新型蚁群算法及其在边坡工程中的应用研究
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摘要
边坡稳定分析是岩土工程领域的重要课题之一,其主要的分析方法有极限平衡法、极限分析法、有限元强度折减法等。极限平衡法由于方法简单、使用经验丰富,所以有限元等数值计算方法还不能完全替代极限平衡方法,目前它仍然是分析边坡稳定性的主要方法之一。
在使用极限平衡法对边坡的稳定性进行分析时,最大的困难在于确定最危险滑动面及其对应的安全系数,由于工程实际中的边坡滑动大多为非圆弧滑动面,因此,本文的重点放在对非圆弧滑动面的搜索上。针对一般滑动面搜索,蚁群算法因其并行性、全局收敛性、鲁棒性、对目标函数无约束等特点而得到了广泛的应用。但蚁群算法也存在搜索效率低和搜索过程中易陷入局部最优解的缺点,因些,本文提出了两种改进的算法:奖惩蚁群算法、相遇蚁群算法,前者把每次搜索过程中的较优解和普通解分离开来,以使算法能较快地收敛于最优解;而后者则是把相遇策略用到了搜索过程中,以期算法有更好的搜索空间和多样性的解。另外,本文还提出了将一种筛选蚁群聚类算法,并且将该方法也成功地应用于岩土边坡的稳定性分析,并取得了较好的效果。本文内容分为七章,简要介绍如下:
第一章介绍了边坡稳定分析的重要性以及边坡稳定分析常用方法的优缺点,得出了临界滑动面搜索方法研究的重要性,针对存在的问题,确定了本文的研究工作内容。
第二章先简单介绍了蚁群算法的基本原理,随后用算法求解旅行商问题(TSP)问题来说明算法的模型。
第三章首先分蚁群算法的一般改进思想,然后分析了算法搜索时间长的原因,在此基础上,提出了奖惩蚁群算法,算法的主要是思想是把每次搜索完成后的蚂蚁分成优秀蚂蚁和普通的蚂蚁,相应路径上的信息素的更新则依据蚂蚁建立路径的排名来进行。通过一系列TSP问题的实验验证,改进算法已能和处理TSP问题的最优算法相媲美。
第四章针对现在蚁算法的一般改进过于强调算法的收敛速度,却忽略了解的搜索空间及解的多样性提高的问题,提出了相遇蚁群算法,算法在搜索过程中所得到的路径都由两只相遇的蚂蚁来构成,并在算法中设置了一个基本的阈值,用来防止由于相遇蚂蚁太少而不能形成解的问题。同奖惩蚁群算法一样,该改进方法也被应用于一系列的TSP问题,并把所得的结果和现在已知的最优结果相比,从结果可以看出,这种改进算法,其全局搜索能力较之基本蚁群算法有明显的提高,并且不易陷入局部最优解。
第五章首先阐述了一般蚁群聚类问题的基本原理及其所存在的一些不足,在此基础上,提出了筛选蚁群聚类算法,该方法的思想起源于传统蚁群聚类算法中,蚂蚁因随机移动而浪费了大量的计算机资源,并且最终导致算法所得的聚类质量不高这一现象,因此,改进的方法是让蚁群直接对待聚类的对象进行操作,并且以一定的概率反复筛选出每个对象堆中最不适合的个体,并把该个体移动到和它最相称的对象堆中去,以此来形成高质量聚类。
第六章介绍了边坡滑动面的构建方法,并给出了相应的临界滑动面搜索的搜索原理以及蚁群算法应用于滑动面搜索的方式,并把前文提出的两种改进算法分别应用于临界滑动面搜索的工程实例中,同时把文中提出的改进的蚁群聚类算法也应用岩土工程边坡稳定性的分析,从这些应用中可以看出,蚁群算法适用于解决边坡工程问题。
第七章对本文研究进行了总结,并且对下一步工作进行了展望。
Slope stability analysis is one of the most important tasks in the geotechnical engineering and it is always performed by Limit equilibrium method, Limiting analysis and Finite element strength reduction. Due to the simplicity, the limit equilibrium method plays an important role in the slope stability analysis, although the numerical methods such as FEM have becoming more and more important for the analysis of slope stability.
To locate the critical slip surface and its relevant safety factor is very difficult while using the FEM. In this thesis, the emphasis is laid on the searching of noncircular slip surfaces because of the situation involved in the practical engineering. While searching the general slip surface, the ant colony optimization is adopted for its distinct advantages, such as parallelism, global convergence, robustness, and fewer limitations of the objective function. But the efficiency of the algorithm is lower and it’s easy to get trapped in the local optimization. To make up the anterior shortcomings, two kinds of ant colony optimization are proposed: Premium-Penalty Ant Colony Optimization and Meeting Ant Colony Optimization. To quicken the convergence, the first algorithm focuses on distinguishing the excellent ants from ordinary ones in its searching procedure. The latter tries to enlarge the searching space and diversify the searching solutions by the meeting strategy. What’s more, the Abstraction Ant Clustering Algorithm is proposed in this thesis. It’s applied to the stability analysis problems of the slope engineering and receives better results. The thesis is constituted by the following seven chapters:
In the first chapter, the significance of soil slope stability analysis is introduced. The general methods of solving the slope stability analysis are illustrated. At the same time, the advantages and disadvantages of all these methods are introduced too. All these discussions lead to the necessity of the location of critical slip surface. Based on the existing problems, the objective of this thesis is put forward.
