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Particle Swarm Optimization
Seolhee Lee
2018. 02. 14.
Introduction
중앙대학교 기계지능 연구실 2
• Particle Swarm Optimization(PSO) is proposed by Kennedy and Eberhart in 1995
• A concept for optimization of nonliner functions using particle swarm methodology
• Inspired by simulation social behavior of bird flocking or fish schooling.
Introduction
중앙대학교 기계지능 연구실 3
Concept
• Each particle calculates its new velocity based on its own best experience and the
best experience of the swarm, and repeats moving particles.
x
y
fitness
min
max
search space
Introduction
중앙대학교 기계지능 연구실 4
Concept
• Each particle calculates its new velocity based on its own best experience and the
best experience of the swarm, and repeats moving particles.
x
y
fitness
min
max
search space
Introduction
중앙대학교 기계지능 연구실 5
Concept
• Each particle calculates its new velocity based on its own best experience and the
best experience of the swarm, and repeats moving particles.
x
y
fitness
min
max
search space
Introduction
중앙대학교 기계지능 연구실 6
Concept
• Each particle calculates its new velocity based on its own best experience and the
best experience of the swarm, and repeats moving particles.
x
y
fitness
min
max
search space
Algorithm
중앙대학교 기계지능 연구실 7
• PSO is Initialized with random particles
• Particles move through the search space and are evaluated according to
the objective function in every iteration.
• Each particle stores personally, globally best value and position
(called pbest, gbest)
• Each particle modifies its position according to its current position,
velocity, the distance between its current position and pbest, gbest.
How it works
Algorithm
중앙대학교 기계지능 연구실 8
Initialize particles
Evaluate fitness values for each particle
Update particle best
Update global best
Swarm converged?
Update particle velocity
End
Yes
No
Flowchart
Algorithm
중앙대학교 기계지능 연구실 9
𝑉𝑖𝑛+1 = 𝑤𝑉𝑖
𝑛 + 𝑐1𝑟1𝑛 𝑃𝑖
𝑛 − 𝑋𝑖𝑛 + 𝑐2𝑟2
𝑛 𝐺 − 𝑋𝑖𝑛
Particle update
inertia Personal influence Social influence
𝑋𝑖𝑛+1 = 𝑋𝑖
𝑛 + 𝑉𝑖𝑛+1
• 𝑋𝑖: 𝑖th particle’s position
• 𝑉𝑖: 𝑖th particle’s velocity
• 𝑃𝑖:best position of 𝑖th particle (pbest)
• 𝐺:best position of swarm (gbest)
• 𝑐1, 𝑐2: weight related to pbest, gbest
• 𝑟𝑖 , 𝑟2: random variables
Algorithm
중앙대학교 기계지능 연구실 10
𝑉𝑖𝑛+1 = 𝑤𝑉𝑖
𝑛 + 𝑐1𝑟1𝑛 𝑃𝑖
𝑛 − 𝑋𝑖𝑛 + 𝑐2𝑟2
𝑛 𝐺 − 𝑋𝑖𝑛
Particle update
inertia Personal influence Social influence
𝑋𝑖𝑛+1 = 𝑋𝑖
𝑛 + 𝑉𝑖𝑛+1
Makes the particle move
in the same direction and
with the same velocity
Makes the particle return
to the place that most
satisfied it in the past
Makes the particle
follow the best
neighbors direction
Algorithm
중앙대학교 기계지능 연구실 11
𝑃𝑖𝑛
𝐺
𝑣𝑖𝑛
𝑋𝑖𝑛
𝑋𝑖𝑛+1
𝑉𝑖𝑛+1
𝑤𝑉𝑖𝑛
𝑉𝑖𝑛+1 = 𝑤𝑉𝑖
𝑛 +𝑐1𝑟1𝑛 𝑃𝑖
𝑛 − 𝑋𝑖𝑛 + 𝑐2𝑟2
𝑛 𝐺 − 𝑋𝑖𝑛
Particle update
Conclusion
중앙대학교 기계지능 연구실 12
• Simple implementation
• Few algorithm parameters
• Global optimization
Advantage
Disadvantage
• easy to fall into Local minimum