A novel hybrid PSO based on levy flight and wavelet mutation for global optimization

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Metaheuristic Computing

Background:

• Particle Swarm Optimization (PSO) is widely used but prone to premature convergence in multimodal problems.
• Loss of population diversity is a key factor contributing to PSO's early convergence.
• Existing optimization algorithms require enhancements for complex, high-dimensional problems.

Purpose of the Study:

• To propose a novel hybrid optimization algorithm, PSOLFWM, by integrating PSO with wavelet and levy flight theories.
• To improve population diversity and search efficiency of PSO for complex optimization tasks.
• To enhance the convergence speed and accuracy of optimization solutions.

Main Methods:

• Hybridization of Particle Swarm Optimization (PSO) with Levy Flight (LF) and Wavelet Theory (WT).
• Incorporation of LF's random wandering and WT's mutation operations to boost population diversity.
• Performance evaluation using classical test functions and comparison against 19 recent optimization algorithms.

Main Results:

• PSOLFWM demonstrated superior convergence speed and accuracy compared to benchmark algorithms.
• The algorithm exhibited enhanced search stability and anti-interference capabilities in high-dimensional and dynamic tests.
• Statistical analyses (t-Test, Wilcoxon's rank sum test) confirmed significant performance improvements over comparison methods.

Conclusions:

• The proposed PSOLFWM algorithm effectively addresses the premature convergence issue in PSO.
• PSOLFWM offers improved performance, stability, and robustness for complex optimization problems.
• The integration of levy flight and wavelet theory provides a promising direction for developing advanced optimization algorithms.