In the second chapter, the basic theory of ant colony optimization is introduced. The procedure of the algorithm is illustrated by applying to the TSP problem.
The ordinary improvements of ant colony optimization are putted forward in the beginning of the third chapter. Then, the shortcoming of long searching time is illustrated. Based on anterior discussion, the Premium-Penalty Ant Colony Optimization is proposed. In order to quicken the convergence of the algorithm, in the new algorithm, all the ants are divided into two groups, which include the excellent group and the ordinary one. After the iteration, the updating of pheromone on all tours is manipulated according to the ants’rank. As proved by the simulation experiments, the Premium-Penalty Ant Colony Optimization is ranked among the best Ant Colony Optimizations for tackling the TSP problems.
Nowadays, most of the ant colony algorithms’improvements focus on the exploitation of gather information to guide future search of ant colony towards better solution space but neglect the exploration of new tours and diversification of the solutions. Under the perspective, the Meeting Ant Colony Optimization is proposed, which combine pairs of searching ants together to expand the diversification of the search. To make up the influence caused by limited number of meeting ants, a threshold constant is applied to make the algorithm function normally. Just as the methods used in the premium penalty ant colony optimization, the Meeting Colony Optimization is applied to a series of TSP problems too. From the results, it’s obliviously that the global searching ability of the new optimization is improved as contrasted with the basic ant colony algorithm. At the same time, the local optimum can be avoided by the new optimization.
In the fifth chapter, a basic ant clustering algorithm is introduced and its shortcomings are illustrated. Under this perspective, Abstraction Ant Clustering Algorithm is proposed. In the traditional ant clustering algorithm, the searching ant wastes lots of computer resources by random moving and the final quality of the clustering is effected too. In the new algorithm, the use of the grid as ants’working space has been abolished and the clusters are visited by the ants directly. The unsuitable objects in each cluster are picked out with probability and then they are transferred to their most suitable clusters. In this way, a high quality of clustering and sorting of the elements is obtained.
In the sixth chapter, the generation of general slip surface is illustrated. At the same time, the model of searching the soil slip surface is proposed too. Based on the anterior discussion, all the new ant colony algorithms are applied to the slope stability analysis problems. As proved by the results of these computational examples, the ant colony optimization is easy to be adopted in the slope engineering.
In the last chapter, the main achievements of this thesis are summarized and the further research of this field is pointed out.
在使用极限平衡法对边坡的稳定性进行分析时,最大的困难在于确定最危险滑动面及其对应的安全系数,由于工程实际中的边坡滑动大多为非圆弧滑动面,因此,本文的重点放在对非圆弧滑动面的搜索上。针对一般滑动面搜索,蚁群算法因其并行性、全局收敛性、鲁棒性、对目标函数无约束等特点而得到了广泛的应用。但蚁群算法也存在搜索效率低和搜索过程中易陷入局部最优解的缺点,因些,本文提出了两种改进的算法:奖惩蚁群算法、相遇蚁群算法,前者把每次搜索过程中的较优解和普通解分离开来,以使算法能较快地收敛于最优解;而后者则是把相遇策略用到了搜索过程中,以期算法有更好的搜索空间和多样性的解。另外,本文还提出了将一种筛选蚁群聚类算法,并且将该方法也成功地应用于岩土边坡的稳定性分析,并取得了较好的效果。本文内容分为七章,简要介绍如下:
第一章介绍了边坡稳定分析的重要性以及边坡稳定分析常用方法的优缺点,得出了临界滑动面搜索方法研究的重要性,针对存在的问题,确定了本文的研究工作内容。
第二章先简单介绍了蚁群算法的基本原理,随后用算法求解旅行商问题(TSP)问题来说明算法的模型。
第三章首先分蚁群算法的一般改进思想,然后分析了算法搜索时间长的原因,在此基础上,提出了奖惩蚁群算法,算法的主要是思想是把每次搜索完成后的蚂蚁分成优秀蚂蚁和普通的蚂蚁,相应路径上的信息素的更新则依据蚂蚁建立路径的排名来进行。通过一系列TSP问题的实验验证,改进算法已能和处理TSP问题的最优算法相媲美。
第四章针对现在蚁算法的一般改进过于强调算法的收敛速度,却忽略了解的搜索空间及解的多样性提高的问题,提出了相遇蚁群算法,算法在搜索过程中所得到的路径都由两只相遇的蚂蚁来构成,并在算法中设置了一个基本的阈值,用来防止由于相遇蚂蚁太少而不能形成解的问题。同奖惩蚁群算法一样,该改进方法也被应用于一系列的TSP问题,并把所得的结果和现在已知的最优结果相比,从结果可以看出,这种改进算法,其全局搜索能力较之基本蚁群算法有明显的提高,并且不易陷入局部最优解。
第五章首先阐述了一般蚁群聚类问题的基本原理及其所存在的一些不足,在此基础上,提出了筛选蚁群聚类算法,该方法的思想起源于传统蚁群聚类算法中,蚂蚁因随机移动而浪费了大量的计算机资源,并且最终导致算法所得的聚类质量不高这一现象,因此,改进的方法是让蚁群直接对待聚类的对象进行操作,并且以一定的概率反复筛选出每个对象堆中最不适合的个体,并把该个体移动到和它最相称的对象堆中去,以此来形成高质量聚类。
第六章介绍了边坡滑动面的构建方法,并给出了相应的临界滑动面搜索的搜索原理以及蚁群算法应用于滑动面搜索的方式,并把前文提出的两种改进算法分别应用于临界滑动面搜索的工程实例中,同时把文中提出的改进的蚁群聚类算法也应用岩土工程边坡稳定性的分析,从这些应用中可以看出,蚁群算法适用于解决边坡工程问题。
第七章对本文研究进行了总结,并且对下一步工作进行了展望。
Slope stability analysis is one of the most important tasks in the geotechnical engineering and it is always performed by Limit equilibrium method, Limiting analysis and Finite element strength reduction. Due to the simplicity, the limit equilibrium method plays an important role in the slope stability analysis, although the numerical methods such as FEM have becoming more and more important for the analysis of slope stability.
