连续域蚁群算法的改进研究及在参数估计中的应用
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摘要
蚁群算法是在20世纪90年代早期提出的一种群智能随机优化算法,其优越的分布式搜索模式在组合优化问题的求解中取得了成功,引起了许多学者的极大关注。蚁群算法本质上是离散的,在求解连续域优化问题时,往往存在收敛速度慢、易陷入局部最优等缺点。如何对蚁群算法在连续空间的寻优方式进行改进,以提高其优化性能,这正是本文研究的主要内容。
在分析总结了用于连续域优化的蚁群算法的基础上,对蚂蚁构建解的过程和在保持种群多样性上进行了改进,提出了一种新的含维变异算子的连续域改进蚁群算法(DMCACO)。该算法采用动态随机抽取策略来确定目标个体,引导蚁群进行全局的快速搜索；当前最优蚂蚁在邻域内以模式探测的方式进行小步长的局部精细搜索。同时,引入了不同于传统变异方式的维变异算子,且变异保持的策略使变异可以更为充分和均匀。对测试函数的仿真结果表明,该算法具有较好的优化性能。
接着,结合改进的约束处理机制,将本文提出的连续域蚁群算法扩展到用于求解约束优化问题。通过引入目标满意度函数和惩罚满意度函数的概念,构建了基于惩罚函数法的新的适应度函数,其中的系数随种群的可行解比例动态自适应变化,不会过大或过小。另外,采取了当前最优不可行解向最优可行解转移的搜索策略,有效利用了约束边界附近不可解的信息。然后通过13个标准测试函数验证了算法的有效性。
最后,将改进的连续域蚁群算法用于求解多元线性回归模型和非线性Logistic回归模型的参数估计问题。通过算例仿真结果可知,本文所提算法为求解回归模型的参数估计问题提供了一条有效的途径。
The ant colony algorithm was put forward in early 1990s, which is a kind of intelligent stochastic optimization algorithm. Its predominant dis-tributed search pattern achieves success in solving combinational prob-lems, and brings great attention of many scholars. Ant colony algorithm is discrete in nature and always has defects such as slow convergence rate and easily plunging into the local optimum when solving the continuous optimization problem. So, It's the major work of this thesis that how to improve the searching way of ant colony algorithm in continuous space and advance its optimal performance.
Based on the analysis of the ant colony algorithms have being used in continuous domains, a novel continuous domains Ant colony algorithm with dimension mutation operator(DMACO) is presented. Mainly, it im-proves the process of ant solution construction and the way of keeping the diversity of ant population. In this algorithm, target individuals which lead the ant colony to do global rapid search are determined by the way of dynamic and stochastic extraction, and the current optimal ant searches subtly in small step with pattern detection nearly. At the same time, the dimension mutation operator is introduced in this algorithm, which is dif-ferent from traditional mutation means. And the mutation is more suffi-cient and homogeneous owing to the strategy of mutation-keeping. Simulating to the test functions, the result demonstrates that the optimal performance of the algorithm is better.
Then, the continuous domains ACO presented is expanded to solve constrained optimization problem, combined with advanced constraint processing mechanism. Based on penalty function method, the author structures a new fitness function by introducing the concept of target sat-isfaction function and penalty satisfaction function. The coefficient in this method is changed dynamically and self-adaptively following the propor-tion of feasible solution, no too large or too small. In addition, the search-ing strategy and the present optimal infeasible solution transferring to the present optimal feasible solution, is adopted to make use of the message about infeasible solution near the constraint boundary effectively. Then the effectiveness of the algorithm is tested on 13 benchmark functions. Finally, the advanced continuous domains ACO is used to solve the pa-rameter estimation problem of multi-linear regression model and nonlin-ear Logistic regression model. From the simulation result of examples, we can know that the algorithm presented is an efficient way to solve the parameter estimation problem of regression model.
在分析总结了用于连续域优化的蚁群算法的基础上,对蚂蚁构建解的过程和在保持种群多样性上进行了改进,提出了一种新的含维变异算子的连续域改进蚁群算法(DMCACO)。该算法采用动态随机抽取策略来确定目标个体,引导蚁群进行全局的快速搜索；当前最优蚂蚁在邻域内以模式探测的方式进行小步长的局部精细搜索。同时,引入了不同于传统变异方式的维变异算子,且变异保持的策略使变异可以更为充分和均匀。对测试函数的仿真结果表明,该算法具有较好的优化性能。
接着,结合改进的约束处理机制,将本文提出的连续域蚁群算法扩展到用于求解约束优化问题。通过引入目标满意度函数和惩罚满意度函数的概念,构建了基于惩罚函数法的新的适应度函数,其中的系数随种群的可行解比例动态自适应变化,不会过大或过小。另外,采取了当前最优不可行解向最优可行解转移的搜索策略,有效利用了约束边界附近不可解的信息。然后通过13个标准测试函数验证了算法的有效性。
最后,将改进的连续域蚁群算法用于求解多元线性回归模型和非线性Logistic回归模型的参数估计问题。通过算例仿真结果可知,本文所提算法为求解回归模型的参数估计问题提供了一条有效的途径。
The ant colony algorithm was put forward in early 1990s, which is a kind of intelligent stochastic optimization algorithm. Its predominant dis-tributed search pattern achieves success in solving combinational prob-lems, and brings great attention of many scholars. Ant colony algorithm is discrete in nature and always has defects such as slow convergence rate and easily plunging into the local optimum when solving the continuous optimization problem. So, It's the major work of this thesis that how to improve the searching way of ant colony algorithm in continuous space and advance its optimal performance.
Based on the analysis of the ant colony algorithms have being used in continuous domains, a novel continuous domains Ant colony algorithm with dimension mutation operator(DMACO) is presented. Mainly, it im-proves the process of ant solution construction and the way of keeping the diversity of ant population. In this algorithm, target individuals which lead the ant colony to do global rapid search are determined by the way of dynamic and stochastic extraction, and the current optimal ant searches subtly in small step with pattern detection nearly. At the same time, the dimension mutation operator is introduced in this algorithm, which is dif-ferent from traditional mutation means. And the mutation is more suffi-cient and homogeneous owing to the strategy of mutation-keeping. Simulating to the test functions, the result demonstrates that the optimal performance of the algorithm is better.
Then, the continuous domains ACO presented is expanded to solve constrained optimization problem, combined with advanced constraint processing mechanism. Based on penalty function method, the author structures a new fitness function by introducing the concept of target sat-isfaction function and penalty satisfaction function. The coefficient in this method is changed dynamically and self-adaptively following the propor-tion of feasible solution, no too large or too small. In addition, the search-ing strategy and the present optimal infeasible solution transferring to the present optimal feasible solution, is adopted to make use of the message about infeasible solution near the constraint boundary effectively. Then the effectiveness of the algorithm is tested on 13 benchmark functions. Finally, the advanced continuous domains ACO is used to solve the pa-rameter estimation problem of multi-linear regression model and nonlin-ear Logistic regression model. From the simulation result of examples, we can know that the algorithm presented is an efficient way to solve the parameter estimation problem of regression model.
引文
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