Solving the maximum cut problem using Harris Hawk Optimization algorithm

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.