【作者】 杜文晖；

【导师】 王雪峰；

【作者基本信息】 西安科技大学 ， 应用数学， 2010， 硕士

【摘要】 为了更好的解决实际生活中的多目标优化问题,综合已有的理论和算法,提出了一种新的多目标优化遗传算法。在原有遗传算法基础上改进了遗传操作算子,并采用Pareto秩的方法来确定个体的适应度,为了使秩越小的个体被选择的概率越大,文中定义了一个与Pareto秩成反比例的函数。根据轮盘赌方法来进行选择操作、采用算数交叉算子和非均匀变异算子,并在运算过程增加了一个临时存储器,用来存放当前种群的Pareto最优解,将新加入的个体与当前临时存储器中的个体进行比较,将劣于新加入个体的解从临时存储器中删掉,始终保持这个存储器中的群体是最优的。为了提高算法在局部的搜索能力,在算法搜索过程中增加了一个黄金分割搜索,以提高算法的收敛速度,使其更快的逼近全局最优解。黄金分割搜索算法是经典的一维搜索方法,为了利用其良好的搜索能力,将其扩展到n维空间,并给出了具体算法步骤。通过对3个算例进行分析,检验了算法的有效性;任何一种算法都不是万能的,都是有其使用范围的,通过一个反例来说明给出的新的多目标遗传算法也不例外。最后通过Wolpert(沃伯特)和Macready(麦克雷)教授提出的无搜索和优化免费午餐定理(No Free Lunch定理)对这种观点加以说明,即算法在提高了对某类问题的解决速度的同时,必然降低了对另外一类问题的解决速度。更多还原

【Abstract】 In order to solve multi-objective optimization problem in the real-life, according to the existing theory and algorithms, a new multi-objective genetic algorithms was presented. Based on the original genetic algorithm, to improve genetic operators, Pareto rank methods used to determine the individual fitness, the smaller the rank the greater the probability of the individual being selected, I define a function which is the inverse function of Pareto rank. According to roulette selection method, using arithmetic crossover and non-uniform mutation operator, in the computing process, increased a memory to store the current population of Pareto optimal solution, the new individuals was joined the temporary memory , compared with the current individual of memory, from the temporary memory, the individual which is worse than the new entrants’individual will be deleted. In the temporary memory, the solution of the individual is always optimal. To improve the local search capability of the algorithm, the artist applies a golden section search in the search process of the algorithm to improve the convergence speed. Golden section search is the classic one-dimensional search method, in order to use its good search capabilities; the artist extends it to the n-dimension of space, and gives the specific steps of the algorithm. According to the numerical examples, the artist tests the effectiveness of the algorithm; any of the algorithms are not omnipotent, which of all have the area, through a counter-example to illustrate the given new multi-objective genetic algorithm is no exception. Professor Wolpert and Macready presented a free search and optimization of free lunch theorem (No Free Lunch Theorem). According to the theorem , to support this view in the paper. The algorithm improved the speed of certain types of problem solving, while the other will inevitably reduce the settlement rate of a class of problems.更多还原