The general equation   used to update the weights in each iteration is, (1) (2) The positive constants and are called as cognitive and social acceleration coefficients.
and are two random functions in the interval [0,1].
Some of the time varying inertia weight modified methods are listed in Table 1. Model and Methodology Figure 1 depicts a basic block diagram used in adaptive equalization  .
The input is the random bipolar sequence = ±1 and channel impulse response is raised cosine pulse.
Adaptive algorithms are utilized in equalization to find the optimum coefficients.
The normal gradient based adaptive algorithms such as Least Mean Square (LMS), Recursive least squares (RLS), Affine Projection algorithm (APA) and their variants     applied in channel equalization converge to local minima    while optimizing the filter tap weights.
The PSO algorithm can be improved by modifying its inertia weight parameter and other parameters.
Inertia weight parameter was initially introduced by Shi and Eberhart in  .
The derivative free algorithms find the global minima by passing through local and global search processes.
PSO is one of the derivative free optimization algorithms which search the minima locally and globally.