In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms...In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.展开更多
To improve the efficiency and accuracy of path planning for fan inspection tasks in thermal power plants,this paper proposes an intelligent inspection robot path planning scheme based on an improved A^(*)algorithm.The...To improve the efficiency and accuracy of path planning for fan inspection tasks in thermal power plants,this paper proposes an intelligent inspection robot path planning scheme based on an improved A^(*)algorithm.The inspection robot utilizes multiple sensors to monitor key parameters of the fans,such as vibration,noise,and bearing temperature,and upload the data to the monitoring center.The robot’s inspection path employs the improved A^(*)algorithm,incorporating obstacle penalty terms,path reconstruction,and smoothing optimization techniques,thereby achieving optimal path planning for the inspection robot in complex environments.Simulation results demonstrate that the improved A^(*)algorithm significantly outperforms the traditional A^(*)algorithm in terms of total path distance,smoothness,and detour rate,effectively improving the execution efficiency of inspection tasks.展开更多
The traditional A^(*)algorithm exhibits a low efficiency in the path planning of unmanned surface vehicles(USVs).In addition,the path planned presents numerous redundant inflection waypoints,and the security is low,wh...The traditional A^(*)algorithm exhibits a low efficiency in the path planning of unmanned surface vehicles(USVs).In addition,the path planned presents numerous redundant inflection waypoints,and the security is low,which is not conducive to the control of USV and also affects navigation safety.In this paper,these problems were addressed through the following improvements.First,the path search angle and security were comprehensively considered,and a security expansion strategy of nodes based on the 5×5 neighborhood was proposed.The A^(*)algorithm search neighborhood was expanded from 3×3 to 5×5,and safe nodes were screened out for extension via the node security expansion strategy.This algorithm can also optimize path search angles while improving path security.Second,the distance from the current node to the target node was introduced into the heuristic function.The efficiency of the A^(*)algorithm was improved,and the path was smoothed using the Floyd algorithm.For the dynamic adjustment of the weight to improve the efficiency of DWA,the distance from the USV to the target point was introduced into the evaluation function of the dynamic-window approach(DWA)algorithm.Finally,combined with the local target point selection strategy,the optimized DWA algorithm was performed for local path planning.The experimental results show the smooth and safe path planned by the fusion algorithm,which can successfully avoid dynamic obstacles and is effective and feasible in path planning for USVs.展开更多
To address the shortcomings of traditional Genetic Algorithm (GA) in multi-agent path planning, such as prolonged planning time, slow convergence, and solution instability, this paper proposes an Asynchronous Genetic ...To address the shortcomings of traditional Genetic Algorithm (GA) in multi-agent path planning, such as prolonged planning time, slow convergence, and solution instability, this paper proposes an Asynchronous Genetic Algorithm (AGA) to solve multi-agent path planning problems effectively. To enhance the real-time performance and computational efficiency of Multi-Agent Systems (MAS) in path planning, the AGA incorporates an Equal-Size Clustering Algorithm (ESCA) based on the K-means clustering method. The ESCA divides the primary task evenly into a series of subtasks, thereby reducing the gene length in the subsequent GA process. The algorithm then employs GA to solve each subtask sequentially. To evaluate the effectiveness of the proposed method, a simulation program was designed to perform path planning for 100 trajectories, and the results were compared with those of State-Of-The-Art (SOTA) methods. The simulation results demonstrate that, although the solutions provided by AGA are suboptimal, it exhibits significant advantages in terms of execution speed and solution stability compared to other algorithms.展开更多
Aiming to address the limitations of the standard Chimp Optimization Algorithm(ChOA),such as inadequate search ability and susceptibility to local optima in Unmanned Aerial Vehicle(UAV)path planning,this paper propose...Aiming to address the limitations of the standard Chimp Optimization Algorithm(ChOA),such as inadequate search ability and susceptibility to local optima in Unmanned Aerial Vehicle(UAV)path planning,this paper proposes a three-dimensional path planning method for UAVs based on the Improved Chimp Optimization Algorithm(IChOA).First,this paper models the terrain and obstacle environments spatially and formulates the total UAV flight cost function according to the constraints,transforming the path planning problem into an optimization problem with multiple constraints.Second,this paper enhances the diversity of the chimpanzee population by applying the Sine chaos mapping strategy and introduces a nonlinear convergence factor to improve the algorithm’s search accuracy and convergence speed.Finally,this paper proposes a dynamic adjustment strategy for the number of chimpanzee advance echelons,which effectively balances global exploration and local exploitation,significantly optimizing the algorithm’s search performance.To validate the effectiveness of the IChOA algorithm,this paper conducts experimental comparisons with eight different intelligent algorithms.The experimental results demonstrate that the IChOA outperforms the selected comparison algorithms in terms of practicality and robustness in UAV 3D path planning.It effectively solves the issues of efficiency in finding the shortest path and ensures high stability during execution.展开更多
