改进的分布估计算法及其在优化设计中的应用

发布时间：2018-05-15 02:09

本文选题：分布估计算法 + MIMIC算法　；参考：《太原科技大学》2017年硕士论文

【摘要】：优化设计已经成为一门独立的学科,并且逐渐地渗透在各个行业中.优化设计发展初期使用的手段是传统优化算法,随着群智能进化算法的发展,如今,越来越多的群智能算法应用在优化设计中,分布估计算法作为一种基于概率模型的群进化算法,有着较强的全局搜索能力,但是该算法后期容易对解空间过于依赖,使得进化较慢,本文创新点是对MIMIC算法进行改进,提出两种有效的,可行的,求精能力强的算法,将改进后的算法应用在两个简单优化设计实例中,体现出改进后的算法在实际应用中的价值,为解决优化设计问题提供了一种新的思路和方法.本文的主要工作:在MIMIC算法进化过程中加入了局部搜索能力强的模式搜索法,提出一种结合模式搜索法的混合MIMIC算法.算法是在种群进化过程中,在当前群体里随机选取若干点作为初始点,进行模式搜索,将得到的个体作为新群体的一部分增加种群的多样性.利用算法对六个测试函数进行测试,通过三个性能指标,即固定进化代数内的最优值,到达确定阈值时的进化代数和达标率验证改进后的算法是有效的,可行的,求精能力有所改进的算法.并通过不同维数下MIMIC算法和改进后的算法结果的比较,得到维数越高,MIMIC算法和改进后的MIMIC算法的寻优能力越低,说明函数的复杂度对算法的收敛能力有影响,但是维数越高,改进后的MIMIC算法的优势越明显.在MIMIC算法种群进化过程中加入旋转方向法,提出一种结合旋转方向法的混合MIMIC算法.算法是在MIMIC算法选择完优势群体后,在当前群体中随机选取若干点作为初始点进行旋转方向法搜索,将得到的个体作为新群体中的一部分,改善种群进化后期个性差异较小的不足之处.通过测试函数测试其性能,得到改进后的算法既结合了MIMIC算法全局搜索能力强的优势,又结合了旋转方向法局部求精能力强的优势,且算法不要求目标函数必须可导,是解决目标函数不可导或者求导麻烦的一种有效的算法.将结合旋转方向法的混合MIMIC算法应用在蜗杆传动模型中,寻找合适的蜗杆头数,模数,直径系数使得蜗轮齿圈体积最小,优化结果表明改进后的算法最优值和进化代数小于标准MIMIC算法,将得到的结果进行圆整,并与常规优化设计相比,体积减少了31%,说明改进后的算法在蜗杆传动模型中是可行的.将结合模式搜索法的混合MIMIC算法应用在焊接梁模型中,这是一个最小化总费用问题,将改进后的算法的优化结果与标准MIMIC算法的结果以及已知的两种算法的结果相比较,改进后的算法结果明显小于其他算法,表明改进后的算法在焊接梁优化设计中是有效的.
[Abstract]:Optimization design has become an independent subject, and gradually infiltrated into various industries. With the development of swarm intelligence evolutionary algorithm, more and more swarm intelligence algorithms are used in optimization design. As a probabilistic model based swarm evolution algorithm, the distribution estimation algorithm has a strong global search ability. However, it is easy to rely on the solution space too much in the later stage of the algorithm, which makes the evolution slow. The innovation of this paper is to improve the MIMIC algorithm. Two effective, feasible and powerful algorithms are proposed. The improved algorithm is applied to two simple optimization design examples, which reflects the value of the improved algorithm in practical application. It provides a new way of thinking and method for solving the problem of optimal design. The main work of this paper is as follows: in the evolution of MIMIC algorithm, a new hybrid MIMIC algorithm is proposed, which has strong local search ability. In the process of population evolution, the algorithm selects a number of points randomly as initial points in the current population and carries out pattern search. The resulting individuals are regarded as part of the new population to increase the diversity of the population. Using the algorithm to test six test functions, through three performance indexes, that is, the optimal value in the fixed evolutionary algebra, the evolutionary algebra when the threshold is determined and the reaching rate to verify that the improved algorithm is effective and feasible. An improved algorithm for refinement. By comparing the results of MIMIC algorithm and improved algorithm under different dimensions, the higher the dimension is, the lower the optimization ability of MIMIC algorithm and improved MIMIC algorithm is, which indicates that the complexity of function has an effect on the convergence ability of the algorithm, but the higher the dimension is, the higher the dimension is. The advantages of the improved MIMIC algorithm are more obvious. In this paper, a hybrid MIMIC algorithm based on rotation direction is proposed by adding the rotation direction method into the evolution process of the MIMIC algorithm. After the MIMIC algorithm selects the dominant population, the algorithm selects a number of points randomly as the initial point in the current population for the rotation direction method search, and takes the individual as a part of the new population. The deficiency of improving the personality difference in the late evolutionary stage of the population. By testing its performance, the improved algorithm not only combines the advantages of global search ability of MIMIC algorithm, but also combines the advantages of local refinement ability of rotation direction method, and the algorithm does not require that the objective function must be differentiable. It is an effective algorithm to solve the problem that the objective function is nondifferentiable or derivable. The hybrid MIMIC algorithm combined with the rotation direction method is applied to the worm gear transmission model to find the appropriate worm head number, modulus and diameter coefficient to minimize the volume of the worm gear ring. The optimization results show that the optimal value and evolutionary algebra of the improved algorithm are smaller than that of the standard MIMIC algorithm. The results obtained are rounded, and compared with the conventional optimization design, the volume of the improved algorithm is reduced by 31%, which shows that the improved algorithm is feasible in the worm transmission model. The hybrid MIMIC algorithm combined with the pattern search method is applied to the welding beam model. It is a problem of minimizing the total cost. The optimization results of the improved algorithm are compared with the results of the standard MIMIC algorithm and the results of the two known algorithms. The result of the improved algorithm is obviously smaller than that of other algorithms, which shows that the improved algorithm is effective in the optimization design of welded beam.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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