{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:41:42Z","timestamp":1760143302651,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:00:00Z","timestamp":1759968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Pinning control is a key strategy for stabilizing complex networks through a limited set of nodes. However, determining the optimal number and location of pinned nodes under dynamic and structural constraints remains a computational challenge. This work proposes an improved version of the Phymastichus\u2013Hypothenemus Algorithm\u2014Minimized and Determinated (PHA-MD) to solve multi-constraint, hybrid optimization problems in pinning control without requiring a predefined number of control nodes. Inspired by the parasitic behavior of Phymastichus coffea on Hypothenemus hampei, the algorithm models each agent as a parasitoid capable of propagating influence across a network, inheriting node importance and dynamically expanding search dimensions through its \u201coffspring.\u201d Unlike its original formulation, PHA-MD integrates variable-length encoding and V-stability assessment to autonomously identify a minimal yet effective pinning set. The method was evaluated on benchmark network topologies and compared against state-of-the-art heuristic algorithms. The results show that PHA-MD consistently achieves asymptotic stability using fewer pinned nodes while maintaining energy efficiency and convergence robustness. These findings highlight the potential of biologically inspired, dimension-adaptive algorithms in solving high-dimensional, combinatorial control problems in complex dynamical systems.<\/jats:p>","DOI":"10.3390\/a18100637","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:47:08Z","timestamp":1760104028000},"page":"637","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Phymastichus\u2013Hypothenemus Algorithm for Minimizing and Determining the Number of Pinned Nodes in Pinning Control of Complex Networks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5321-0840","authenticated-orcid":false,"given":"Jorge A.","family":"Lizarraga","sequence":"first","affiliation":[{"name":"Departamento de Investigaci\u00f3n, Centro de Ense\u00f1anza T\u00e9cnica Industrial, Guadalajara 44638, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8339-6605","authenticated-orcid":false,"given":"Alberto J.","family":"Pita","sequence":"additional","affiliation":[{"name":"Departamento de Investigaci\u00f3n, Centro de Ense\u00f1anza T\u00e9cnica Industrial, Guadalajara 44638, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8076-4008","authenticated-orcid":false,"given":"Javier","family":"Ruiz-Leon","sequence":"additional","affiliation":[{"name":"CINVESTAV, Unidad Guadalajara, Guadalajara 45017, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9600-779X","authenticated-orcid":false,"given":"Alma Y.","family":"Alanis","sequence":"additional","affiliation":[{"name":"CUCEI, Universidad de Guadalajara, Guadalajara 44430, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7095-9984","authenticated-orcid":false,"given":"Luis F.","family":"Luque-Vega","sequence":"additional","affiliation":[{"name":"Department of Technological and Industrial Processes, ITESO, Tlaquepaque 45604, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8148-3600","authenticated-orcid":false,"given":"Roc\u00edo","family":"Carrasco-Navarro","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, ITESO, Tlaquepaque 45604, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-7398","authenticated-orcid":false,"given":"Carlos","family":"Lara-\u00c1lvarez","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Matem\u00e1ticas, Unidad Zacatecas, Zacatecas 98160, Zacatecas, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4299-7083","authenticated-orcid":false,"given":"Yehoshua","family":"Aguilar-Molina","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Computacionales e Ingenier\u00edas, Centro Universitario de los Valles de la Universidad de Guadalajara, Ameca 46600, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0743-842X","authenticated-orcid":false,"given":"H\u00e9ctor A.","family":"Guerrero-Osuna","sequence":"additional","affiliation":[{"name":"Posgrado en Ingenier\u00eda y Tecnolog\u00eda Aplicada, Unidad Acad\u00e9mica de Ingenier\u00eda El\u00e9ctrica, Universidad Aut\u00f3noma de Zacatecas, Zacatecas 98000, Zacatecas, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1038\/35065725","article-title":"Exploring complex networks","volume":"410","author":"Strogatz","year":"2001","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Alon, U. 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