**3. Present best and global best optimization**

If design or Input variables that give the optimization like maximization or minimization of objective function *f(X)* can be represented with X\* (**Figure 1**).

Pints P1, P2, P3, P4, P5, P6 are known as Present best or Local best solutions and the P7 is known as the Global best solution for the given system.

*Particle Swarm Optimization DOI: http://dx.doi.org/10.5772/intechopen.107156*

#### **Figure 1.**

*Local minima and global minima [1].*

Objective of this given system has a present or local best solution at X\* point, then *f X*\* <sup>≤</sup>*f X*½ � for every X value and in single variable of x for a closed region of *<sup>a</sup>*≤*<sup>x</sup>* <sup>≤</sup>*b:*
