# Global Best Particle Swarm Optimization #

## Name #

Particle Swarm Optimization (PSO), Global Best PSO (GBPSO), gbest PSO

## Taxonomy #

Particle Swarm Optimization is a population-based metaheuristic optimization algorithm inspired by the social behavior of flocking birds or schooling fish. It is closely related to other swarm intelligence algorithms like Ant Colony Optimization (ACO) and Artificial Bee Colony (ABC).

- Artificial Intelligence
- Computational Intelligence
- Swarm Intelligence
- Particle Swarm Optimization
- Global Best Particle Swarm Optimization

- Particle Swarm Optimization

- Swarm Intelligence

- Computational Intelligence

## Strategy #

In Global Best Particle Swarm Optimization, a swarm of particles moves through a multi-dimensional search space, adjusting their positions and velocities based on their own best-known position (personal best) and the best-known position of the entire swarm (global best). The movement of each particle is influenced by its current velocity, its personal best position, and the global best position, with the goal of discovering better solutions as the swarm evolves over time.

### Initialization #

The algorithm begins by initializing a swarm of particles with random positions and velocities within the search space. Each particle’s position represents a potential solution to the optimization problem, and its velocity determines the direction and magnitude of its movement in the next iteration.

### Evaluation and Update #

In each iteration, the fitness of each particle’s current position is evaluated using an objective function. If a particle’s current position is better than its personal best, the personal best is updated. If any particle’s current position is better than the global best, the global best is updated.

### Velocity and Position Update #

The velocity of each particle is then updated based on its previous velocity, the difference between its current position and its personal best, and the difference between its current position and the global best. The velocity update is controlled by inertia weight and acceleration coefficients, which balance the influence of the particle’s own experience and the swarm’s collective knowledge.

After updating the velocities, each particle’s position is updated by adding its new velocity to its current position. This process of evaluation, update, and movement continues for a predetermined number of iterations or until a satisfactory solution is found.

## Procedure #

### Data Structures #

- Particle: Represents a potential solution, containing the following attributes:
- Position: The particle’s current position in the search space
- Velocity: The particle’s current velocity
- Personal Best: The best position the particle has visited

- Swarm: A collection of particles

### Parameters #

- Swarm Size: The number of particles in the swarm
- Inertia Weight: Controls the influence of a particle’s previous velocity on its current velocity
- Cognitive Acceleration Coefficient: Determines the influence of a particle’s personal best on its movement
- Social Acceleration Coefficient: Determines the influence of the global best on a particle’s movement
- Max Iterations: The maximum number of iterations before termination

### Pseudocode #

- Initialize a swarm of particles with random positions and velocities
- Evaluate the fitness of each particle’s position
- Set each particle’s personal best to its initial position
- Set the global best to the best position among all particles
- While termination criteria are not met (e.g., max iterations):
- For each particle in the swarm:
- Update the particle’s velocity based on its previous velocity, personal best, and global best
- Update the particle’s position by adding its new velocity
- Evaluate the fitness of the particle’s new position
- If the new position is better than the particle’s personal best, update the personal best

- If any particle’s new position is better than the global best, update the global best

- For each particle in the swarm:
- Return the global best as the solution

## Considerations #

### Advantages #

- Simple and easy to implement
- Efficient in exploring the search space and avoiding local optima
- Suitable for a wide range of optimization problems
- Can be parallelized for improved performance

### Disadvantages #

- May converge prematurely if the swarm diversity is lost
- Sensitive to the choice of parameters (inertia weight, acceleration coefficients)
- May require a large number of iterations to find the global optimum

## Heuristics #

### Parameter Selection #

- Swarm Size: Typically ranges from 20 to 50 particles, depending on the problem complexity
- Inertia Weight: Usually set between 0.4 and 0.9, with higher values promoting exploration and lower values encouraging exploitation
- Acceleration Coefficients: Commonly set between 1.5 and 2.5, with the cognitive and social coefficients often having equal values

### Initialization #

- Initialize particles’ positions randomly within the search space bounds
- Initialize velocities randomly, typically within a fraction of the position bounds

### Boundary Handling #

- Enforce search space bounds by clamping particles’ positions to the allowed range
- Alternatively, use a “reflect” or “wrap” strategy to keep particles within the search space

### Termination Criteria #

- Set a maximum number of iterations based on the problem complexity and available computational resources
- Terminate if the global best solution does not improve for a specified number of iterations
- Use a relative or absolute tolerance on the objective function value to determine convergence

### Hybrid Approaches #

- Combine PSO with local search techniques (e.g., hill climbing) to refine solutions near the end of the optimization process
- Integrate PSO with other metaheuristics (e.g., genetic algorithms) to balance exploration and exploitation

### Variant Selection #

- Consider using variants like Constriction Coefficient PSO or Fully Informed Particle Swarm (FIPS) to improve convergence properties
- Explore adaptive variants (e.g., Adaptive PSO) that adjust parameters dynamically based on swarm performance