# An Overview of Variants and Advancements of PSO Algorithm
## 1 Introduction  
In today's complex life, everyone knowingly and unknowingly takes decisions that may be related to single or multiple objectives. The eventual goal of these decisions is to maximize the benefit or to minimize the loss. From all of the available options, we prefer to choose the best option. So, optimization is a process of finding as effective as possible an outcome, or it is an act of choosing the best option from among the available options with the objective of maximization or minimization and with or without any given set of constraints. It has several components, such as decision variables, constraints and objectives. It is a well-known topic among numerous scholars and research groups engaged in the development and advancement of any area of science, engineering, technology, mathematics, philosophy and many more. Attempts are always made to continuously improve the existing work. There is a long list of algorithms available in the literature. These can be classified as exact and approximate algorithms. Due to the limitations of the exact methods, research is more tilted towards the approximate methods. Approximate methods are mainly heuristic and metaheuristic. The metaheuristic algorithms are non-deterministic in nature. Broadly, there are three main branches of metaheuristic algorithms: Evolutionary algorithms (EA); physics and chemistry-based algorithms; and swarm intelligence-based algorithms. Inspired by the principles of natural selection and natural genetics, the evolutionary algorithms (EA) are always famous with the research scientists. Some of the evolutionary algorithms (EA) are genetic algorithms, virulence optimization algorithms, differential search algorithms, biogeography-based algorithms, differential evolution algorithms, cultural algorithms, etc. The physics and chemistry-based algorithms are those algorithms that mimicked some physical and/or chemical laws i.e., their inspiration source is from physics and chemistry. Famous algorithms in the category of physics and chemistry algorithms are: big bang-big crunch, galaxy-based search algorithm, spiral optimization, electro-magnetism optimization, black hole, charged system search, etc. Swarm intelligence(SI) is a major branch of computational intelligence, based on studying the collective behavior of swarms in nature that interact with each other locally in the absence of any kind of supervision. Swarm intelligence is also termed as collective intelligence. Examples of SI include ant colonies, birds flocking, animal herding, bacterial growth, fish schooling, etc. Until now, a wide variety of research has been carried out on various swarm intelligence algorithms to solve different optimization problems (which has been elaborated in Table 1). The list of swarm intelligence algorithms is too long to explain each and every algorithm, such as the particle swarm optimization (PSO), ant colony optimization (ACO), firefly algorithm (FA), honey bee algorithm (HBA), grey wolf optimization (GWO), bat algorithm (BA), krill herd algorithm (KHA), cuckoo search algorithm (CSA), flower pollination algorithm (FPA), lion optimization algorithm (LOA), salp swarm algorithm (SA), cat algorithm (CA) and many more to come. The success of these algorithms in terms of the lesser number of iterations, less computational efforts, etc. is largely based on their parameter tuning and parametric control. These algorithms have a common objective of searching for a good quality solution using less computational effort. For this objective, according to the researchers, there should be a proper balance between the exploration and exploitation abilities of the algorithm. Exploration is the process of searching entirely new regions of a whole searching space, whereas exploitation is the process of searching only those regions of a search space those are near to the already visited and searched area.