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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Bibliographic Details
Published in:Algorithms Vol. 18; no. 10; p. 637
Main Authors: 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
Language:English
Published: Basel MDPI AG 01.10.2025
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a18100637