Adaptive equalization is crucial in mitigating distortions and compensating for frequency response variations in communication systems. It aims to enhance signal quality by adjusting the characteristics of the received signal. Particle swarm optimization (PSO) algorithms have shown promise in optimizing the tap weights of the equalizer. However, there is a need to enhance the optimization capabilities of PSO further to improve the equalization performance. This paper provides a comprehensive study of the issues and challenges of adaptive filtering by comparing different variants of PSO and analyzing the performance by combining PSO with other optimization algorithms to achieve better convergence, accuracy, and adaptability. Traditional PSO algorithms often suffer from high computational complexity and slow convergence rates, limiting their effectiveness in solving complex optimization problems. To address these limitations, this paper proposes a set of techniques aimed at reducing the complexity and accelerating the convergence of PSO.