Particle Swarm Optimization (PSO) is an algorithm inspired by flocking behavior that was created in 1995 to solve optimization problems. It keeps track of the target value, the global best value of the particle closest to the target (gBest), and a stopping value. Each particle represents a possible solution and has a velocity, data, and personal best value (pBest) of how close it has come to the target. The algorithm initializes particles, calculates fitness values, updates personal and global best values, changes velocities to update data, and repeats until a maximum number of iterations or minimum error is reached. PSO can be used to solve navigation and traveling salesman problems in the Pacman video game world.

1. Particle Swarm Optimization
to solve navigation and traveling salesman
problems in the Pacman world.
By David Rigan

2. Introduction
Inspired by the flocking and schooling patterns of birds and fish, Particle Swarm
Optimization (PSO) was invented by Russell Eberhart and James Kennedy in
1995. Originally, these two started out developing computer software simulations
of birds flocking around food sources, then later realized how well their algorithms
worked on optimization problems.

3. Key Value
The algorithm keeps track of three global variables:
● Target value or condition
● Global best (gBest) value indicating which particle's data is currently closest
to the Target
● Stopping value indicating when the algorithm should stop if the Target isn't
found
Each particle consists of:
● Data representing a possible solution
● A Velocity value indicating how much the Data can be changed
● A personal best (pBest) value indicating the closest the particle's Data has
ever come to the Target

4. Figure 1. A few common population topologies
(neighborhoods). (A) Single-sighted, where
individuals only compare themselves to the next
best. (B) Ring topology, where each individual
compares only to those to the left and right. (C)
Fully connected topology, where everyone is
compared together. (D) Isolated, where
individuals only compare to those within
specified groups.
Population Topologies
Figure 1.

5. Flow Diagram
Figure 2. Flow diagram illustrating the
particle swarm optimization algorithm.
Figure 2

6. Pseudocode
For each particle
{
Initialize particle
}
Do until maximum iterations or minimum error criteria
{
For each particle
{
Calculate Data fitness value
If the fitness value is better than pBest
{
Set pBest = current fitness value
}
If pBest is better than gBest
{
Set gBest = pBest
}
}
For each particle
{
Calculate particle Velocity
Use gBest and Velocity to update particle Data
}

7. Track Layout
● Initial States
● Target

8. DEMO
Particle Swarm Optimization
to solve navigation and traveling salesman
problems in the Pacman world.

9. Source
http://mnemstudio.org/particle-swarm-introduction.htm
http://inst.eecs.berkeley.edu/~cs188/fa18/projects.html