改进蚁群算法及在路径规划问题的应用研究
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摘要
路径规划问题是组合优化和运筹学领域研究的热点问题之一，具有重要的理论和现实意义。蚁群优化算法是受蚁群觅食行为启发而提出的一类群智能优化算法，该算法能有效地解决具有NP-Hard特性的组合优化问题。由于蚁群算法在求解离散问题的优势和对路径的敏感性，使它对路径规划问题的求解一直备受关注。
本文针对旅行售货员问题、多智能体的编队控制问题、车辆路由问题以及智能体路径规划问题，分别提出改进的蚁群算法进行求解。主要的研究内容和创新点如下：
1.提出了一种求解旅行售货员问题的改进蚁群算法。该算法在信息素更新过程中，使用一种信息素局部更新和全局动态更新结合的方法，使当前最优路径上的信息素能够根据当前最优解动态地进行调配，避免算法陷入停滞状态。在局部搜索过程中，仅对部分走出更优路径的售货员使用2-opt方法，提高了求解的精度，加快了最优解的收敛速度。仿真实验验证了算法的有效性，与其它算法相比，算法在求解质量和收敛速度上都显示出了良好的性能。
2.提出了一种多智能体编队控制问题的改进蚁群算法。针对多智能体在编队过程中的最短编队距离问题，使用改进的蚁群算法对其求解。该算法每次迭代时，会给每个智能体一个随机的初始位置，以增强搜索的多样性。在搜索过程中，使用智能体当前位置与目标位置距离的倒数作为启发式信息，以引导智能体向路径更短的目标位置进行移动。局部搜索过程采用一种交换搜索的方式，能够扩大搜索的范围，加快最优解的收敛速度。仿真实验验证了算法的有效性。
3.提出一种带容量约束车辆路由问题的改进蚁群算法。该算法使用一种新的车辆位置初始化方式，增加了车辆走出最优路径的可能性。在搜索过程中，使用客户之间路径的节省量作为启发式信息，以引导车辆向路径更节省的客户移动。信息素更新采用一种动态更新的方法，能够根据当前车辆所构建路径的情况对信息素进行更新，避免算法陷入停滞状态。局部搜索除使用2-opt方法外，针对不同车辆访问的客户，还增加了交换搜索和插入搜索，以扩大搜索的范围。仿真实验验证了算法的有效性。
4.提出了一种静态环境下智能体路径规划问题的端点逼近蚁群算法，该算法使用栅格法对智能体的工作环境进行建模。算法使用折返迭代的方式对目标进行搜索。在搜索过程中，以移动方向上一定范围内最大信息素和目标引导函数作为启发式因子。并且，采用两种信息素对蚂蚁进行引导。根据蚂蚁对栅格访问和信息素散播的特点，提出一种端点（起始点与目标点）逼近的方法，它能够使起始点和目标点在迭代过程中逐步地相向移动，缩短了起始点和目标点之间的距离，加快了最优解的收敛速度。仿真实验验证了算法的有效性。
Path planning problems have become one of hot research areas in the field ofcombinatorial optimization and operations research. The researches in this area haveimportant significance on theory and practice. Ant colony optimization (ACO) is anovel nature-inspired metaheuristic algorithm based on real ants foraging behavior.The ACO belongs to the class of swarm intelligence algorithm, which obtainedencouraging results for solving of NP-hard combinatorial optimization problems.Because of the advantages of the ACO on solving discrete problems and beingsensitive to path, more and more attentions are paid to solve path planning problemsusing the ACO.
In this paper improved ant colony algorithms (ACAs) are proposed to solve thefour path planning problems: traveling salesman problem, multiple agent formationcontrol problem, capacitated vehicle routing problem and agent path planningproblem. The main achievements and contents are listed below.
1. An improved ACA is proposed for traveling salesman problems, in which anapproach of local and global dynamic pheromone updating is presented. Byusing the approach of local and global dynamic phenomenon updating, thedistribution of pheromone can be adjusted according to the current route status.The approach of2-opt is only used for some current optimal routes, which canspeed up the convergence of the optimal solution. Simulation resultsdemonstrate the proposed algorithm is efficient.
2. Multi-agent formation control problems are researched. A new kind of problemnamed minimum formation distance problem in multi-agents systems is solved.An improved ACA is proposed to solve this kind of problem. In the process ofsearching, the reciprocal of the distance between agent’s current position andtarget position is chosen as the heuristic information. An exchange search approach is used to expand the scope of the search and speed up theconvergence of the optimal solution. Simulation results demonstrate theproposed algorithm is efficient.
3. An improved ACA is proposed for capacitated vehicle routing problems. A newinitialization of vehicle’s position with an optimal and random selection is usedto increase the possibility of obtaining the optimal path. In the process ofsearching, the saving path among customers is chosen as the heuristicinformation to make the vehicles be more sensitive to the optimal path. Theapproach of local and global dynamic phenomenon updating is used to adjustthe distribution of phenomenon according to vehicles’ routes. Except themethod of2-opt, insertion and exchange search methods are also used to expandthe scope of the search for the clients on different vehicles’ routes. Thesimulation results demonstrate the proposed algorithm works well andefficiently.
4. An ACA using endpoint approximation is proposed for agent path planningproblem under a unknown and static environment. In this algorithm the modelof agent 's workspace is established with grid method and fold-back iterating isused to search the aims. The most pheromone in a moving direction range and agoal guiding function are chosen as the heuristic information during thesearching process. Meanwhile, two kinds of pheromone are used to guide ants.Furthermore, according to the features of the pheromone strewing in the gridsand ants visiting grids, an endpoint approximation method is proposed to makethe starting point and the end point gradually move towards each other in theiterative process, shortening the distance between the starting point and the endpoint and accelerating the speed of convergence. The simulation resultsdemonstrate that the proposed algorithm has much high efficiency.
