Particle Swarm Optimization

Nvidia denies DOJ antitrust investigation claims

Author

Ishaan Mahajan
September 10, 2024

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🧠 Particle Swarm Optimization

Humans often mimic nature in various fields, from aviation to algorithms. Particle Swarm Optimization (PSO) is one such nature-inspired algorithm, modeled after the behavior of swarms in search of optimal solutions in complex, high-dimensional spaces.

Use-Case and Problem Formulation

High-dimensional spaces, such as those encountered in supply chain optimization, are challenging to navigate. Traditional methods like grid search become computationally expensive as dimensions increase.

PSO Components and Solution

In PSO, particles represent candidate solutions. Each particle adjusts its position based on its velocity, personal best, and global best, influenced by inertia, personal learning, and social learning rates. The particles explore new solutions in each iteration, guided by these factors, allowing the swarm to efficiently search for the optimal result. The algorithm balances exploration of the solution space and exploitation of known good solutions, without resorting to brute-force methods.

Results and Comparison

PSO solves the problem within seconds, while a brute-force grid search takes considerably longer, especially as dimensions increase. Despite the introduction of noise in sampling, PSO consistently finds solutions close to the optimal. In comparison, grid search is computationally prohibitive for high-dimensional problems, highlighting PSO’s efficiency.

Visualization

The article visualizes the search process, showing how the distribution of particles changes over iterations. Though only two dimensions are displayed at a time, the white dot (global best particle) and smaller dots (other particles) demonstrate the dynamic search process, providing insight into how PSO explores complex solution landscapes.

Conclusion

PSO is a powerful and efficient algorithm for solving high-dimensional optimization problems, outperforming traditional methods like grid search. By leveraging swarm intelligence, PSO offers an effective balance between exploration and convergence toward an optimal solution.

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