A novel method of global optimal path planning for mobile robot was proposed based on the improved Dijkstra algorithm and ant system algorithm. This method includes three steps: the first step is adopting the MAKLINK ...A novel method of global optimal path planning for mobile robot was proposed based on the improved Dijkstra algorithm and ant system algorithm. This method includes three steps: the first step is adopting the MAKLINK graph theory to establish the free space model of the mobile robot, the second step is adopting the improved Dijkstra algorithm to find out a sub-optimal collision-free path, and the third step is using the ant system algorithm to adjust and optimize the location of the sub-optimal path so as to generate the global optimal path for the mobile robot. The computer simulation experiment was carried out and the results show that this method is correct and effective. The comparison of the results confirms that the proposed method is better than the hybrid genetic algorithm in the global optimal path planning.展开更多
The utilization of biomimicry of bacterial foraging strategy was considered to develop an adaptive control strategy for mobile robot, and a bacterial foraging approach was proposed for robot path planning. In the prop...The utilization of biomimicry of bacterial foraging strategy was considered to develop an adaptive control strategy for mobile robot, and a bacterial foraging approach was proposed for robot path planning. In the proposed model, robot that mimics the behavior of bacteria is able to determine an optimal collision-free path between a start and a target point in the environment surrounded by obstacles. In the simulation, two test scenarios of static environment with different number obstacles were adopted to evaluate the performance of the proposed method. Simulation results show that the robot which reflects the bacterial foraging behavior can adapt to complex environments in the planned trajectories with both satisfactory accuracy and stability.展开更多
This paper presents the rigorous study of mobile robot navigation techniques used so far.The step by step investigations of classical and reactive approaches are made here to understand the development of path plannin...This paper presents the rigorous study of mobile robot navigation techniques used so far.The step by step investigations of classical and reactive approaches are made here to understand the development of path planning strategies in various environmental conditions and to identify research gap.The classical approaches such as cell decomposition(CD),roadmap approach(RA),artificial potential field(APF);reactive approaches such as genetic algorithm(GA),fuzzy logic(FL),neural network(NN),firefly algorithm(FA),particle swarm optimization(PSO),ant colony optimization(ACO),bacterial foraging optimization(BFO),artificial bee colony(ABC),cuckoo search(CS),shuffled frog leaping algorithm(SFLA)and other miscellaneous algorithms(OMA)are considered for study.The navigation over static and dynamic condition is analyzed(for single and multiple robot systems)and it has been observed that the reactive approaches are more robust and perform well in all terrain when compared to classical approaches.It is also observed that the reactive approaches are used to improve the performance of the classical approaches as a hybrid algorithm.Hence,reactive approaches are more popular and widely used for path planning of mobile robot.The paper concludes with tabular data and charts comparing the frequency of individual navigational strategies which can be used for specific application in robotics.展开更多
In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured naviga...In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured navigation system,which consists of the integration of sensors sources,map formatting,global and local path planners,and the base controller,aims to enable the robot to follow the shortest smooth path delicately.Grid-based mapping is used for scoring paths efficiently,allowing the determination of collision-free trajectories from the initial to the target position.This work considers the evolutionary algorithms,the mutated cuckoo optimization algorithm(MCOA)and the genetic algorithm(GA),as a global planner to find the shortest safe path among others.A non-uniform motion coefficient is introduced for MCOA in order to increase the performance of this algorithm.A series of experiments are accomplished and analyzed to confirm the performance of the global planner implemented on a holonomic mobile robot.The results of the experiments show the capacity of the planner framework with respect to the path planning problem under various obstacle layouts.展开更多