An improved version of the sparse A^(*)algorithm is proposed to address the common issue of excessive expansion of nodes and failure to consider current ship status and parameters in traditional path planning algorith...An improved version of the sparse A^(*)algorithm is proposed to address the common issue of excessive expansion of nodes and failure to consider current ship status and parameters in traditional path planning algorithms.This algorithm considers factors such as initial position and orientation of the ship,safety range,and ship draft to determine the optimal obstacle-avoiding route from the current to the destination point for ship planning.A coordinate transformation algorithm is also applied to convert commonly used latitude and longitude coordinates of ship travel paths to easily utilized and analyzed Cartesian coordinates.The algorithm incorporates a hierarchical chart processing algorithm to handle multilayered chart data.Furthermore,the algorithm considers the impact of ship length on grid size and density when implementing chart gridification,adjusting the grid size and density accordingly based on ship length.Simulation results show that compared to traditional path planning algorithms,the sparse A^(*)algorithm reduces the average number of path points by 25%,decreases the average maximum storage node number by 17%,and raises the average path turning angle by approximately 10°,effectively improving the safety of ship planning paths.展开更多
To tackle the path planning problem,this study introduced a novel algorithm called two-stage parameter adjustment-based differential evolution(TPADE).This algorithm draws inspiration from group behavior to implement a...To tackle the path planning problem,this study introduced a novel algorithm called two-stage parameter adjustment-based differential evolution(TPADE).This algorithm draws inspiration from group behavior to implement a two-stage scaling factor variation strategy.In the initial phase,it adapts according to environmental complexity.In the following phase,it combines individual and global experiences to fine-tune the orientation factor,effectively improving its global search capability.Furthermore,this study developed a new population update method,ensuring that well-adapted individuals are retained,which enhances population diversity.In benchmark function tests across different dimensions,the proposed algorithm consistently demonstrates superior convergence accuracy and speed.This study also tested the TPADE algorithm in path planning simulations.The experimental results reveal that the TPADE algorithm outperforms existing algorithms by achieving path lengths of 28.527138 and 31.963990 in simple and complex map environments,respectively.These findings indicate that the proposed algorithm is more adaptive and efficient in path planning.展开更多
For autonomous Unmanned Aerial Vehicles(UAVs)flying in real-world scenarios,time for path planning is always limited,which is a challenge known as the anytime problem.Anytime planners address this by finding a collisi...For autonomous Unmanned Aerial Vehicles(UAVs)flying in real-world scenarios,time for path planning is always limited,which is a challenge known as the anytime problem.Anytime planners address this by finding a collision-free path quickly and then improving it until time runs out,making UAVs more adaptable to different mission scenarios.However,current anytime algorithms based on A^(*)have insufficient control over the suboptimality bounds of paths and tend to lose their anytime properties in environments with large concave obstacles.This paper proposes a novel anytime path planning algorithm,Anytime Radiation A^(*)(ARa A^(*)),which can generate a series of suboptimal paths with improved bounds through decreasing search step sizes and can generate the optimal path when time is sufficient.The ARa A^(*)features two main innovations:an adaptive variable-step-size mechanism and elliptic constraints based on waypoints.The former helps achieve fast path searching in various environments.The latter allows ARa A^(*)to control the suboptimality bounds of paths and further enhance search efficiency.Simulation experiments show that the ARa A^(*)outperforms Anytime Repairing A^(*)(ARA^(*))and Anytime D^(*)(AD^(*))in controlling suboptimality bounds and planning time,especially in environments with large concave obstacles.Final flight experiments demonstrate that the paths planned by ARa A^(*)can ensure the safe flight of quadrotors.展开更多
Solving the path planning problem of Autonomous Underwater Vehicles(AUVs)is crucial for reducing energy waste and improving operational efficiency.However,two main challenges hinder further development:Firstly,existin...Solving the path planning problem of Autonomous Underwater Vehicles(AUVs)is crucial for reducing energy waste and improving operational efficiency.However,two main challenges hinder further development:Firstly,existing algorithms often treat this as a single-objective optimization problem,whereas in reality,it should be multi-objective,considering factors such as distance,safety,and smoothness simultaneously.Secondly,the limited availability of optimization results arises due to they are single-path,which fail to meet real-world conditions.To address these challenges,first of all,an improved AUV path planning model is proposed,in which the collisions of path and obstacles are classified more specifically.Subsequently,a novel Altruistic Nurturing Algorithm(ANA)inspired by natural altruism is introduced.In the algorithm,nurturing cost considering Pareto rank and crowd distance is introduced as guidance of evolution to avoid futile calculation,abandonment threshold is self-adaptive with descendant situation to help individuals escape from local optima and double selection strategy combining crowd and k-nearest neighbors selection helps to get a better-distributed Pareto front.Experimental results comparing ANA with existing algorithms in AUV path planning demonstrate its superiority.Finally,a user-friendly interface,the Multi-Objective AUV Path Planner,is designed to provide users with a group of paths for informed decisionmaking.展开更多
