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