【作者】 王亚利；

【导师】 王宇平；

【作者基本信息】 西安电子科技大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 遗传算法是模拟自然界生物进化过程与机制来求解优化问题的一类自组织、自适应的随机搜索算法,是一种非常通用的优化算法,其编码技术和遗传操作比较简单,对优化问题的限制性条件要求很低,具有很强的并行性和全局搜索能力。它能解决很多类实际问题,目前已经在机器学习、模式识别、图像处理、优化控制、组合优化和管理决策等领域得到了很好的应用。首先,本文简要介绍遗传算法的发展起源、基本原理、基本框架及目前的发展研究状况。其次,研究一类双层规划问题。双层规划问题拥有广泛的应用领域,因此这类问题的算法研究具有重大意义。然而,由于其自身的非凸性及不可微性,寻找最优解是很困难的,要得到非线性双层规划问题的全局最优解就更困难了。本文针对一类特殊的非线性两层规划,利用下层目标函数的单调性,将下层规划的可行域划分成若干有界区间,从而整个双层规划可转化为几个并行且独立的单层规划问题。该方法有效的简化了原问题的计算复杂度,针对上层规划,设计了遗传算法,并给出了算法的收敛性证明。最后进行了数值仿真,结果表明该算法具有高效性和鲁棒性。最后,为了提高BP神经网络在训练权值时的有效性,提出一种基于GA和PSO相结合的算法—GA-PSO算法。在GA-PSO算法中,产生下一代个体时,不仅采用交叉和变异算子,而且利用PSO重新定义局部最优粒子。因此该算法不仅可以避免陷入局部最优,并且具有很好的全局搜索能力。通过对三元奇偶问题和IRIS模式分类问题的仿真,GA-PSO结果明显好于单纯地用GA或PSO进行BP神经网络权值训练。更多还原

【Abstract】 Genetic algorithm is one kind of self-organized and adaptive random searching algorithm that simulates the evolution process and mechanism in nature for the optimization problems. Its coding technique and genetic operator are simpler. It has few requests to the condition of constraints in an optimization problem. It is very good at parallel and global search. It can apply to a wide range of the problems such as machine learning, pattern recognition, image disposal, optimization controller, combinatorial optimization, manage decision-making and so on.First, the origination and development, basic principle and basic framework of genetic algorithm are introduced in the thesis.Next, the bi-level programming problem (BLPP) is studied. Note that bi-level programming problem has wide applications, thus the research on algorithms for this problem is of great significance. Unfortunately, it is very difficult to determine its solution because of its inherent non-convexity and non-differentiability. In particular, it is more difficult to get a globe optimal solution of non-linear BLPP. For a special class of nonlinear bi-level programming, by using the monotonicity of the related functions, the feasible solution set of the lower-level problem is divided into a certain number of bounded intervals, and the bi-level programming can be transformed into several parallel and independent one-level programming problems. In this way, the original problem is simplified. For upper-level programming, a genetic algorithm is designed and its global convergence is proved. At last the numerical simulation results show that the algorithm is more effective and robust.Finally, in order to enhance the efficiency of the training algorithm in the back-propagation (BP) neural networks, a GA-PSO algorithm is proposed by integrating genetic algorithm (GA) and particle swarm optimization (PSO) technique. In GA-PSO, new individuals are created not only by crossover and mutation operations in GA, but also by PSO technique using redefined local optimization swarm. So it can both avoid local minimum and have good global search ability. By simulations on 3-odd-even-model and IRIS pattern-classification model, the superiority of GA-PSO to both GA and PSO in the weight training of the artificial neural networks is demonstrated.更多还原