基于实数遗传算法的有约束优化问题初始内点的求解方法研究

发布时间：2018-04-21 02:22

本文选题：约束优化问题 + 初始内点　；参考：《东北农业大学》2017年硕士论文

【摘要】：约束优化问题所涉及的领域非常广泛,为系统的优化和管理提供了有力的支持。约束极值问题的理论和方法来源于最优化理论和优化设计,主要研究内容是在众多的方案中如何找到那个最优的方案。内点法和复合形法等优化算法是求解这一类问题较为常用的方法。但在应用内点法和复合形法等优化算法时,首先要找到一个初始内点。对于有些问题,由于缺少先验知识,很难人为给出一个可行的初始内点,所以,对有约束优化问题初始内点的研究就有了重大的理论意义和应用价值。为此,本文在这一方面进行了深入的分析与研究,给出了基于实数遗传算法来求解约束优化问题初始内点的一种新方法。本文通过对国内外有关文献的深入研究,采用数学、计算机科学等多学科的综合分析法,以制约函数法的相关理论为基础,提出了基于改进实数遗传算法求解有约束优化问题初始内点的模型,并进行了示例计算。取得的主要研究成果如下:(1)本文经研究分析给出了求解约束优化问题初始内点的一种方法——实数遗传算法。相对传统方法需要约束条件是可导的,本文提出的新方法则没有这些要求,因此更具有普适性。(2)提出了基于改进实数遗传算法求解有约束优化问题初始内点的数学模型。(3)给出了用实数遗传算法求解约束优化问题初始内点时适应度函数的构造方法与模型。(4)本文给出的进化策略具有如下特点:1)在交叉操作时将交叉概率取1,以保证所有的父代配对个体都需要进行交叉,即:选择这样的交叉概率能够增加产生子代个体的数量,能够增大产生更加优秀个体的可能性,使算法的运算速度能够得到提高。2)将交叉产生的个体与父代中精英保留的m个个体放在一起排序,重新选出精英保留的m个个体。这样可以避免交叉操作产生的优秀个体在变异操作过程中遭到破坏的不足,使得交叉操作产生的优秀个体能够得到生存。3)对变异操作后的个体排序,然后用精英保留的m个优秀个体对变异操作后最差的m个个体进行替换,形成新的种群。这样既有效的保证了种群的多样性,同时又使得求得的最优结果不会比前一次求得的结果差。(5)进行了实例计算,结果表明该方法是一种行之有效的方法。由于该方法不用对约束条件进行求导,所以较传统方法具有更广泛的实用性。
[Abstract]:Constrained optimization problems involve a wide range of fields and provide strong support for system optimization and management. The theory and method of constrained extremum problem come from optimization theory and optimization design. The main research content is how to find the optimal scheme in many schemes. Optimization algorithms such as interior point method and complex method are commonly used to solve this kind of problems. But when we apply the interior point method and the complex method, we must find an initial interior point. For some problems, due to the lack of prior knowledge, it is difficult to artificially give a feasible initial interior point. Therefore, the study of initial interior point of constrained optimization problems has great theoretical significance and application value. In this paper, a new method of solving the initial interior point of constrained optimization problem based on real genetic algorithm is presented. In this paper, through the in-depth study of relevant literature at home and abroad, the comprehensive analysis method of mathematics, computer science, and so on, is adopted, which is based on the relevant theories of the restriction function method. A model for solving initial interior points of constrained optimization problems based on improved real genetic algorithm is proposed and an example is given. The main research results are as follows: (1) in this paper, a real genetic algorithm is presented to solve the initial interior point of constrained optimization problem. Compared with the traditional method, the constraint condition is derivable, but the new method presented in this paper does not have these requirements. Therefore, a mathematical model based on improved real genetic algorithm for solving initial interior point of constrained optimization problem is proposed. The fitness function of real genetic algorithm for solving initial interior point of constrained optimization problem is given. The evolutionary strategy given in this paper has the following characteristics: 1: 1) in order to ensure that all parent pairs need to cross each other, the crossover probability is taken as 1 in the crossover operation. That is, choosing such a crossover probability can increase the number of individuals who produce offspring, increase the likelihood of producing better individuals, The computation speed of the algorithm can be improved. 2) the cross generated individuals are sorted together with the m individuals retained by the elite in the parent generation, and the m individuals retained by the elite generation are re-selected. In this way, we can avoid the deficiency that the excellent individual generated by the crossover operation will be destroyed in the mutation operation, so that the excellent individual generated by the crossover operation can get survival. 3) the individual after the mutation operation can be sorted. A new population was formed by replacing the worst m individuals with the best ones retained by the elite. This not only effectively guarantees the diversity of the population, but also makes the optimal result not worse than the previous one. The result shows that this method is an effective method. The method is more practical than the traditional method because it does not have to derive the constraint conditions.
【学位授予单位】：东北农业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

【参考文献】