To locate the critical slip surface and its relevant safety factor is very difficult while using the FEM. In this thesis, the emphasis is laid on the searching of noncircular slip surfaces because of the situation involved in the practical engineering. While searching the general slip surface, the ant colony optimization is adopted for its distinct advantages, such as parallelism, global convergence, robustness, and fewer limitations of the objective function. But the efficiency of the algorithm is lower and it’s easy to get trapped in the local optimization. To make up the anterior shortcomings, two kinds of ant colony optimization are proposed: Premium-Penalty Ant Colony Optimization and Meeting Ant Colony Optimization. To quicken the convergence, the first algorithm focuses on distinguishing the excellent ants from ordinary ones in its searching procedure. The latter tries to enlarge the searching space and diversify the searching solutions by the meeting strategy. What’s more, the Abstraction Ant Clustering Algorithm is proposed in this thesis. It’s applied to the stability analysis problems of the slope engineering and receives better results. The thesis is constituted by the following seven chapters:
In the first chapter, the significance of soil slope stability analysis is introduced. The general methods of solving the slope stability analysis are illustrated. At the same time, the advantages and disadvantages of all these methods are introduced too. All these discussions lead to the necessity of the location of critical slip surface. Based on the existing problems, the objective of this thesis is put forward.
In the second chapter, the basic theory of ant colony optimization is introduced. The procedure of the algorithm is illustrated by applying to the TSP problem.
The ordinary improvements of ant colony optimization are putted forward in the beginning of the third chapter. Then, the shortcoming of long searching time is illustrated. Based on anterior discussion, the Premium-Penalty Ant Colony Optimization is proposed. In order to quicken the convergence of the algorithm, in the new algorithm, all the ants are divided into two groups, which include the excellent group and the ordinary one. After the iteration, the updating of pheromone on all tours is manipulated according to the ants’rank. As proved by the simulation experiments, the Premium-Penalty Ant Colony Optimization is ranked among the best Ant Colony Optimizations for tackling the TSP problems.
Nowadays, most of the ant colony algorithms’improvements focus on the exploitation of gather information to guide future search of ant colony towards better solution space but neglect the exploration of new tours and diversification of the solutions. Under the perspective, the Meeting Ant Colony Optimization is proposed, which combine pairs of searching ants together to expand the diversification of the search. To make up the influence caused by limited number of meeting ants, a threshold constant is applied to make the algorithm function normally. Just as the methods used in the premium penalty ant colony optimization, the Meeting Colony Optimization is applied to a series of TSP problems too. From the results, it’s obliviously that the global searching ability of the new optimization is improved as contrasted with the basic ant colony algorithm. At the same time, the local optimum can be avoided by the new optimization.
In the fifth chapter, a basic ant clustering algorithm is introduced and its shortcomings are illustrated. Under this perspective, Abstraction Ant Clustering Algorithm is proposed. In the traditional ant clustering algorithm, the searching ant wastes lots of computer resources by random moving and the final quality of the clustering is effected too. In the new algorithm, the use of the grid as ants’working space has been abolished and the clusters are visited by the ants directly. The unsuitable objects in each cluster are picked out with probability and then they are transferred to their most suitable clusters. In this way, a high quality of clustering and sorting of the elements is obtained.
In the sixth chapter, the generation of general slip surface is illustrated. At the same time, the model of searching the soil slip surface is proposed too. Based on the anterior discussion, all the new ant colony algorithms are applied to the slope stability analysis problems. As proved by the results of these computational examples, the ant colony optimization is easy to be adopted in the slope engineering.
In the last chapter, the main achievements of this thesis are summarized and the further research of this field is pointed out.
引文
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