In the current era of intelligent technologies,comprehensive and precise regional coverage path planning is critical for tasks such as environmental monitoring,emergency rescue,and agricultural plant protection.Owing ...In the current era of intelligent technologies,comprehensive and precise regional coverage path planning is critical for tasks such as environmental monitoring,emergency rescue,and agricultural plant protection.Owing to their exceptional flexibility and rapid deployment capabilities,unmanned aerial vehicles(UAVs)have emerged as the ideal platforms for accomplishing these tasks.This study proposes a swarm A^(*)-guided Deep Q-Network(SADQN)algorithm to address the coverage path planning(CPP)problem for UAV swarms in complex environments.Firstly,to overcome the dependency of traditional modeling methods on regular terrain environments,this study proposes an improved cellular decomposition method for map discretization.Simultaneously,a distributed UAV swarm system architecture is adopted,which,through the integration of multi-scale maps,addresses the issues of redundant operations and flight conflicts inmulti-UAV cooperative coverage.Secondly,the heuristic mechanism of the A^(*)algorithmis combinedwith full-coverage path planning,and this approach is incorporated at the initial stage ofDeep Q-Network(DQN)algorithm training to provide effective guidance in action selection,thereby accelerating convergence.Additionally,a prioritized experience replay mechanism is introduced to further enhance the coverage performance of the algorithm.To evaluate the efficacy of the proposed algorithm,simulation experiments were conducted in several irregular environments and compared with several popular algorithms.Simulation results show that the SADQNalgorithmoutperforms othermethods,achieving performance comparable to that of the baseline prior algorithm,with an average coverage efficiency exceeding 2.6 and fewer turning maneuvers.In addition,the algorithm demonstrates excellent generalization ability,enabling it to adapt to different environments.展开更多
To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO al...To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and inte-grates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evo-lution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection opti-mization of paths, gradually reducing algorithmic space, accele-rating convergence, and enhances path cooperativity. Simula-tion experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demon-strate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. More-over it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collabora-tive path planning. The experiments are conducted in three col-laborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality.展开更多
The path planning problem of complex wild environment with multiple elements still poses challenges.This paper designs an algorithm that integrates global and local planning to apply to the wild environmental path pla...The path planning problem of complex wild environment with multiple elements still poses challenges.This paper designs an algorithm that integrates global and local planning to apply to the wild environmental path planning.The modeling process of wild environment map is designed.Three optimization strategies are designed to improve the A-Star in overcoming the problems of touching the edge of obstacles,redundant nodes and twisting paths.A new weighted cost function is designed to achieve different planning modes.Furthermore,the improved dynamic window approach(DWA)is designed to avoid local optimality and improve time efficiency compared to traditional DWA.For the necessary path re-planning of wild environment,the improved A-Star is integrated with the improved DWA to solve re-planning problem of unknown and moving obstacles in wild environment with multiple elements.The improved fusion algorithm effectively solves problems and consumes less time,and the simulation results verify the effectiveness of improved algorithms above.展开更多
In order to solve the problem of path planning of tower cranes,an improved ant colony algorithm was proposed.Firstly,the tower crane was simplified into a three-degree-of-freedom mechanical arm,and the D-H motion mode...In order to solve the problem of path planning of tower cranes,an improved ant colony algorithm was proposed.Firstly,the tower crane was simplified into a three-degree-of-freedom mechanical arm,and the D-H motion model was established to solve the forward and inverse kinematic equations.Secondly,the traditional ant colony algorithm was improved.The heuristic function was improved by introducing the distance between the optional nodes and the target point into the function.Then the transition probability was improved by introducing the security factor of surrounding points into the transition probability.In addition,the local path chunking strategy was used to optimize the local multi-inflection path and reduce the local redundant inflection points.Finally,according to the position of the hook,the kinematic inversion of the tower crane was carried out,and the variables of each joint were obtained.More specifically,compared with the traditional ant colony algorithm,the simulation results showed that improved ant colony algorithm converged faster,shortened the optimal path length,and optimized the path quality in the simple and complex environment.展开更多
