求解非线性规划问题的遗传算法设计与实现【精品毕业设计】(完整版)

摘要

非线性规划在工程、管理、经济、科研、军事等方面都有广泛的应用。传统的解决非线性规划问题的方法，如梯度法、罚函数法、拉格朗日乘子法等，稳定性差，对函数初值和函数性态要求较高，且容易陷入局部最优解。

遗传算法是模拟达尔文的遗传选择和自然淘汰的生物进化过程的计算模型。遗传算法是一种全局搜索算法，简单、通用、鲁棒性强，对目标函数既不要求连续，也不要求可导，适用于并行分布处理，应用范围广。

本文在分析传统的非线性规划算法的不足和遗传算法的优越性的基础上，将遗传算法应用于非线性规划。算法引进惩罚函数的概念，构造带有惩罚项的适应度函数；通过实数编码，转轮法选择，双点交叉，均匀变异，形成了求解非线性规划问题的遗传算法。与传统的非线性规划算法——外点罚函数法的比较结果表明该算法在一定程度上有效地克服了传统的非线性规划算法稳定性差，对函数初值和函数性态要求较高，且容易陷入局部最优解的缺陷，收敛更合理，性能更稳定。

关键词：非线性规划；遗传算法；罚函数法

ABSTRACT

Non-linear programming has a wide range of applications in engineering, management, economic, scientific, and military aspects. Traditional methods to solve the non-linear programming problem, such as the gradient method, penalty method, Lagrange multiplier method, have poor stability. They are sensitive to the function initial value and request the objective function to be continuous and differential. The results are also easily trapped into local optimal solution.

Genetic algorithm is a kind of calculate model which simulates Darwin's genetic selection and biological evolution of natural selection. Genetic algorithm is a global search algorithm. It has simple, universal, robust features,and does not request the objective function to be continuous and differential, and is suitable in parallel distribution processing. Genetic algorithm is widely applied in many areas.

Based on the analysis of the disadvantage of traditional non-linear programming algorithm and the advantage of genetic algorithm, genetic algorithm is applied to non-linear programming in this paper. The introduction of the concept of penalty function is used to construct the fitness function with punishment. By using real-coded, Roulette Wheel selection method, two-point crossover, uniform mutation, we formed a genetic algorithm to solve the non-linear programming problem. Compared with the most classical and widely used traditional non-linear programming problem algorithm –SUMT algorithm, the results show that the new algorithm could effectively overcome the defect of the traditional algorithm in a certain extent. The new algorithm is more stable, less sensitive to the function initial value and conditions, and always could receive the optimal solution or approximate optimal solution. Its convergence results are more reasonable, the performance is more stable.

Key Words: Non-linear Programming; Genetic Algorithm; SUMT Algorithm

目录

1 概论 (1)

1.1 背景介绍 (1)

1.1.1 非线性规划简介 (1)

1.1.2 遗传算法简介 (1)

1.2 研究内容 (2)

2 非线性规划 (3)

2.1 非线性规划的概念 (3)

2.2 非线性规划的数学模型 (3)

2.3 非线性规划的求解方法 (4)

2.3.1 一维最优化方法 (4)

2.3.2 无约束最优化方法 (4)

2.3.3 约束最优化方法 (5)

2.4 非线性规划的应用 (5)

3 传统非线性规划算法——外点罚函数法 (6)

3.1 算法概述 (6)

3.2 算法描述 (6)

3.3 算法性能分析 (7)

3.4 外点罚函数法的程序设计 (8)

3.4.1程序步骤 (8)

3.4.2程序流程图 (8)

4 遗传算法 (10)

4.1 遗传算法概述 (10)

4.1.1 遗传算法的生物学基础 (10)

4.1.2 遗传算法的一般结构 (10)

4.1.3 遗传算法的特点 (12)