Non-dominated Sorting Genetic Algorithm And Its Applications

Multi-objective optimization is a difficult problem and a research focus in the fields of science and engineering. Classical multi-objective optimization methods have several shortcomings in solving high dimension, multi-modal problems. In order to solve these problems, researchers have developed many multi-objects optimization genetic algorithms based on Simple Genetic Algorithm. Among them, Non-dominated Sorting Genetic Algorithm (NSGA) and its improved method (NSGA-II) have been developed quickly and applied widely. In this paper, basic theory of NSGA and NSGA-II are studied. The application fields of algorithms are extended, and a new scheme of function approximation is proposed.The main contents are as follows:1) The basic theory and process of Genetic Algorithm are systematically introduced. The present Multi-objects optimization genetic algorithms and its disadvantages are described. The basic theory of NSGA and its shortcomings are discussed. Fast Non-dominated Sorting Approach, Crowding Distance, Crowded-Compared Operator and Elitist Approach proposed by NSGA-II and its process are studied.2) NSGA-II is introduced into Variable Structure Control System (VSC System). Aiming at the shortcoming that the control parameter can be only chosen by experience, parameters of the VSC System are optimized by NSGA-II. The overshoot and chattering of the MIMO system are reduced, the dynamic response time is shortened, and robustness is guaranteed to system parameter variationsand external disturbance. Simulation results show the validity of the scheme.3) A scheme of function approximation based on Support Vector Machine (SVM) and NSGAllis proposed. When using SVM regression, which is one of the traditional methods of function approximation, the parameters and kernel function should be chosen by experience. Factor of experience affects results too much. In this paper, Structural Risk Minimization Principle of SVM was firstly combined with NSGA II, and kernel function could be automatically chosen according to its computational complexity. Simulation shows that the approximation function the scheme gained is closer to the original than the conventional SVM function approximation.