Particle swarm optimization: surfing the waves

Swarm Intelligence (SI) describes the evolving collective intelligence of population/groups of autonomous agents with a low level of intelligence. Particle Swarm Optimization (PSO) is an evolutionary algorithm inspired by animal social behaviour. PSO achieves performance by iteratively directing its particles toward the optimum using its social and cognitive components. Various modifications have been applied to PSO focusing on addressing a variety of methods for adjusting PSO's parameters (i.e., parameter adjustment), social interaction of the particles (i.e., neighbourhood topology) and ways to address the search objectives (i.e., sub-swarm topology). The PSO approach can easily fit in different search optimization categories such as Self Learning, Unsupervised Learning, Stochastic Search, Population-based, and Behaviour-based Search. This study addresses these principal aspects of PSO. In addition, conventional and Basic PSO are introduced and their shortcomings are discussed. Later on, various suggestions and modifications proposed by literature are introduced and discussed.

Particle swarm optimization is a heuristic global optimization method put forward originally by Doctor Kennedy and Eberhart in 1995. Various efforts have been made for solving unimodal and multimodal problems as well as two dimensional to multidimensional problems. Efforts were put towards topology of communication, parameter adjustment, initial distribution of particles and efficient problem solving capabilities. Here we presented detail study of PSO and limitation in present work. Based on the limitation we proposed future direction. I. INTRODUCTION Swarm Intelligence (SI) is an innovative distributed intelligent paradigm for solving optimization problems that originally took its inspiration from the biological examples by swarming, flocking and herding phenomena in vertebrates. Particle Swarm Optimization (PSO) incorporates swarming behaviors observed in flocks of birds, schools of fish, or swarms of bees, and even human social behavior, from which the idea is emerged. PSO is a population-based optimization tool, which could be implemented and applied easily to solve various function optimization problems, or the problems that can be transformed to function optimization problems. As an algorithm, the main strength of PSO is its fast convergence, which compares favorably with many global optimization algorithms like Genetic Algorithms (GA), Simulated Annealing (SA) and other global optimization algorithms. While population-based heuristics are more costly because of their dependency directly upon function values rather than derivative information, they are however susceptible to premature convergence, which is especially the case when there are many decision variables or dimensions to be optimized. Particle swarm optimization is a heuristic global optimization method put forward originally by Doctor Kennedy and Eberhart in 1995. While searching for food, the birds are either scattered or go together before they locate the place where they can find the food. While the birds are searching for food from one place to another, there is always a bird that can smell the food very well, that is, the bird is perceptible of the place where the food can be found, having the better food resource information. Because they are transmitting the information, especially the good information at any time while searching the food from one place to another, conduced by the good information, the birds will eventually flock to the place where food can be found. As far as particle swam optimization algorithm is concerned, solution swam is compared to the bird swarm, the birds' moving from one place to another is equal to the development of the solution swarm, good information is equal to the most optimist solution, and the food resource is equal to the most optimist solution during the whole course. The most optimist solution can be worked out in particle swarm optimization algorithm by the cooperation of each individual. The particle without quality and volume serves as each individual, and the simple behavioral pattern is regulated for each particle to show the complexity of the whole particle swarm. In PSO, the potential solution called particles fly through the problem space by following the current optimum particles. Each particles keeps tracks of its coordinates in the problem space which are associated with the best solution (fitness) achieved so far. This value is called as pbest. Another best value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the neighbors of the particle. This value is called lbest. When a particle takes all the population as its topological neighbors, the best value is a global best and is called gbest. The particle swarm optimization concept consists of, at each time step, changing the velocity of (accelerating) each particle toward its pbest and lbest (for lbest version). Acceleration is weighted by random term, with separate random numbers being generated for acceleration towards pbest and lbest locations. After finding the best values, the particle updates its velocity and positions with following equations.

2011

Particle Swarm Optimization (PSO) is a biologically inspired computational search and optimization method developed in 1995 by Eberhart and Kennedy based on the social behaviors of birds flocking or fish schooling. A number of basic variations have been developed due to improve speed of convergence and quality of solution found by the PSO. On the other hand, basic PSO is more appropriate to process static, simple optimization problem. Modification PSO is developed for solving the basic PSO problem. The observation and review 46 related studies in the period between 2002 and 2010 focusing on function of PSO, advantages and disadvantages of PSO, the basic variant of PSO, Modification of PSO and applications that have implemented using PSO. The application can show which one the modified or variant PSO that haven't been made and which one the modified or variant PSO that will be developed.

