An Algorithm Based on the Improved Particle Swarm Optimization

Abstract

As Aiming at the shortage of the basic particle swarm algorithm is easy to fall into local solution,this paper makes the improvement to the inertia weight factor based on basic particle swarm algorithm called Non-Linear Decreasing Random Inertia Weight Particle Swarm Optimization. Experiments show that the performance of the improved algorithm outperforms standard algorithm. Keywords-particle swarm optimization; parameter estimation; inertia weight I. INTRODUCTION Regression analysis can be used to predict and control, in natural science, social science and technology. It has important applications, and is the most important tool statistics. By regression analysis, multivariate linear regression analysis is the most widely used multivariate quantitative analysis method. It is widely application domain in industry, agriculture, medicine, social investigation, biological information processing. In the regression analysis, the maximum likelihood estimation method is a basic method when estimating the unknown system parameters, before the application of the maximum likelihood estimation method, a function of the unknown model parameters is first established, called Likelihood Function. Maximum likelihood estimation of the parameters of the model is the parameter estimate that is the choice of the maximum value of the likelihood function(1). Due to high order matrix inverse operation, the conventional maximum likelihood estimation calculation process is complicated, and the program structure is not universal. In recent years, along with the development of the genetic algorithm, simulated annealing technique, ant colony algorithm and particle swarm algorithm, the use of intelligent algorithm for parameter estimation of multivariate regression model has gradually become a hot. Yuguang Chen(2) propose a multivariate regression model of engine based on genetic algorithm according to the parameters of car engine; Qi Shen (3) put forward the particle swarm optimization algorithm is used to select multiple linear regression variables, and applies it to the relationship study of the chemistry of aromatic amine carcinogenic activity of structure-activity; Xinjie Wu(4) the particle swarm algorithm is used to estimate the parameters in multivariate linear regression, and three linear regression analysis was verified as an example; Qian Huo(5) put forward the application of genetic algorithm is used to the study of multivariate nonlinear regression model parameters, and with examples, the validity and practicability of the algorithm is verified. For the maximum likelihood estimation method, this paper presents a multiple linear regression model parameter estimation algorithm based on the improved particle swarm optimization algorithm, and the algorithm is simple, practical and efficient. II. PARTICAL SWARM OPTIMIZATION Particle Swarm Optimization (PSO) is a kind of the evolutionary computation technique based on swarm intelligence, this technique was first proposed by Eberhart and Kennedy in 1995(6), from the research on the bird (fish) preying behavior. Its main advantage is simple, easy to implement, less parameters, and producing high quality solutions in a relatively short period of time. A large number of testing functions show that, it has faster convergence speed compared with the traditional optimization techniques (7, 8). PSO initializes into a group of random particle (stochastic), by tracking the optimal particle to search for the optimal solution. When PSO in solving optimization problems, each candidate solution is a position of a bird in the search space, called these birds particle. Each particle has its own position and speed (to determine the direction and distance of flight), and each particle's performance depends on the optimization objective function to determine the fitness value. Each particle memorizes and follows the optimal particle current to search in the solution space. At the same time each iterative process is not completely random, if find a better solution, according to this solution to find the next solution. In a D dimension target search space, M particles form a group, In the T iteration, Pi particle position vector can be expressed as: