Major advances in particle swarm optimization: theory, analysis, and application

Over the ages, nature has constantly been a rich source of inspiration for science, with much still to discover about and learn from. Swarm Intelligence (SI), a major branch of artificial intelligence, was rendered to model the collective behavior of social swarms in nature. Ultimately, Particle Swarm Optimization algorithm (PSO) is arguably one of the most popular SI paradigms. Over the past two decades, PSO has been applied successfully, with good return as well, in a wide variety of fields of science and technology with a wider range of complex optimization problems, thereby occupying a prominent position in the optimization field. However, through in-depth studies, a number of problems with the algorithm have been detected and identified; e.g., issues regarding convergence, diversity, and stability. Consequently, since its birth in the mid-1990s, PSO has witnessed a myriad of enhancements, extensions, and variants in various aspects of the algorithm, specifically after the twentieth century, and the related research has therefore now reached an impressive state. In this paper, a rigorous yet systematic review is presented to organize and summarize the information on the PSO algorithm and the developments and trends of its most basic as well as of some of the very notable implementations that have been introduced recently, bearing in mind the coverage of paradigm, theory, hybridization, parallelization, complex optimization, and the diverse applications of the algorithm, making it more accessible. Ease for researchers to determine which PSO variant is currently best suited or to be invented for a given optimization problem or application. This up-to-date review also highlights the current pressing issues and intriguing open challenges haunting PSO, prompting scholars and researchers to conduct further research both on the theory and application of the algorithm in the forthcoming years