2013

Particle Swarm Optimization (PSO) that is famous as a heuristic robust stochastic optimization technique works in field of Artificial Intelligence (AI). This technique of optimization is inspired by certain behaviors of animals such as bird flocking. The base of PSO method is on swarm intelligence that has a huge effect on solving problem in social communication. Hence, the PSO is a useful and valuable technique with goal of maximizing or minimizing of certain value that has been used in wide area and different fields such as large field of engineering, physics, mathematics, chemistry and etc. in this paper, following a brief introduction to the PSO algorithm, the method of that is presented and it’s important factors and parameters are summarized. The main aim of this paper is to overview, discuss of the available literature of the PSO algorithm yearly.

Particle swarm optimization is a stochastic, population-based computer problem-solving algorithm; it is a kind of swarm intelligence that is based on social- principles and provides insights into social behavior, as well as contributing to social-psychological engineering applications. The aim of this paper is to give fundamental insight into the particle swarm optimization algorithm

Entropy, 2020

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 improvemen...

Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06, 2006

This paper presents a gregarious particle swarm optimization algorithm (G-PSO) in which the particles explore the search space by aggressively scouting the local minima with the help of only social knowledge. To avoid premature convergence of the swarm, the particles are re-initialized with a random velocity when stuck at a local minimum. Furthermore, G-PSO adopts a "reactive" determination of the step size, based on feedback from the last iterations. This is in contrast to the basic particle swarm algorithm, in which the particles explore the search space by using both the individual "cognitive" component and the "social" knowledge and no feedback is used for the self-tuning of algorithm parameters. The novel scheme presented, besides generally improving the average optimal values found, reduces the computation effort.

Swarm Intelligence, 2007

Particle swarm optimization (PSO) has undergone many changes since its introduction in 1995. As researchers have learned about the technique, they have derived new versions, developed new applications, and published theoretical studies of the effects of the various parameters and aspects of the algorithm. This paper comprises a snapshot of particle swarming from the authors' perspective, including variations in the algorithm, current and ongoing research, applications and open problems.

The optimization of a system is the quest for its best performance. Thus physical systems tend to reach minimum energy states, while biological systems optimize their own genetic code and behaviour to better cope with the environment. If an artificial system or the model of a natural system can be parameterized, its optimization consists of seeking the best combination of feasible values of those parameters which results in its best performance. This thesis deals with the ‘particle swarm optimization’ method, which differs from traditional methods in that it poses no restriction to the functions involved. The method was inspired by social behaviour observed in nature, and hence its robustness lies in that it is not deterministically implemented to optimize so that there is no problem-specific implementation that may be inadequate for a different problem. An extensive study of the coefficients at the core of the method is carried out partly theoretically, partly heuristically, and partly visualizing trajectories. The influence of their settings on the form and speed of convergence is analyzed, and guidelines as to how to obtain the desired behaviour are provided. Different structures of the social network and additional heuristics are studied and tested on unconstrained benchmark problems. Finally, a robust pseudo adaptive constraint-handling mechanism is proposed. The fully working algorithm is tested on a classical benchmark suite of constrained problems and successfully applied to well-known engineering problems. Results reported by other authors are also provided for reference. The ‘particle swarm optimizer’ developed in this thesis is a global, single-solution, single-objective, gradient-free, population-based method, which is able to handle continuous –exceptionally, discrete variables by rounding-off–, constrained and unconstrained, single-objective problems regardless of whether the functions involved are or are not linear, convex, unimodal, differentiable, smooth, continuous, or even explicit.

In this paper, a new particle swarm optimization method (NPSO) is proposed. It is compared with the regular particle swarm optimizer (PSO) invented by Kennedy and Eberhart in 1995 based on four different benchmark functions. PSO is motivated by the social behavior of organisms, such as bird flocking and fish schooling. Each particle studies its own previous best solution to the optimization problem, and its group's previous best, and then adjusts its position (solution) accordingly. The optimal value will be found by repeating this process. In the NPSO proposed here, each particle adjusts its position according to its own previous worst solution and its group's previous worst to find the optimal value. The strategy here is to avoid a particle's previous worst solution and its group's previous worst based on similar formulae of the regular PSO. Under all test cases, simulation shows that the NPSO always finds better solutions than PSO.