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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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the flowchart of binary 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)


If fitness(X) >fitness(Gbest)


Update velocity

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



Return the best solution

a binary pso
A Binary PSO

A Particle

Position vector,

(m is the total number of particles).

(n is the dimension of data).

Velocity vector,

is limited by

a binary pso1
A Binary PSO
  • 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.

a binary pso2
A Binary PSO

Updating the velocity of a particle:


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:


= random value.


an improved binary pso ipso
An Improved Binary PSO (IPSO)



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

an improved binary pso ipso1

1) if



2) if



An Improved Binary PSO (IPSO)

Analyzing the sigmoid function:

The properties of the sigmoid function

3) if



an improved binary pso ipso2
An Improved Binary PSO (IPSO)

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:


= random value.

The whole of bits of a particle


an improved binary pso ipso3
An Improved Binary PSO (IPSO)

2) A simple modification of the formula of velocity update

The whole of bits of particles

Calculation for the distance of two position.



Step 1) Calculate the difference of bits for

a = 4

b = 3

Step 2) Calculate the distance between


an improved binary pso ipso4
An Improved Binary PSO (IPSO)

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


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