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西安科技大学毕业设计（论文） 分类号 密级

学校代码 学号 0608060124

指导教师： 学科专业：

西安科技大学

学 士 学 位 论 文

题目：非线性规划问题的粒子群算法

作者：

专业技术职称： 申请学位日期：

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西安科技大学毕业设计（论文） 摘 要

优化技术是一种以数学为基础，用于求解各种组合优化问题的应用技术。最优化问题是人们在工程技术、科学研究、和经济管理等诸多领域中经常碰到的问题，它是指在满足一定的约束条件下，寻找一组参数值，使目标函数达到最大或最小。最优化问题根据其目标函数、约束条件的性质以及优化变量的取值范围可以分为许多类型，例如：根据目标函数和约束条件是否均为线性表达式，把最优化问题划分为线性规划问题和非线性规划问题。针对不同的最优化问题，提出了许多不同的优化方法，如牛顿法、共轭梯度法、Polar-Ribiere 法、拉格朗日乘子法等。这些优化算法能很好地找到问题的局部最优点，是成熟的局部优化算法。

但是随着人类生存空间的扩大以及认识与改造世界范围的拓展，人们发现由于问题的复杂性、约束性、非线性、建模困难等特点，解析性优化算法已不能满足人们的要求，需要寻找一种适合于大规模并行且具有智能特征的优化算法。现代进化类方法如人工神经网络、遗传算法、禁忌搜索法、模拟退火法和蚁群算法等在解决大规模的问题时体现出强大的潜力，它们可以在合理的时间限制内逼近优化问题的较好可行解。其中，遗传算法和蚁群算法被称为智能优化算法，其基本思想是通过模拟自然界生物的行为来构造随机优化算法。

近年来，另一种智能优化算法—粒子群算法（particle swarm optimization，简称PSO）越来越受到学者的关注。粒子群算法是美国社会心理学家JamesKennedy 和电气工程师Russell Eberhart 在1995 年共同提出的，它是受到鸟群社会行为的启发并利用了生物学家Frank Heppner 的生物群体模型而提出的。它用无质量无体积的粒子作为个体，并为每个粒子规定简单的社会行为规则，通过种群间个体协作来实现对问题最优解的搜索。由于算法收敛速度快，设置参数少，容易实现，能有效地解决复杂优化问题，在函数优化、神经网络训练、图解处理、模式识别以及一些工程领域都得到了广泛的应用。

关键字：非线性规划；粒子群算法；智能算法

ABSTRACT

Optimization technology is based on mathematics and can solve various combinatorial optimization problems. Many problems possess a set of parameters to be optimized, especially in the fields of engineering technology, scientific research and economic management.

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西安科技大学毕业设计（论文） Optimization is to look for a set of parameters in definite restriction with the aim of minimizing or maximizing the objective function. According to quality of objective function and restrict condition and scope of variable, optimization problem can be divided into lots of types. For example, if objective function and restrict condition are both lineal expression, this problem belongs to linear programming problem, if not, it belongs to nonlinear programming problem. Different methods have been presented to sovle different kinds of problems, such as Newton's method, conjugate gradient method, Polar-Ribiere's method, Lagrange Multiplier Method etc. These methods can nicely find local extreme in different problems.

However, with the development of human living space and the scope of understanding and transforming the world, people have found that because of the complexity, binding, nonlinear, modeling difficulties characteristic, it is not easy to find a satisfying analytic solutions. It’s necessary to find a optimization algorithm suiting for large-scale parallel Operation with smart features. Modern evolution methods such as artificial neural networks, genetic algorithms, Taboo search method, simulated annealing, and ant colony algorithm etc., reflect a strong potential in solving large-scale problems. They can approximate the better feasible solution for the optimization problem within a reasonable period of time. The Genetic Algorithm and ant colony algorithm are known as intelligent optimization algorithm, and their basic idea is to construct stochastic optimization algorithms by simulating the behavior of the natural world.

In recent years, another kind of intelligent optimization algorithm – PSO algorithm (particle swarm optimization, or PSO) increasingly accesses to the concerns of scholars. PSO algorithm is proposed by American social psychologist James Kennedy and electrical engineer Russell Eberhart in 1995, and it is inspired by bird populations' social behavior and uses the biological group model of biologist Frank Heppner. It uses particles without quality and volumes individuals, provides simple social rules of conduct for each particle, and searches the optimal solution to the problem through individual collaboration among populations. The algorithm converges fast, needing less parameters.Also it is easily achieved, and can effectively solve complex optimization problems. It has been widely used in function optimization, neural network training, graphic processing, pattern recognition as well as some engineering fields.

Key Words:Nonlinear Programming; PSO(Particle Swarm optimization);Intelligent algorithm

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