Jorge A. LizarragaAlberto J. PitaJavier Ruiz-LeonAlma Y. AlanisLuis F. Luque-VegaRocío Carrasco-NavarroCarlos Lara-ÁlvarezYehoshua Aguilar-MolinaHéctor A. Guerrero-Osuna2025-11-052025-11-052025-10-09Lizarraga, J. A., Pita, A. J., Ruiz-Leon, J., Alanis, A. Y., Luque-Vega, L. F., Carrasco-Navarro, R., Lara-Álvarez, C., Aguilar-Molina, Y., & Guerrero-Osuna, H. A. (2025). Phymastichus–Hypothenemus Algorithm for Minimizing and Determining the Number of Pinned Nodes in Pinning Control of Complex Networks. Algorithms, 18(10), 637. https://doi.org/10.3390/a181006371999-4893https://hdl.handle.net/11117/11926Pinning 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.enghttps://creativecommons.org/licenses/by-nc/4.0/deed.esBiological BasisComplex NetworkEnergy-efficient ControlHeuristic OptimizationPinning ControlNonlinear optimizationinfo:eu-repo/semantics/article