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A parallel adaptive quantum genetic algorithm for the controllability of arbitrary networks.

Yuhong Li1, Guanghong Gong1, Ni Li1,2

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Summary
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We developed a novel quantum genetic algorithm to efficiently find minimum control nodes for complex networks. This method optimizes network controllability, especially for large-scale systems.

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Area of Science:

  • Complex networks
  • Control theory
  • Quantum computing

Background:

  • Network controllability is crucial for understanding and managing complex systems.
  • Identifying minimum control nodes is a computationally challenging optimization problem.
  • Existing methods struggle with large-scale networks.

Purpose of the Study:

  • To propose a novel, efficient algorithm for determining minimum control nodes in arbitrary networks.
  • To optimize network controllability using a quantum genetic algorithm approach.
  • To investigate the relationship between optimal control nodes and network statistical properties.

Main Methods:

  • Transformed network controllability into a combinatorial optimization problem using the Popov-Belevitch-Hautus rank condition.
  • Developed an algorithm-parallel adaptive quantum genetic algorithm (A-p AQGA).
  • Experimented with canonical and real-world networks of varying sizes.

Main Results:

  • The A-p AQGA rapidly determines minimum control nodes for network control.
  • The algorithm demonstrates superior optimization of network controllability, particularly for large networks.
  • Established links between optimal control nodes and network statistical characteristics.

Conclusions:

  • The proposed A-p AQGA offers an effective solution for optimizing controllability in large and extra-large networks.
  • This approach enhances the practical application of control theory in complex systems.
  • The findings provide insights into network structure and control strategies.