本文针对旅行售货员问题、多智能体的编队控制问题、车辆路由问题以及智能体路径规划问题，分别提出改进的蚁群算法进行求解。主要的研究内容和创新点如下：
1.提出了一种求解旅行售货员问题的改进蚁群算法。该算法在信息素更新过程中，使用一种信息素局部更新和全局动态更新结合的方法，使当前最优路径上的信息素能够根据当前最优解动态地进行调配，避免算法陷入停滞状态。在局部搜索过程中，仅对部分走出更优路径的售货员使用2-opt方法，提高了求解的精度，加快了最优解的收敛速度。仿真实验验证了算法的有效性，与其它算法相比，算法在求解质量和收敛速度上都显示出了良好的性能。
2.提出了一种多智能体编队控制问题的改进蚁群算法。针对多智能体在编队过程中的最短编队距离问题，使用改进的蚁群算法对其求解。该算法每次迭代时，会给每个智能体一个随机的初始位置，以增强搜索的多样性。在搜索过程中，使用智能体当前位置与目标位置距离的倒数作为启发式信息，以引导智能体向路径更短的目标位置进行移动。局部搜索过程采用一种交换搜索的方式，能够扩大搜索的范围，加快最优解的收敛速度。仿真实验验证了算法的有效性。
3.提出一种带容量约束车辆路由问题的改进蚁群算法。该算法使用一种新的车辆位置初始化方式，增加了车辆走出最优路径的可能性。在搜索过程中，使用客户之间路径的节省量作为启发式信息，以引导车辆向路径更节省的客户移动。信息素更新采用一种动态更新的方法，能够根据当前车辆所构建路径的情况对信息素进行更新，避免算法陷入停滞状态。局部搜索除使用2-opt方法外，针对不同车辆访问的客户，还增加了交换搜索和插入搜索，以扩大搜索的范围。仿真实验验证了算法的有效性。
4.提出了一种静态环境下智能体路径规划问题的端点逼近蚁群算法，该算法使用栅格法对智能体的工作环境进行建模。算法使用折返迭代的方式对目标进行搜索。在搜索过程中，以移动方向上一定范围内最大信息素和目标引导函数作为启发式因子。并且，采用两种信息素对蚂蚁进行引导。根据蚂蚁对栅格访问和信息素散播的特点，提出一种端点（起始点与目标点）逼近的方法，它能够使起始点和目标点在迭代过程中逐步地相向移动，缩短了起始点和目标点之间的距离，加快了最优解的收敛速度。仿真实验验证了算法的有效性。
Path planning problems have become one of hot research areas in the field ofcombinatorial optimization and operations research. The researches in this area haveimportant significance on theory and practice. Ant colony optimization (ACO) is anovel nature-inspired metaheuristic algorithm based on real ants foraging behavior.The ACO belongs to the class of swarm intelligence algorithm, which obtainedencouraging results for solving of NP-hard combinatorial optimization problems.Because of the advantages of the ACO on solving discrete problems and beingsensitive to path, more and more attentions are paid to solve path planning problemsusing the ACO.
In this paper improved ant colony algorithms (ACAs) are proposed to solve thefour path planning problems: traveling salesman problem, multiple agent formationcontrol problem, capacitated vehicle routing problem and agent path planningproblem. The main achievements and contents are listed below.
1. An improved ACA is proposed for traveling salesman problems, in which anapproach of local and global dynamic pheromone updating is presented. Byusing the approach of local and global dynamic phenomenon updating, thedistribution of pheromone can be adjusted according to the current route status.The approach of2-opt is only used for some current optimal routes, which canspeed up the convergence of the optimal solution. Simulation resultsdemonstrate the proposed algorithm is efficient.
2. Multi-agent formation control problems are researched. A new kind of problemnamed minimum formation distance problem in multi-agents systems is solved.An improved ACA is proposed to solve this kind of problem. In the process ofsearching, the reciprocal of the distance between agent’s current position andtarget position is chosen as the heuristic information. An exchange search approach is used to expand the scope of the search and speed up theconvergence of the optimal solution. Simulation results demonstrate theproposed algorithm is efficient.
3. An improved ACA is proposed for capacitated vehicle routing problems. A newinitialization of vehicle’s position with an optimal and random selection is usedto increase the possibility of obtaining the optimal path. In the process ofsearching, the saving path among customers is chosen as the heuristicinformation to make the vehicles be more sensitive to the optimal path. Theapproach of local and global dynamic phenomenon updating is used to adjustthe distribution of phenomenon according to vehicles’ routes. Except themethod of2-opt, insertion and exchange search methods are also used to expandthe scope of the search for the clients on different vehicles’ routes. Thesimulation results demonstrate the proposed algorithm works well andefficiently.
4. An ACA using endpoint approximation is proposed for agent path planningproblem under a unknown and static environment. In this algorithm the modelof agent 's workspace is established with grid method and fold-back iterating isused to search the aims. The most pheromone in a moving direction range and agoal guiding function are chosen as the heuristic information during thesearching process. Meanwhile, two kinds of pheromone are used to guide ants.Furthermore, according to the features of the pheromone strewing in the gridsand ants visiting grids, an endpoint approximation method is proposed to makethe starting point and the end point gradually move towards each other in theiterative process, shortening the distance between the starting point and the endpoint and accelerating the speed of convergence. The simulation resultsdemonstrate that the proposed algorithm has much high efficiency.
引文
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