# An Enhanced Particle Swarm Optimization (PSO) Algorithm Employing Quasi-Random Numbers
## 1 Introduction
The algorithms are compared for the four benchmark problems. The time-varying inertia factor was introduced to improve the converge performance of the PSO [20; 21]. The authors in [22] introduced a time-varying acceleration coefficient in addition to the time-varying inertia factor. They introduced a PSO concept called a self-organizing hierarchical particle swarm optimizer with a time-varying acceleration coefficient. For the velocity update in PSO, only the social part and cognitive part were considered, and to avoid stagnation in the search space, a time-varying mutation step size was used as well. An adaptive particle swarm optimization (APSO) that features better search efficiency than the classical particle swarm optimization (PSO) is presented in [23]. It was engineered to perform a global search over the entire search space with faster convergence speed. The APSO algorithm was carried out in two main steps. In the first step, the algorithm evaluated the population distribution and particle fitness based on which a real-time evolutionary state was estimated. This enabled the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters in real-time to improve the search efficiency and convergence speed in the subsequent step. The multimodal PSO approach proposed in [24] addressed the issues associated with poor local search ability and the requirement of prior knowledge to initialize the PSO algorithm parameters. The authors in [24] proposed an optimizer based on a distance-based locally informed PSO variant. The algorithm eliminated the need to specify the _niche_ parameters in the PSO and enhanced its fine-searching capabilities. To guide the search direction of the particles, each particle used local best information instead of the global best as in the conventional PSO, and the neighborhood of the particle was measured using the Euclidean distance to perform the local best search. In [25], a hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) was proposed. The SA-PSO algorithm takes advantage of the good solution quality provided by the simulated annealing and fast searching ability inherent to the particle swarm optimization. It was concluded that the hybrid algorithm could have higher efficiency, better quality and faster convergence speed than conventional PSO variants. An economic environmental hydrothermal scheduling problem classified as a multi-objective nonlinear constrained optimization was solved using PSO [26]. The algorithm adopted an elite archive set to conserve Pareto optimal solutions and provide multiple evolutionary directions for individuals, while neighborhood searching and chaotic mutation strategies enhance the search capability and diversity of the population. The PSO algorithm also incorporated a constraint handling scheme designed to adjust the constraint violation of hydro and thermal plants. To avoid parameter selection and overcome the premature convergence problem in the PSO optimization, an adaptive fuzzy particle swarm optimization based on a fuzzy inference system, which incorporated a variable neighborhood search strategy and hybrid evolution, was proposed in [27] and applied to the parameter estimation of nonlinear Hydro Turbine Regulation Systems. The results concluded that the new algorithm's pa rameter error and the objective function were significantly smaller than the other algorithms. The estimated model could accurately reflect the dynamic characteristics of the real system, proving that the fuzzy PSO variant was an effective and efficient parameter estimation method. Support vector machine (SVM)-based classifiers need accurate parameter estimation for high-accuracy classification, and in [28], an improved variant of the PSO is used to estimate the SVM parameters. Specifically, dynamic adjustment of inertia is proposed to optimize the parameters of the SVM.