Motion planning is critical to realize the autonomous operation of mobile robots.As the complexity and randomness of robot application scenarios increase,the planning capability of the classical hierarchical motion pl...Motion planning is critical to realize the autonomous operation of mobile robots.As the complexity and randomness of robot application scenarios increase,the planning capability of the classical hierarchical motion planners is challenged.With the development of machine learning,the deep reinforcement learning(DRL)-based motion planner has gradually become a research hotspot due to its several advantageous feature.The DRL-based motion planner is model-free and does not rely on the prior structured map.Most importantly,the DRL-based motion planner achieves the unification of the global planner and the local planner.In this paper,we provide a systematic review of various motion planning methods.Firstly,we summarize the representative and state-of-the-art works for each submodule of the classical motion planning architecture and analyze their performance features.Then,we concentrate on summarizing reinforcement learning(RL)-based motion planning approaches,including motion planners combined with RL improvements,map-free RL-based motion planners,and multi-robot cooperative planning methods.Finally,we analyze the urgent challenges faced by these mainstream RLbased motion planners in detail,review some state-of-the-art works for these issues,and propose suggestions for future research.展开更多
Path planning of a mobile robot in the presence of multiple moving obstacles is found to be a complicated problem.A planning algorithm capable of negotiating both static and moving obstacles in an unpredictable(on-lin...Path planning of a mobile robot in the presence of multiple moving obstacles is found to be a complicated problem.A planning algorithm capable of negotiating both static and moving obstacles in an unpredictable(on-line)environment is proposed.The proposed incremental algorithm plans the path by considering the quadrants in which the current positions of obstacles as well as target are situated.Also,the governing equations for the shortest path are derived.The proposed mathematical model describes the motion(satisfying constraints of the mobile robot)along a collision-free path.Further,the algorithm is applicable to dynamic environments with fixed or moving targets.Simulation results show the effectiveness of the proposed algorithm.Comparison of results with the improved artificial potential field(iAPF)algorithm shows that the proposed algorithm yields shorter path length with less computation time.展开更多
Ant colony optimization (ACO) algorithm was modified to optimize the global path. In order to simulate the real ant colonies, according to the foraging behavior of ant colonies and the characteristic of food, concepti...Ant colony optimization (ACO) algorithm was modified to optimize the global path. In order to simulate the real ant colonies, according to the foraging behavior of ant colonies and the characteristic of food, conceptions of neighboring area and smell area were presented. The former can ensure the diversity of paths and the latter ensures that each ant can reach the goal. Then the whole path was divided into three parts and ACO was used to search the second part path. When the three parts pathes were adjusted, the final path was found. The valid path and invalid path were defined to ensure the path valid. Finally, the strategies of the pheromone search were applied to search the optimum path. However, when only the pheromone was used to search the optimum path, ACO converges easily. In order to avoid this premature convergence, combining pheromone search and random search, a hybrid ant colony algorithm(HACO) was used to find the optimum path. The comparison between ACO and HACO shows that HACO can be used to find the shortest path.展开更多
To solve dynamic obstacle avoidance problems, a novel algorithm was put forward with the advantages of wireless sensor network (WSN). In view of moving velocity and direction of both the obstacles and robots, a mathem...To solve dynamic obstacle avoidance problems, a novel algorithm was put forward with the advantages of wireless sensor network (WSN). In view of moving velocity and direction of both the obstacles and robots, a mathematic model was built based on the exposure model, exposure direction and critical speeds of sensors. Ant colony optimization (ACO) algorithm based on bionic swarm intelligence was used for solution of the multi-objective optimization. Energy consumption and topology of the WSN were also discussed. A practical implementation with real WSN and real mobile robots were carried out. In environment with multiple obstacles, the convergence curve of the shortest path length shows that as iterative generation grows, the length of the shortest path decreases and finally reaches a stable and optimal value. Comparisons show that using sensor information fusion can greatly improve the accuracy in comparison with single sensor. The successful path of robots without collision validates the efficiency, stability and accuracy of the proposed algorithm, which is proved to be better than tradition genetic algorithm (GA) for dynamic obstacle avoidance in real time.展开更多
Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which res...Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot′s hand and does not change the number of the path′s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.展开更多
Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method res...Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method resulted in the heavier on line computational burden for the robot controller. In this paper, aiming at this drawback, the authors propose a new kind of real time accurate hand path tracking and joint trajectory planning method for robots. Through selecting some extra knots on the specified hand path by a certain rule, which enables the number of knots on each segment to increase from two to four, and through introducing a sinusoidal function and a cosinoidal function to the joint displacement equation of each segment, this method can raise the path tracking accuracy of robot′s hand greatly but does not increase the computational burden of robot controller markedly.展开更多
Autonomous mobile robot navigation is one of the most emerging areas of research by using swarm intelligence. Path planning and obstacle avoidance are most researched current topics like navigational challenges for mo...Autonomous mobile robot navigation is one of the most emerging areas of research by using swarm intelligence. Path planning and obstacle avoidance are most researched current topics like navigational challenges for mobile robot. The paper presents application and implementation of Firefly Algorithm(FA)for Mobile Robot Navigation(MRN) in uncertain environment. The uncertainty is defined over the changing environmental condition from static to dynamic. The attraction of one firefly towards the other firefly due to variation of their brightness is the key concept of the proposed study. The proposed controller efficiently explores the environment and improves the global search in less number of iterations and hence it can be easily implemented for real time obstacle avoidance especially for dynamic environment. It solves the challenges of navigation, minimizes the computational calculations, and avoids random moving of fireflies. The performance of proposed controller is better in terms of path optimality when compared to other intelligent navigational approaches.展开更多
针对双向快速随机扩展树(rapidly-exploring random trees-connect,RRT-Connect)算法的随机性强、搜索效率低、路径规划时间过长等问题,提出一种改进的RRT-Connect算法。该算法在起始点与目标点连线的中垂线上设置第三节点,采用高斯分...针对双向快速随机扩展树(rapidly-exploring random trees-connect,RRT-Connect)算法的随机性强、搜索效率低、路径规划时间过长等问题,提出一种改进的RRT-Connect算法。该算法在起始点与目标点连线的中垂线上设置第三节点,采用高斯分布限制第三节点的采样区域,避免第三采样节点距离中点较远导致的路径冗余。算法通过第三节点分别向起始点和目标点生成2棵随机树,结合贪婪算法思想以及引入动态步长的方法,提高算法的规划效率。仿真结果表明,改进的RRT-Connect算法相较于传统RRT-Connect算法,平均运行时间缩短了48.7%,平均迭代次数减少了38.9%,平均路径长度减少了25.2%。另外,针对传统的九点标定法精度的问题,提出一种改进的九点标定方法,该方法通过获取机械臂在空间同一点的多组位姿计算机械臂第六轴长度,在已知机械臂各关节角和轴长情况下,计算得到机械臂末端执行器安装后第六轴的长度,从而提高手眼标定的精度。试验结果表明,改进的方法相较于传统九点标定法其精度平均提高了2.09%。最后,在机械臂平台验证改进的RRT-Connect算法和改进的九点标定法,试验结果表明,改进的RRT-Connect算法相较于DRRT-Connect(dynamicRRT-Connect)算法在路径规划总时间和总长度上分别减少了8.28%和4.79%,改进的九点标定法相较于传统的九点标定法抓取精度提高了3%。展开更多
针对城市场景下载人电动垂直起降飞行器(electric vertical takeoff and landing,eVTOL)路径规划问题进行了研究。首先,使用危险度栅格法进行三维城市空间建模,对选定型号的eVTOL飞行器,以航程、运行风险和高度变化为目标函数,结合飞行...针对城市场景下载人电动垂直起降飞行器(electric vertical takeoff and landing,eVTOL)路径规划问题进行了研究。首先,使用危险度栅格法进行三维城市空间建模,对选定型号的eVTOL飞行器,以航程、运行风险和高度变化为目标函数,结合飞行器自身特性及环境限制,构建了多约束条件的载人eVTOL路径规划模型。然后,设计了一种改进人工电场算法(im-proved artificial electric field algorithm,IAEFA),在传统人工电场算法(artificial electric field algorithm,AEFA)的基础上增加了自适应库伦参数,并在库伦常数的计算中引入递减系数,以此进行仿真求解。实验结果显示,所构建的模型可以达到预期效果。使用改进算法进行路径规划的求解效果更优,相较传统粒子群算法和人工电场法,航程更短,高度变化更小且运行更为安全。最后,根据对照实验确定递减系数的取值,当递减系数取值为1.5时,改进算法的求解效果最优。展开更多
文摘A novel method of global optimal path planning for mobile robot was proposed based on the improved Dijkstra algorithm and ant system algorithm. This method includes three steps: the first step is adopting the MAKLINK graph theory to establish the free space model of the mobile robot, the second step is adopting the improved Dijkstra algorithm to find out a sub-optimal collision-free path, and the third step is using the ant system algorithm to adjust and optimize the location of the sub-optimal path so as to generate the global optimal path for the mobile robot. The computer simulation experiment was carried out and the results show that this method is correct and effective. The comparison of the results confirms that the proposed method is better than the hybrid genetic algorithm in the global optimal path planning.
