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An approximation algorithm for graph partitioning via deterministic annealing neural network.

Zhengtian Wu1, Hamid Reza Karimi2, Chuangyin Dang3

  • 1School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China; Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy.

Neural Networks : the Official Journal of the International Neural Network Society
|June 8, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a deterministic annealing neural network algorithm to find approximate solutions for the NP-hard graph partitioning problem. The novel method effectively identifies high-quality solutions, outperforming existing algorithms in simulations.

Keywords:
Combinatorial optimizationDeterministic annealing neural network algorithmGraph partitioningNP-hard problemNeural network

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Area of Science:

  • Computer Science
  • Operations Research
  • Artificial Intelligence

Background:

  • Graph partitioning is a critical NP-hard combinatorial optimization problem with broad industrial applications.
  • Existing methods for graph partitioning often struggle to find optimal or near-optimal solutions efficiently.

Purpose of the Study:

  • To develop and evaluate a novel deterministic annealing neural network algorithm for solving the graph partitioning problem.
  • To demonstrate the effectiveness of this new approach in obtaining high-quality approximate solutions.

Main Methods:

  • The proposed algorithm utilizes a continuation method, reducing a barrier parameter from a large positive number to zero.
  • It finds minimum points of a barrier problem by iteratively updating Lagrange multipliers in a feasible descent direction.
  • The algorithm inherently satisfies variable bounds (0 to 1) within its iterative procedure.

Main Results:

  • The deterministic annealing neural network algorithm successfully generated approximate solutions for the graph partitioning problem.
  • Comparative simulations on 100 test samples showed the proposed algorithm's effectiveness against four established algorithms.

Conclusions:

  • The deterministic annealing neural network algorithm offers a viable and effective approach for tackling the graph partitioning problem.
  • This method provides a promising alternative for complex optimization tasks in industry and management.