Study Of Particle Swarm Optimization In Discrete Optimization Problem

Optimization is an important branch of mathematics and a young subject which is extensively used, and it aims at choosing the optimum one from many candidate schemes to solve a practical problem. Many scientific, engineering and economic problems need the optimization of a set of parameters with the aim of minimizing or maximizing the objective function. For example, how to choose the parameter in the engineering design can make the design scheme satisfy the need and decrease the cost, and how to allocate the limit resource can make the design scheme satisfy the need and get better economic benefit. Optimization exits in all kinds of fields of human activities.The application of optimization methods is very extensive, and it involves a lot of problems and these problems have different characteristics. According to different principles, they can be divided into different classes. For example, according to the value type of the decision-making variable, they can be divided into two classes, function optimization problem and combination optimization problem (namely, discrete optimization problem). The discrete optimization problem is an important optimization problem, and with the development of computer science, the science of the management and the technology of the modernized produce, it is getting more and more attention by the subjects of operational research, applications mathematics, computer science and management science. Since many years, people are trying to look for efficient algorithms to solve the combination problem, and many efficient algorithms have been proposed, but NP problem is still a science difficulty problem in the 21century, and it is not solved in the complexity field of the theory informatics yet.Modern optimization methods such as artificial neural network, tabu search, genetic algorithm and ant colony algorithm etc., have shown capabilities of finding optimal solutions to many real-word complex problems within a reasonable amount of time. These methods have forged close ties with neural science, artificial intelligence, statistical mechanics, and biology evolution etc., some of them are called intelligent optimization algorithms, such as genetic algorithm and ant colony algorithm.Recently, particle swarm optimization (PSO) algorithm has been gradually attracted more attention over another intelligent algorithm .PSO was brought forward by Dr. Eberhart and Dr. Kenney in 1995. It was a population based stochastic method motivated by the social behavior of bird flock. PSO shares many similarities with EA&GA. PSO is simple in concept, few in parameters, and easy in implementation.