【作者】 陈宇；

【导师】 孙永军； 刘全占；

【作者基本信息】 西安电子科技大学 ， 工程硕士（专业学位）， 2021， 硕士

【摘要】 随着计算机的发展和工业科技的进步,优化问题的规模和复杂度快速增长,这对各种优化方法提出了更高的要求。元启发式算法作为求解优化问题的方法之一,因其参数简单,不依赖优化问题的具体函数形式,全局搜索能力强而得到了广泛的应用。随着优化问题维度增加,优化问题的求解空间呈指数上升,复杂度也随之迅速提升。很多优化算法都会遭受“维度诅咒”,其性能随维度增加而迅速下降。针对复杂高维优化问题,本文通过改进鲸鱼优化算法的开发和探索能力,来提高算法的优化性能。当优化问题存在不对称、最优值转移、病态、旋转等特征时,各种优化算法都很难找到最优解。本文提出了一种离散区域限制差分进化算法(DRDE),有效的提升差分进化算法的探索与开发性能,用于求解这类复杂的低维优化问题。本文主要工作如下:(1)对元启发式算法进行了介绍,着重介绍了鲸鱼优化算法,差分进化算法的基本原理。介绍了元启发式算法,复杂高维以及低维优化问题的国内外研究现状。对复杂高维以及低维优化函数进行了分类介绍。(2)针对复杂高维函数优化问题,考虑到鲸鱼优化算法存在早熟,求解精度低,搜索停滞,收敛速度慢等问题,提出了一种多种群改进鲸鱼算法(MIWOA)。首先,MIWOA根据适应度将种群分为较好的群体和较差的群体。较好的种群被用来提高开发性能,较差的种群被用来提高探索性能,以此充分利用个体特点来提升算法的探索和开发性能。其次,MIWOA利用加权中心学习策略提高了探索能力和收敛速度,引入二次插值算法进一步提高算法的开发性能。最后,利用控制参数来平衡开发和探索过程。仿真结果表明,MIWOA在复杂高维优化问题上的求解精度、收敛速度和执行时间上均优于其他对比算法。(3)针对复杂低维优化问题,提出了一种离散区域限制差分进化算法(DRDE)。首先,DRDE算法引入了离散搜索策略和区域限制策略来搜索最有希望的解区域,缩小搜索范围,降低全局搜索的复杂度。在此基础上,引入了Lévy飞行过程以及鲸鱼开发过程进一步提升算法的开发性能和收敛速度。另外,算法还引入了平衡探索和开发过程的控制参数。将DRDE算法在CEC’2013低维测试函数上与最新相关算法进行比较。实验结果表明,DRDE算法求解精度,收敛速度均大幅提升。更多还原

【Abstract】 With the development of computer,the progress of industrial science and technology,the scale and complexity of optimization problems also increase rapidly,which puts forward higher requirements for various optimization methods.As one of the methods to solve optimization problems,meta heuristic algorithm has been widely used because of its simple parameters,independent of the specific function form of optimization problems and strong global search ability.With the increase of the dimension of optimization problem,the space of optimization problem increases exponentially,and the complexity increases rapidly.Many optimization algorithms will suffer from ”dimension curse”,and its performance decreases rapidly with the increase of dimension.In order to solve the complex highdimensional optimization problems,this thesis improves the exploitation and exploration ability of whale optimization algorithm and improves the optimization performance.When the optimization problem has the characteristics of asymmetry,overlap,ill condition and offset,it is difficult to find the optimal solution.In this thesis,a discrete region limited difference evolution algorithm(DRDE)is proposed to improve the exploration and exploitation performance of the algorithm,and is used to solve complex low-dimensional optimization problems.The main work of this thesis is as follows:(1)This thesis introduces the meta heuristic algorithm,and focuses on the basic principles of whale optimization algorithm and differential evolution algorithm.This thesis introduces the current research status of meta heuristic algorithm,complex high-dimensional and lowdimensional optimization problems.The classification of complex high-dimensional and low-dimensional optimization functions is introduced.(2)Considering that whale algorithm has some problems such as prematurity,low precision,search stagnation and slow convergence rate when dealing with complex high-dimensional function optimization problems,this thesis proposes an improved whale optimization algorithm(MIWOA)is proposed.Firstly,MIWOA divides the population into better and worse groups according to the fitness.The better population is used to improve the exploitation performance,and the poor population is used to improve the exploration performance,so as to make full use of the individual characteristics to improve the exploration and exploitation performance of the algorithm.Secondly,MIWOA improves the ability of exploration and convergence by using weighted center learning strategy,and introduces the quadratic interpolation algorithm to further improve the exploitation performance of the algorithm.Finally,the control parameters are used to balance the exploitation and exploration process.The simulation results show that MIWOA is superior to other comparison algorithms in solving complex and high-dimensional optimization problems in terms of precision,convergence speed and execution time.(3)In order to solve the complex low-dimensional optimization problems,a discrete region limited difference evolution algorithm(DRDE)is proposed.Firstly,DRDE algorithm introduces discrete region search strategy and region restriction strategy to search the most promising solution region,narrow the search range and reduce the complexity of global search.On this basis,the Lévy flight process and whale exploitation process are introduced to further improve the exploitation performance and convergence speed of the algorithm.In addition,the algorithm also introduces the control parameters of the balance exploration and exploitation process.The DRDE algorithm is compared with the latest correlation algorithm on CEC’2013 low-dimensional test function.The experimental results show that the DRDE algorithm has a great improvement in accuracy and convergence speed.更多还原