【作者】 张丹；

【导师】 夏桂梅；

【作者基本信息】 太原科技大学 ， 数学， 2017， 硕士

【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.更多还原

【Abstract】 Optimization design has become an independent discipline,and gradually penetrated in various industries.The traditional optimization algorithm is used in the early development of optimization design.With the development of swarm intelligence evolutionary algorithm,more and more swarm intelligence algorithms are applied in the optimization design.Estimation of distributed algorithm is known as a swarm evolutionary algorithm which is based on probability model and has strong global searching ability.The evolution of the algorithm is too dependent on the solution space,makes evolution process is slow.The innovation of this paper is to improve the MIMIC algorithm.,put forward two algorithms with effective calculation,feasible solution and high-precision,and then we apply it into two simple examples of optimization design.The results show that the algorithm proposed in this paper is important in practical application.Particularly,it provides a new idea and method for solving the optimization problem.The main contributions of this paper as follows:In the evolution process of MIMIC algorithm,adding a pattern search method with strong local search ability.A hybrid MIMIC algorithm that combined with pattern search method is proposed.To Increase the diversity of the population,first,we will selects a number of points in the current population as the initial point for pattern search,and then translate it as a part of the new population.The effective of algorithm for the six test functions is measured by the following three performance indicators: optimal evolution within a fixed value,algebraic evolution,compliance rate to verify the feasibility and validity of the method,the improved algorithm refinement.And through the comparison of MIMIC algorithm and the improved algorithm in different dimensions after the results obtained,the higher the dimension,the MIMIC algorithm and improved MIMIC algorithm optimization ability is low,the effect of convergence ability of the complexity function of the algorithm,but the higherthe dimension,the improved MIMIC algorithm is more obvious advantages.By combining MIMIC algorithm with Rosenbrock algorithm in the evolution,we proposed a hybrid MIMIC algorithm combined with Rosenbrock algorithm.To solve the shortcomings of population evolution later smaller individual differences,we will select some dominant group in the MIMIC algorithm,and then randomly select some point in current population,and save as the starting point of the rotation direction search method.The new point will be a part of the new group.The results show that the improved algorithm combines the MIMIC algorithm global search ability with the Rosenbrock algorithm of local refinement ability.Besides,the algorithm does not require the objective function is differentiable.So,it is an effective algorithm for solving the objective functions which are not differentiable or derivative.The proposed algorithm which combined MIMIC algorithm with Rosenbrock algorithm has been applied to the worm model.It is useful to find the appropriate value of worm head,modulus and diameter coefficient and making the smallest worm gear ring volume.The optimization results show that the improved algorithm of optimal value and evolution are smaller than the standard MIMIC algorithm.Rounding the results,and then compare with the conventional design optimization,the volume decreasing 31%,this shows that the improved algorithm is feasible in worm model.The hybrid MIMIC algorithm have been applied to the welding beam model,which is a minimization of the total cost problem.By comparing with the standard MIMIC algorithm and other two algorithms,we find that the results of improved algorithm in significantly less than other algorithms,which demonstrate that the improved the algorithm is effective in welding beam model.更多还原