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# Binary Particle Swarm Optimization (PSO) - PowerPoint PPT Presentation

Binary Particle Swarm Optimization (PSO). Particle m. …. Particle 1. The Flowchart of Binary PSO. Generate and initialize particles with random position (X) and velocity (V). Evaluate position (Fitness). Update Position. If fitness(X) >fitness(Pbest) Pbest=X.

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Presentation Transcript

…..

Particle 1

The Flowchart of Binary PSO

Generate and initialize particles with random position (X) and velocity (V)

Evaluate position (Fitness)

Update Position

If fitness(X) >fitness(Pbest)

Pbest=X

If fitness(X) >fitness(Gbest)

Gbest=X

Update velocity

Termination criterion is met? (e.g., Gbest=sufficient good fitness or maximum generations)

Yes

No

Return the best solution

A Particle

Position vector,

(m is the total number of particles).

(n is the dimension of data).

Velocity vector,

is limited by

• A particle = a solution or a gene subset.

• If bit is 1,gene is selected.

If bit is 0,gene is unselected.

Particle position

Gene expression data

A subset of selected genes by a particle

An example of a particle position representation in PSO for gene selection.

Updating the velocity of a particle:

Inertia

W = inertial weight.

= velocity for particle i at dimension d.

Personal influence

= acceleration constant.

= random value.

= position for particle i at dimension d.

= the best previous position of the ith particle.

Global influence

= acceleration constant.

= random value.

= the global best position of all particles.

Updating the position of a particle:

if

= random value.

else

Idea

Action

Position update

A new and simple rule

Based on the whole of bits of a particle

(Not based on single bit)

Velocity update

Particle velocity should be positive

=>

or

2) if

=>

or

An Improved Binary PSO (IPSO)

Analyzing the sigmoid function:

The properties of the sigmoid function

3) if

=>

or

1) Modify the rule of position update:

• The diagnostic goal = to develop a medical procedure based on the least number of possible genes for accurate disease detection.

• Many previous works (biological and computational researches) have proved that a smaller number of genes can possible to produce higher classification accuracy.

A new and simple rule of position update:

if

= random value.

The whole of bits of a particle

else

2) A simple modification of the formula of velocity update

The whole of bits of particles

Calculation for the distance of two position.

Example:

and

Step 1) Calculate the difference of bits for

a = 4

b = 3

Step 2) Calculate the distance between

and

3) A Fitness Function:

is leave-one-out-cross-validation (LOOCV) accuracy on the training set using the only genes in

is the number of selected genes in

M is the total number of genes for each sample

and

are two priority weights corresponding to the importance of accuracy and the number of selected genes, respectively.