基金Project(61173032)supported by the National Natural Science Foundation of ChinaProject(20090406)supported by the Tianjin Scientific and Technological Development Fund of Higher Education of China
文摘The utilization of biomimicry of bacterial foraging strategy was considered to develop an adaptive control strategy for mobile robot, and a bacterial foraging approach was proposed for robot path planning. In the proposed model, robot that mimics the behavior of bacteria is able to determine an optimal collision-free path between a start and a target point in the environment surrounded by obstacles. In the simulation, two test scenarios of static environment with different number obstacles were adopted to evaluate the performance of the proposed method. Simulation results show that the robot which reflects the bacterial foraging behavior can adapt to complex environments in the planned trajectories with both satisfactory accuracy and stability.
文摘This paper presents the rigorous study of mobile robot navigation techniques used so far.The step by step investigations of classical and reactive approaches are made here to understand the development of path planning strategies in various environmental conditions and to identify research gap.The classical approaches such as cell decomposition(CD),roadmap approach(RA),artificial potential field(APF);reactive approaches such as genetic algorithm(GA),fuzzy logic(FL),neural network(NN),firefly algorithm(FA),particle swarm optimization(PSO),ant colony optimization(ACO),bacterial foraging optimization(BFO),artificial bee colony(ABC),cuckoo search(CS),shuffled frog leaping algorithm(SFLA)and other miscellaneous algorithms(OMA)are considered for study.The navigation over static and dynamic condition is analyzed(for single and multiple robot systems)and it has been observed that the reactive approaches are more robust and perform well in all terrain when compared to classical approaches.It is also observed that the reactive approaches are used to improve the performance of the classical approaches as a hybrid algorithm.Hence,reactive approaches are more popular and widely used for path planning of mobile robot.The paper concludes with tabular data and charts comparing the frequency of individual navigational strategies which can be used for specific application in robotics.
基金Supported by National Natural Science Foundation of P.R.China(50275150)National Research Foundation for the Doctoral Program of Higher Education of P.R.China(20040533035)
文摘In this paper,a comparative study of the path planning problem using evolutionary algorithms,in comparison with classical methods such as the A*algorithm,is presented for a holonomic mobile robot.The configured navigation system,which consists of the integration of sensors sources,map formatting,global and local path planners,and the base controller,aims to enable the robot to follow the shortest smooth path delicately.Grid-based mapping is used for scoring paths efficiently,allowing the determination of collision-free trajectories from the initial to the target position.This work considers the evolutionary algorithms,the mutated cuckoo optimization algorithm(MCOA)and the genetic algorithm(GA),as a global planner to find the shortest safe path among others.A non-uniform motion coefficient is introduced for MCOA in order to increase the performance of this algorithm.A series of experiments are accomplished and analyzed to confirm the performance of the global planner implemented on a holonomic mobile robot.The results of the experiments show the capacity of the planner framework with respect to the path planning problem under various obstacle layouts.
