The Particle Swarm Optimisation (PSO) algorithm was inspired by the social and biological behaviour of bird flocks searching for food sources. In this nature-based algorithm, individuals are referred to as particles and fly through the search space seeking for the global best position that minimises (or maximises) a given problem. Today, PSO is one of the most well-known and widely used swarm intelligence algorithms and metaheuristic techniques, because of its simplicity and ability to be used in a wide range of applications. However, in-depth studies of the algorithm have led to the detection and identification of a number of problems with it, especially convergence problems and performance issues. Consequently, a myriad of variants, enhancements and extensions to the original version of the algorithm, developed and introduced in the mid-1990s, have been proposed, especially in the last two decades. In this article, a systematic literature review about those variants and improvements is made, which also covers the hybridisation and parallelisation of the algorithm and its extensions to other classes of optimisation problems, taking into consideration the most important ones. These approaches and improvements are appropriately summarised, organised and presented, in order to allow and facilitate the identification of the most appropriate PSO variant for a particular application.

Finding arbitrary roots of polynomials is a fundamental problem in various areas of science and engineering. A myriad of methods was suggested to address this problem, such as the sequential Newton’s method and the Durand–Kerner (D–K) simultaneous iterative method. The sequential iterative methods, on the one hand, need to use a deflation procedure in order to compute approximations to all the roots of a given polynomial, which can produce inaccurate results due to the accumulation of rounding errors. On the other hand, the simultaneous iterative methods require good initial guesses to converge. However, Artificial Neural Networks (ANNs) are widely known by their capacity to find complex mappings between the dependent and independent variables. In view of this, this paper aims to determine, based on comparative results, whether ANNs can be used to compute approximations to the real and complex roots of a given polynomial, as an alternative to simultaneous iterative algorithms like the D–K method. Although the results are very encouraging and demonstrate the viability and potentiality of the suggested approach, the ANNs were not able to surpass the accuracy of the D–K method. The results indicated, however, that the use of the approximations computed by the ANNs as the initial guesses for the D–K method can be beneficial to the accuracy of this method.

Methodologies for automatic non-rapid eye movement and cyclic alternating pattern analysis were proposed to examine the signal from one electroencephalogram monopolar derivation for the A phase, cyclic alternating pattern cycles, and cyclic alternating pattern rate assessments. A population composed of subjects free of neurological disorders and subjects diagnosed with sleep-disordered breathing was studied. Parallel classifications were performed for non-rapid eye movement and A phase estimations, examining a one-dimension convolutional neural network (fed with the electroencephalogram signal), a long short-term memory (fed with the electroencephalogram signal or with proposed features), and a feed-forward neural network (fed with proposed features), along with a finite state machine for the cyclic alternating pattern cycle scoring. Two hyper-parameter tuning algorithms were developed to optimize the classifiers. The model with long short-term memory fed with proposed features was found to be the best, with accuracy and area under the receiver operating characteristic curve of 83% and 0.88, respectively, for the A phase classification, while for the non-rapid eye movement estimation, the results were 88% and 0.95, respectively. The cyclic alternating pattern cycle classification accuracy was 79% for the same model, while the cyclic alternating pattern rate percentage error was 22%.