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Solving the maximum cut problem using Harris Hawk Optimization algorithm.

Md Rafiqul Islam1, Md Shahidul Islam2, Pritam Khan Boni1

  • 1Department of Computer Science, American International University - Bangladesh, Dhaka, Bangladesh.

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|January 8, 2025
PubMed
Summary
This summary is machine-generated.

The max-cut problem, a challenging graph partitioning task, is optimized using a modified Harris Hawk Optimization (HHO) algorithm. This enhanced HHO approach, incorporating crossover, mutation, and repair operators, achieves competitive results on benchmark datasets.

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Area of Science:

  • Combinatorial Optimization
  • Graph Theory
  • Computational Intelligence

Background:

  • The max-cut problem aims to partition graph vertices to maximize the total weight of cut edges.
  • It is a fundamental yet computationally challenging combinatorial optimization problem with broad applications.
  • Existing optimization algorithms like Harris Hawk Optimization (HHO) face limitations such as parameter sensitivity and slow convergence.

Purpose of the Study:

  • To enhance the Harris Hawk Optimization (HHO) algorithm for solving the max-cut problem.
  • To introduce novel operators to improve HHO's precision and efficiency in graph partitioning.
  • To evaluate the performance of the modified HHO algorithm against state-of-the-art methods.

Main Methods:

  • The study proposes a modified Harris Hawk Optimization (MC-HHO) algorithm for the max-cut problem.
  • Key modifications include the integration of crossover, refinement, mutation, adjustment, acceptance criterion, and repair operators.
  • The algorithm was tested on the G-set dataset for performance evaluation.

Main Results:

  • The proposed MC-HHO algorithm demonstrated superior performance on the G-set dataset compared to other state-of-the-art algorithms.
  • MC-HHO achieved significantly more cuts than discrete cuckoo search, PSO-EDA, and TSHEA in various instances.
  • Statistical analysis using the Wilcoxon signed rank test confirmed the superior performance of the proposed method.

Conclusions:

  • The enhanced Harris Hawk Optimization algorithm effectively addresses the challenges of the max-cut problem.
  • MC-HHO offers competitive solution quality and improved performance over existing methods.
  • The integration of specialized operators enhances the algorithm's ability to find optimal graph partitions.