基金supported by the National Natural Science Foundation of China (62173251)the“Zhishan”Scholars Programs of Southeast University+1 种基金the Fundamental Research Funds for the Central UniversitiesShanghai Gaofeng&Gaoyuan Project for University Academic Program Development (22120210022)
文摘Motion planning is critical to realize the autonomous operation of mobile robots.As the complexity and randomness of robot application scenarios increase,the planning capability of the classical hierarchical motion planners is challenged.With the development of machine learning,the deep reinforcement learning(DRL)-based motion planner has gradually become a research hotspot due to its several advantageous feature.The DRL-based motion planner is model-free and does not rely on the prior structured map.Most importantly,the DRL-based motion planner achieves the unification of the global planner and the local planner.In this paper,we provide a systematic review of various motion planning methods.Firstly,we summarize the representative and state-of-the-art works for each submodule of the classical motion planning architecture and analyze their performance features.Then,we concentrate on summarizing reinforcement learning(RL)-based motion planning approaches,including motion planners combined with RL improvements,map-free RL-based motion planners,and multi-robot cooperative planning methods.Finally,we analyze the urgent challenges faced by these mainstream RLbased motion planners in detail,review some state-of-the-art works for these issues,and propose suggestions for future research.
文摘Path planning of a mobile robot in the presence of multiple moving obstacles is found to be a complicated problem.A planning algorithm capable of negotiating both static and moving obstacles in an unpredictable(on-line)environment is proposed.The proposed incremental algorithm plans the path by considering the quadrants in which the current positions of obstacles as well as target are situated.Also,the governing equations for the shortest path are derived.The proposed mathematical model describes the motion(satisfying constraints of the mobile robot)along a collision-free path.Further,the algorithm is applicable to dynamic environments with fixed or moving targets.Simulation results show the effectiveness of the proposed algorithm.Comparison of results with the improved artificial potential field(iAPF)algorithm shows that the proposed algorithm yields shorter path length with less computation time.
基金Projects(60234030, 60404021) supported by the National Natural Science Foundation of China
文摘Ant colony optimization (ACO) algorithm was modified to optimize the global path. In order to simulate the real ant colonies, according to the foraging behavior of ant colonies and the characteristic of food, conceptions of neighboring area and smell area were presented. The former can ensure the diversity of paths and the latter ensures that each ant can reach the goal. Then the whole path was divided into three parts and ACO was used to search the second part path. When the three parts pathes were adjusted, the final path was found. The valid path and invalid path were defined to ensure the path valid. Finally, the strategies of the pheromone search were applied to search the optimum path. However, when only the pheromone was used to search the optimum path, ACO converges easily. In order to avoid this premature convergence, combining pheromone search and random search, a hybrid ant colony algorithm(HACO) was used to find the optimum path. The comparison between ACO and HACO shows that HACO can be used to find the shortest path.
基金Project(60475035) supported by the National Natural Science Foundation of China
文摘To solve dynamic obstacle avoidance problems, a novel algorithm was put forward with the advantages of wireless sensor network (WSN). In view of moving velocity and direction of both the obstacles and robots, a mathematic model was built based on the exposure model, exposure direction and critical speeds of sensors. Ant colony optimization (ACO) algorithm based on bionic swarm intelligence was used for solution of the multi-objective optimization. Energy consumption and topology of the WSN were also discussed. A practical implementation with real WSN and real mobile robots were carried out. In environment with multiple obstacles, the convergence curve of the shortest path length shows that as iterative generation grows, the length of the shortest path decreases and finally reaches a stable and optimal value. Comparisons show that using sensor information fusion can greatly improve the accuracy in comparison with single sensor. The successful path of robots without collision validates the efficiency, stability and accuracy of the proposed algorithm, which is proved to be better than tradition genetic algorithm (GA) for dynamic obstacle avoidance in real time.
