{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:16:55Z","timestamp":1760059015737,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T00:00:00Z","timestamp":1747353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of University and Research","award":["2022S88WAY-CUP B53D23301318"],"award-info":[{"award-number":["2022S88WAY-CUP B53D23301318"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The article presents research on the application of computed tomography with an incomplete dataset to the problem of examining the internal structure of walls. The case of incomplete information in computed tomography often occurs in various applications, e.g., when examining large objects or when examining hard-to-reach objects. Algorithms dedicated to this type of problem can be used to detect anomalies (defects, cracks) in the walls, among other artifacts. Situations of this type may occur, for example, in old buildings, where special caution should be exercised. The approach presented in the article consists of a non-standard solution to the problem of reconstructing the internal structure of the tested object. The classical approach involves constructing an appropriate system of equations based on X-rays, the solution of which describes the structure. However, this approach has a drawback: solving such systems of equations is computationally very complex, because the algorithms used, combined with incomplete information, converge very slowly. In this article, we propose a different approach that eliminates this problem. To simulate the structure of the tested object, we use a hybrid algorithm that is a combination of a metaheuristic optimization algorithm (Group Teaching Optimization Algorithm) and a numerical optimization method (Hook-Jeeves method). In order to solve the considered inverse problem, a functional measuring the fit of the model to the measurement data is created. The hybrid algorithm presented in this paper was used to find the minimum of this functional. This paper also shows computational examples illustrating the effectiveness of the algorithms.<\/jats:p>","DOI":"10.3390\/e27050534","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T10:24:02Z","timestamp":1747391042000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigation of the Internal Structure of Hard-to-Reach Objects Using a Hybrid Algorithm on the Example of Walls"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7255-6951","authenticated-orcid":false,"given":"Rafa\u0142","family":"Brociek","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00f3zef","family":"Szczotka","sequence":"additional","affiliation":[{"name":"Building Investments, Miodowa 31, 43-426 Gumna, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4971-5360","authenticated-orcid":false,"given":"Mariusz","family":"Pleszczy\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0484-8637","authenticated-orcid":false,"given":"Francesca","family":"Nanni","sequence":"additional","affiliation":[{"name":"Department of Enterprise Engineering \u2018Mario Lucertini\u2019, University of Rome \u2018Tor Vergata\u2019 and INSTM RU Roma-Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3336-5853","authenticated-orcid":false,"given":"Christian","family":"Napoli","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Roma, Italy"},{"name":"Institute for Systems Analysis and Computer Science, Italian National Research Council, Via dei Taurini 19, 00185 Roma, Italy"},{"name":"Department of Computational Intelligence, Czestochowa University of Technology, 42-201 Czestochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9056","DOI":"10.1039\/D5CP00654F","article-title":"Quantifying anomalous chemical diffusion through disordered porous rock materials","volume":"27","author":"Rajyaguru","year":"2025","journal-title":"Phys. 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