【作者】 苏勇彦；

【导师】 王攀；

【作者基本信息】 武汉理工大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 在科学技术和工程实践等诸多领域，许多问题都可归结为某种函数的最优化这类数学模型。进化算法作为处理复杂函数最优化、多目标最优化问题的一种有效算法，正日益受到人们的重视。本文对带约束的单目标、多目标进化算法进行了研究。提出了一种新的约束处理算法。该算法既利用不可行解扩大搜索范围，又不引入惩罚因子。新算法引入两个种群：可行种群和不可行种群。通过可行解和不可行解混合交叉的方法扩大解空间的搜索范围。对可行种群和不可行种群分别进行选择操作。选择操作实现对个体适应值的评估，通过优胜劣态的进化原理最终收敛到最优解。避免了惩罚策略中选取惩罚因子的困难，使得约束处理问题简单化。本文从常用的测试函数集中选择十个问题，采用新算法求解这些问题，并与不同的算法得到的结果进行比较。实验结果表明，新算法得到的最优解优于其它算法的结果，且该算法具有一定的稳定性。改进了一种多目标进化算法。新算法对NSGA-Ⅱ的改进主要有两方面：第一，将新的约束处理方法应用到该算法中；第二，不采用原算法中的拥挤度比较算子而采用变种群策略。由于拥挤比较算子在NSGA-Ⅱ算法中的作用是，通过对非支配集F_i中个体进行比较选择一定个体使新的父代种群规模保持不变。本文采用了种群规模动态变化的策略，则不要拥挤比较算子。在实际的工程应用中，由于变量的扰动是不可避免的，需要的是具有鲁棒性的解，即那些当自变量发生微小变化不敏感的解。本文采用改进的NSGA-Ⅱ算法求解微机电系统设计中问题的鲁棒解。通过对两个谐振器参数的求解，得到的Pareto前沿分布均匀、具有一致性，说明该改进算法是可行的。更多还原

【Abstract】 In many fields of science and technology, industries and practice etc, there are a lot of problems can be converted into the kind of mathematical model about certain function optimization.Evolutionary algorithms are one of the effective algorithms for hard optimization and multiobjective optimization problcms, which are attached more and more importance to. This paper studies evolutionary algorithms for single objective and multiobjective optimization.A novel constrain handling algorithm is proposed. This algorithm use infeasible individuals to increase search space and avoid to choose penalty factor. It has two populations, which are feasible population and infeasible population. This method searches the solution space through the mixture crossover of feasible and infeasible solutions, and does the selection operation on feasible and infeasible populations, respectively. Selection operation evaluates fitness function of individuals and it converges to optimum solution according to evolution theory of "survival of the fittest".It avoids the difficulty of selecting the penalty factor in penalty strategy and makes the handling constrain simplify. This paper chooses ten problems from benchmark problems.The problems have been solved by new algorithm and the results have been campared with other algorithms.The results indicate the proposed algorithm is better than others and it has a certain stability.A multiobjective evolutionary algorithm is improved in this paper.New algorithm have two improvements. At first, it uses new method which is proposed in this paper to handle constrain. Second, it introduces dynamics population strategy and eliminates crowded comparison opterator. The function of crowded comparsion operator in NSGA-II is that select some individuals from non-dominated set F_i to keep a determined population in parent generation. It uses the dynamic population strategy, so cowded comparsion operator is not need. Because the variables perturbations cannot be avoided in practice, practitioners are interested in finding the so-called robust solutions which are less sensitive to small changes in variables. To the MEMS designing problems, this paper use an improved NSGA-II algorithm to search robust solutions. The results of resonators’ parameters indicate the proposed algorithm is feasible.更多还原