# An Enhanced Particle Swarm Optimization (PSO) Algorithm Employing Quasi-Random Numbers
## 1 Introduction  
Particle Swarm Optimization (PSO) is a metaheuristic algorithm for optimization problems. PSO was first introduced in 1995 by [PERSON] and [PERSON] [1]. The algorithm is based on the concept of social behavior, where particles (potential solutions) move towards the optimal solution through interactions with other particles in the search space. PSO has been widely used in various fields, including engineering, science, and finance, due to its simplicity, robustness, and efficiency. Despite its success, PSO suffers from several limitations. One of the main limitations is its slow convergence rate, which can be attributed to the premature convergence [2] of the particles towards local optima. This issue can be addressed by introducing efficient improvement techniques in PSO. Several enhancement ideas have been proposed in the past to improve the convergence rate of the PSO algorithm, and they are listed below. Firstly, the inertia weight technique was suggested by [PERSON] and [PERSON] [3]. The inertia weight technique is a well-known approach for enhancing the convergence speed of PSO. The inertia weight is used to control the movement of particles in the search space. The idea is to maintain a balance between exploration and exploitation of the search space. The inertia weight is updated at each iteration based on a predefined formula, which controls the speed and direction of particle movement. Various formulas have been proposed for updating the inertia weight, such as linear, nonlinear, and adaptive. The choice of the inertia weight formula depends on the optimization problem and the PSO parameters. Second, the concept of a mutation operator was proposed [4]. A mutation operator is a powerful tool for enhancing the diversity of the PSO population. The mutation operator randomly modifies the position of a particle to generate a new solution in the search space. This operation can prevent premature convergence by introducing new solutions that may lead to better solutions. The mutation operator can be applied at different stages of the PSO algorithm, such as before or after the velocity update. Similar to the mutation operator, another operator known as the crossover operator has also been applied to the PSO algorithm [5; 6; 7]. This concept involvesthe mixture of the attributes of different solutions to gain exploration and to achieve high diversity in potential results to avoid premature convergence. Third, the opposition-based learning technique was suggested [8]. Opposition-based learning (OBL) is a technique that uses the opposite of the current best solution to generate new solutions. The idea behind OBL is that the opposite of the best solution may represent a good direction for exploration in the search space. OBL can improve the diversity and convergence speed of PSO by generating new solutions that are different from those of the current population. Fourth, hybridization with other metaheuristics has been proposed [9]. Hybridization with other metaheuristics is a common approach for improving the efficiency of PSO. The idea is to combine the strengths of different metaheuristics to overcome their weaknesses. For example, PSO can be combined with genetic algorithms (GA), simulated annealing (SA), or ant colony optimization (ACO). The hybridization approach can enhance the exploration and exploitation capabilities of PSO, leading to better solutions in less time. Fifth, dynamic parameter tuning was presented [9]. The PSO parameters, such as the swarm size, maximum velocity, and acceleration coefficients, significantly impact the algorithm's performance. Dynamic parameter tuning is a technique that adjusts the PSO parameters based on the search history during the optimization process. The idea is to adapt the PSO parameters to the problem characteristics and the search progress to improve the convergence speed and solution quality. In conclusion, efficient improvement techniques in PSO can enhance the algorithm's convergence speed and solution quality.