in simulated porous media","volume":"16","author":"Adler","year":"1990","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF00613583","article-title":"Hydraulic radius and transport in reconstructed model three-dimensional porous media","volume":"17","author":"Bentz","year":"1994","journal-title":"Transp. Porous Media"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0920-4105(98)00077-1","article-title":"A reconstruction technique for three-dimensional porous media using image analysis and Fourier transforms","volume":"21","author":"Liang","year":"1998","journal-title":"J. Petroleum Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1103\/PhysRevE.57.495","article-title":"Reconstructing random media","volume":"57","author":"Yeong","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1103\/PhysRevE.58.224","article-title":"Reconstructing random media. II. Three-dimensional media from two-dimensional cuts","volume":"58","author":"Yeong","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"71","DOI":"10.3390\/opt1010006","article-title":"Micro- and Macro-Scale Measurement of Flow Velocity in Porous Media: A Shadow Imaging Approach for 2D and 3D","volume":"1","author":"Sabbagh","year":"2020","journal-title":"Optics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2374","DOI":"10.1063\/1.334346","article-title":"Measurement of spatial correlation functions using image processing techniques","volume":"57","author":"Berryman","year":"1985","journal-title":"J. Appl. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1007\/s10596-012-9287-1","article-title":"Multiple-point geostatistical modeling based on the cross-correlation functions","volume":"16","author":"Tahmasebi","year":"2012","journal-title":"Comput. Geosci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"066709","DOI":"10.1103\/PhysRevE.85.066709","article-title":"Reconstruction of three-dimensional porous media using a single thin section","volume":"85","author":"Tahmasebi","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1002\/nag.1117","article-title":"A reconstruction method for three-dimensional pore space using multiple-point geology statistic based on statistical pattern recognition and microstructure characterization","volume":"37","author":"Xu","year":"2013","journal-title":"Int. J. Numer. Anal. Methods Geomech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"078002","DOI":"10.1103\/PhysRevLett.110.078002","article-title":"Cross-correlation function for accurate reconstruction of heterogeneous media","volume":"110","author":"Tahmasebi","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s11242-015-0570-1","article-title":"Three-dimensional stochastic characterization of shale SEM images","volume":"110","author":"Tahmasebi","year":"2015","journal-title":"Transp. Porous Media"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.petrol.2016.12.031","article-title":"Pore-scale simulation of flow of CO2 and brine in reconstructed and actual 3D rock cores","volume":"155","author":"Tahmasebi","year":"2017","journal-title":"J. Petroleum Sci. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Karsanina, M.V., Gerke, K.M., Skvortsova, E.B., and Mallants, D. (2015). Universal spatial correlation functions for describing and reconstructing soil microstructure. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0126515"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"023307","DOI":"10.1103\/PhysRevE.97.023307","article-title":"Accurate modeling and evaluation of microstructures in complex materials","volume":"97","author":"Tahmasebi","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s11242-018-1039-9","article-title":"Stochastic reconstruction of an oolitic limestone by generative adversarial networks","volume":"125","author":"Mosser","year":"2018","journal-title":"Transp. Porous Media"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, Z., Li, X., Catherine Brinson, L., Choudhary, A.N., Chen, W., and Agrawal, A. (2018). Microstructural materials design via deep adversarial learning methodology. J. Mech. Des., 140.","DOI":"10.1115\/1.4041371"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"106794","DOI":"10.1016\/j.petrol.2019.106794","article-title":"Coupled generative adversarial and auto-encoder neural networks to reconstruct three-dimensional multi-scale porous media","volume":"186","author":"Shams","year":"2020","journal-title":"J. Petroleum Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_25","unstructured":"Eberhart, R., and Kennedy, J. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_27","unstructured":"Yang, X.-S. (2010). Nature-Inspired Metaheuristic Algorithms, Luniver Press."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","article-title":"A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm","volume":"39","author":"Karaboga","year":"2007","journal-title":"J. Glob. Optim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","article-title":"GSA: A gravitational search algorithm","volume":"179","author":"Rashedi","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ins.2018.11.041","article-title":"A hybrid GSA-GA algorithm for constrained optimization problems","volume":"478","author":"Garg","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_31","first-page":"292","article-title":"A hybrid PSO-GA algorithm for constrained optimization problems","volume":"274","author":"Garg","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1016\/j.energy.2017.10.052","article-title":"A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units","volume":"142","author":"Patwal","year":"2018","journal-title":"Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cie.2012.09.015","article-title":"Multi-objective reliability-redundancy allocation problem using particle swarm optimization","volume":"64","author":"Garg","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Shah, H., Tairan, N., Garg, H., and Ghazali, R. (2018). Global Gbest Guided-Artificial Bee Colony Algorithm for Numerical Function Optimization. Computers, 7.","DOI":"10.3390\/computers7040069"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1023\/A:1020886526282","article-title":"Diffusion and flow in porous domains constructed using process-based and stochastic techniques","volume":"9","author":"Kainourgiakis","year":"2002","journal-title":"J. Porous Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"20359","DOI":"10.1029\/96JB00879","article-title":"Using two-point correlation functions to characterize microgeometry and estimate permeabilities of sandstones and porous glass","volume":"101","author":"Blair","year":"1996","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"78","DOI":"10.25103\/jestr.084.12","article-title":"On 3D reconstruction of porous media by using spatial correlation functions","volume":"8","author":"Papakostas","year":"2015","journal-title":"J. Eng. Sci. Technol. Rev."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Papakostas, G.A. (2015). Improving the recognition performance of moment features by selection. Feature Selection for Data and Pattern Recognition, Springer.","DOI":"10.1007\/978-3-662-45620-0_13"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"114004","DOI":"10.1088\/0957-0233\/22\/11\/114004","article-title":"In vivo MRS metabolite quantification using genetic optimization","volume":"22","author":"Papakostas","year":"2011","journal-title":"Meas. Sci. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Saad, A., Dong, Z., and Karimi, M. (2017). A comparative study on recently-introduced nature-based global optimization methods in complex mechanical system design. Algorithms, 10.","DOI":"10.3390\/a10040120"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ins.2010.07.015","article-title":"A modified artificial bee colony algorithm for real-parameter optimization","volume":"192","author":"Akay","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.ijheatmasstransfer.2014.02.006","article-title":"3D reconstruction and design of porous media from thin sections","volume":"73","author":"Bodla","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_44","unstructured":"(2019, December 01). Hephaestus Laboratory. Available online: http:\/\/hephaestus.teikav.edu.gr\/."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1109\/TSMC.1979.4310076","article-title":"A threshold selection method from gray-level histograms","volume":"9","author":"Otsu","year":"1979","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2802","DOI":"10.1016\/j.ins.2007.01.010","article-title":"A new class of Zernike moments for computer vision applications","volume":"177","author":"Papakostas","year":"2007","journal-title":"Inf. Sci."},{"key":"ref_47","first-page":"1","article-title":"Computation strategies of orthogonal image moments: A comparative study","volume":"216","author":"Papakostas","year":"2010","journal-title":"Appl. Math. Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"4642","DOI":"10.1016\/j.ins.2010.08.045","article-title":"Evaluation of parallel particle swarm optimization algorithms within the CUDATM architecture","volume":"181","author":"Mussi","year":"2011","journal-title":"Inf. Sci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/65\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:07:16Z","timestamp":1760173636000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/65"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,16]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["a13030065"],"URL":"https:\/\/doi.org\/10.3390\/a13030065","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,16]]}}}