基金Foundation of the Robotics Laboratory, Chinese Academy of Sciences (No: RL200002)
文摘Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot′s hand and does not change the number of the path′s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.
基金FoundationoftheRoboticsLaboratoryChineseAcademyofSciences (No :RL2 0 0 0 0 2 )
文摘Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method resulted in the heavier on line computational burden for the robot controller. In this paper, aiming at this drawback, the authors propose a new kind of real time accurate hand path tracking and joint trajectory planning method for robots. Through selecting some extra knots on the specified hand path by a certain rule, which enables the number of knots on each segment to increase from two to four, and through introducing a sinusoidal function and a cosinoidal function to the joint displacement equation of each segment, this method can raise the path tracking accuracy of robot′s hand greatly but does not increase the computational burden of robot controller markedly.
文摘Autonomous mobile robot navigation is one of the most emerging areas of research by using swarm intelligence. Path planning and obstacle avoidance are most researched current topics like navigational challenges for mobile robot. The paper presents application and implementation of Firefly Algorithm(FA)for Mobile Robot Navigation(MRN) in uncertain environment. The uncertainty is defined over the changing environmental condition from static to dynamic. The attraction of one firefly towards the other firefly due to variation of their brightness is the key concept of the proposed study. The proposed controller efficiently explores the environment and improves the global search in less number of iterations and hence it can be easily implemented for real time obstacle avoidance especially for dynamic environment. It solves the challenges of navigation, minimizes the computational calculations, and avoids random moving of fireflies. The performance of proposed controller is better in terms of path optimality when compared to other intelligent navigational approaches.
文摘针对双向快速随机扩展树(rapidly-exploring random trees-connect,RRT-Connect)算法的随机性强、搜索效率低、路径规划时间过长等问题,提出一种改进的RRT-Connect算法。该算法在起始点与目标点连线的中垂线上设置第三节点,采用高斯分布限制第三节点的采样区域,避免第三采样节点距离中点较远导致的路径冗余。算法通过第三节点分别向起始点和目标点生成2棵随机树,结合贪婪算法思想以及引入动态步长的方法,提高算法的规划效率。仿真结果表明,改进的RRT-Connect算法相较于传统RRT-Connect算法,平均运行时间缩短了48.7%,平均迭代次数减少了38.9%,平均路径长度减少了25.2%。另外,针对传统的九点标定法精度的问题,提出一种改进的九点标定方法,该方法通过获取机械臂在空间同一点的多组位姿计算机械臂第六轴长度,在已知机械臂各关节角和轴长情况下,计算得到机械臂末端执行器安装后第六轴的长度,从而提高手眼标定的精度。试验结果表明,改进的方法相较于传统九点标定法其精度平均提高了2.09%。最后,在机械臂平台验证改进的RRT-Connect算法和改进的九点标定法,试验结果表明,改进的RRT-Connect算法相较于DRRT-Connect(dynamicRRT-Connect)算法在路径规划总时间和总长度上分别减少了8.28%和4.79%,改进的九点标定法相较于传统的九点标定法抓取精度提高了3%。
文摘针对城市场景下载人电动垂直起降飞行器(electric vertical takeoff and landing,eVTOL)路径规划问题进行了研究。首先,使用危险度栅格法进行三维城市空间建模,对选定型号的eVTOL飞行器,以航程、运行风险和高度变化为目标函数,结合飞行器自身特性及环境限制,构建了多约束条件的载人eVTOL路径规划模型。然后,设计了一种改进人工电场算法(im-proved artificial electric field algorithm,IAEFA),在传统人工电场算法(artificial electric field algorithm,AEFA)的基础上增加了自适应库伦参数,并在库伦常数的计算中引入递减系数,以此进行仿真求解。实验结果显示,所构建的模型可以达到预期效果。使用改进算法进行路径规划的求解效果更优,相较传统粒子群算法和人工电场法,航程更短,高度变化更小且运行更为安全。最后,根据对照实验确定递减系数的取值,当递减系数取值为1.5时,改进算法的求解效果最优。
