基于Lagrange乘子法的一种新型改进粒子群优化算法  

A New Improved PSO Algorithm Based on the Augmented Lagrange

作　　者：张克[1] 梁昔明[1] 

机构地区：[1]北京建筑大学理学院,北京100044

出　　处：《北京建筑大学学报》2016年第1期74-79,共6页Journal of Beijing University of Civil Engineering and Architecture

基　　金：北京自然科学基金项目(4122022);中央支持地方科研创新团队项目(PXM2013_014210_000173)

摘　　要：社会和生产实践中抽象出来的模型一般为非线性约束优化,而约束优化一般很难直接求解.首先,我们通过引进增广lagrange乘子法,将约束优化转化为有界约束优化,然后引入粒子群优化算法来进行求解,并且我们提出来一种嵌入了最速下降法的改进粒子群优化算法,以此来解决标准粒子群算法中收敛速度慢和精度低的问题,提高了搜索的效率,特别是局部搜索的效率.改进算法有效地结合了粒子群优化算法比较强的全局搜索能力和最速下降法的精细快速的局部搜索能力,相比于标准粒子群优化算法,克服了收敛速度慢的特点.数值实验表明,通过改进的粒子群优化算法可以找到所求优化问题的全局最优解.Since the model abstracted from social practice is generally nonlinear constrained optimization problem,it is difficult to be solved directly. The constrained optimization problem is changed into a bound constrained optimization problem at first using augmented Lagrange multiplier method,and the resulting bound constrained optimization problem is then solved by particle swarm optimization algorithm.The particle swarm optimization（ PSO） algorithm is improved by coupling with steepest descent method to overcome its slow speed convergence and low accuracy computation. Through repeatedly using steepest descent method for several times,the local searching efficiency is improved. The proposed algorithm is combined with the strongly global search ability of PSO and the fast local search ability of steepest descent method,and overcomes the slow speed convergence in basic PSO. Numerical experiment results show that the proposed algorithm is a kind of efficient method for solving the constrained optimization problem.

关 键 词：约束优化问题 LAGRANGE乘子法 粒子群优化算法 最速下降法 数值实验 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]