Phymastichus–Hypothenemus Algorithm for Minimizing and Determining the Number of Pinned Nodes in Pinning Control of Complex Networks

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 Phymastich...

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Veröffentlicht in:	Algorithms Jg. 18; H. 10; S. 637
Hauptverfasser:	Lizarraga, Jorge A., Pita, Alberto J., Ruiz-Leon, Javier, Alanis, Alma Y., Luque-Vega, Luis F., Carrasco-Navarro, Rocío, Lara-Álvarez, Carlos, Aguilar-Molina, Yehoshua, Guerrero-Osuna, Héctor A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Basel MDPI AG 01.10.2025
Schlagworte:	Adaptive algorithms Algorithms Analysis biological basis Combinatorial analysis complex network Constraints Eigenvalues Energy efficiency energy-efficient control Heuristic Heuristic methods heuristic optimization Network topologies Nodes nonlinear optimization Optimization Optimization algorithms Optimization techniques Pinning pinning control Stability Mexico
ISSN:	1999-4893, 1999-4893
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Abstract	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–Hypothenemus Algorithm—Minimized 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 “offspring.” 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.
AbstractList	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–Hypothenemus Algorithm—Minimized 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 “offspring.” 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.
Audience	Academic
Author	Lizarraga, Jorge A. Alanis, Alma Y. Carrasco-Navarro, Rocío Aguilar-Molina, Yehoshua Lara-Álvarez, Carlos Guerrero-Osuna, Héctor A. Pita, Alberto J. Ruiz-Leon, Javier Luque-Vega, Luis F.
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Cites_doi	10.1016/j.biocontrol.2009.01.021 10.1016/j.advengsoft.2015.01.010 10.1016/j.tics.2004.07.008 10.1073/pnas.122653799 10.1007/s13042-019-01053-x 10.1016/j.automatica.2006.11.014 10.1038/nrm2503 10.1038/nature10832 10.1137/S003614450342480 10.1109/TEVC.2008.919004 10.1109/TNN.1998.712192 10.1038/35065725 10.1002/9781118718124 10.1007/978-94-009-5925-5 10.1016/j.advengsoft.2013.12.007 10.1007/s00521-013-1433-8 10.1103/PhysRevE.69.026113 10.1016/j.ins.2011.08.006 10.1017/CBO9780511815478 10.1038/nature10360 10.1109/CCE50788.2020.9299122 10.1007/BF02289527 10.1007/s12555-014-9001-2 10.1126/science.286.5439.509 10.1016/j.advengsoft.2016.01.008 10.1016/0378-8733(78)90021-7 10.1080/00207721.2021.1885082 10.1007/s10898-007-9149-x 10.1016/j.socnet.2004.11.008 10.1109/3477.484436 10.1103/PhysRevE.66.065102 10.3389/fbioe.2022.830037 10.1201/9781420011432 10.1145/50063.51907 10.1109/TPEL.2011.2136439 10.1145/1772690.1772756 10.1109/CCE56709.2022.9975994 10.1079/9781845931292.0000 10.1038/nature08932 10.1007/978-3-642-34578-4
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SubjectTerms	Adaptive algorithms Algorithms Analysis biological basis Combinatorial analysis complex network Constraints Eigenvalues Energy efficiency energy-efficient control Heuristic Heuristic methods heuristic optimization Network topologies Nodes nonlinear optimization Optimization Optimization algorithms Optimization techniques Pinning pinning control Stability
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Title	Phymastichus–Hypothenemus Algorithm for Minimizing and Determining the Number of Pinned Nodes in Pinning Control of Complex Networks
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