Unmanned aerial vehicle(UAV)paths in the field directly affect the efficiency and accuracy of payload data collection.Path planning of UAV advancing along river valleys in wild environments is one of the first and mos...Unmanned aerial vehicle(UAV)paths in the field directly affect the efficiency and accuracy of payload data collection.Path planning of UAV advancing along river valleys in wild environments is one of the first and most difficult problems faced by unmanned surveys of debris flow valleys.This study proposes a new hybrid bat optimization algorithm,GRE-Bat(Good point set,Reverse learning,Elite Pool-Bat algorithm),for unmanned exploration path planning of debris flow sources in outdoor environments.In the GRE-Bat algorithm,the good point set strategy is adopted to evenly distribute the population,ensure sufficient coverage of the search space,and improve the stability of the convergence accuracy of the algorithm.Subsequently,a reverse learning strategy is introduced to increase the diversity of the population and improve the local stagnation problem of the algorithm.In addition,an Elite pool strategy is added to balance the replacement and learning behaviors of particles within the population based on elimination and local perturbation factors.To demonstrate the effectiveness of the GRE-Bat algorithm,we conducted multiple simulation experiments using benchmark test functions and digital terrain models.Compared to commonly used path planning algorithms such as the Bat Algorithm(BA)and the Improved Sparrow Search Algorithm(ISSA),the GRE-Bat algorithm can converge to the optimal value in different types of test functions and obtains a near-optimal solution after an average of 60 iterations.The GRE-Bat algorithm can obtain higher quality flight routes in the designated environment of unmanned investigation in the debris flow gully basin,demonstrating its potential for practical application.展开更多
Reducing casualties and property losses through effective evacuation route planning has been a key focus for researchers in recent years.As part of this effort,an enhanced sparrow search algorithm(MSSA)was proposed.Fi...Reducing casualties and property losses through effective evacuation route planning has been a key focus for researchers in recent years.As part of this effort,an enhanced sparrow search algorithm(MSSA)was proposed.Firstly,the Golden Sine algorithm and a nonlinear weight factor optimization strategy were added in the discoverer position update stage of the SSA algorithm.Secondly,the Cauchy-Gaussian perturbation was applied to the optimal position of the SSA algorithm to improve its ability to jump out of local optima.Finally,the local search mechanism based on the mountain climbing method was incorporated into the local search stage of the SSA algorithm,improving its local search ability.To evaluate the effectiveness of the proposed algorithm,the Whale Algorithm,Gray Wolf Algorithm,Improved Gray Wolf Algorithm,Sparrow Search Algorithm,and MSSA Algorithm were employed to solve various test functions.The accuracy and convergence speed of each algorithm were then compared and analyzed.The results indicate that the MSSA algorithm has superior solving ability and stability compared to other algorithms.To further validate the enhanced algorithm’s capabilities for path planning,evacuation experiments were conducted using different maps featuring various obstacle types.Additionally,a multi-exit evacuation scenario was constructed according to the actual building environment of a teaching building.Both the sparrow search algorithm and MSSA algorithm were employed in the simulation experiment for multiexit evacuation path planning.The findings demonstrate that the MSSA algorithm outperforms the comparison algorithm,showcasing its greater advantages and higher application potential.展开更多
The burgeoning robotics industry has catalyzed significant strides in the development and deployment of industrial and service robotic arms, positioning path planning as a pivotal facet for augmenting their operationa...The burgeoning robotics industry has catalyzed significant strides in the development and deployment of industrial and service robotic arms, positioning path planning as a pivotal facet for augmenting their operational safety and efficiency. Existing path planning algorithms, while capable of delineating feasible trajectories, often fall short of achieving optimality, particularly concerning path length, search duration, and success likelihood. This study introduces an enhanced Rapidly-Exploring Random Tree (RRT) algorithm, meticulously designed to rectify the issues of node redundancy and the compromised path quality endemic to conventional RRT approaches. Through the integration of an adaptive pruning mechanism and a dynamic elliptical search strategy within the Informed RRT* framework, our algorithm efficiently refines the search tree by discarding branches that surpass the cost of the optimal path, thereby refining the search space and significantly boosting efficiency. Extensive comparative analysis across both two-dimensional and three-dimensional simulation settings underscores the algorithm’s proficiency in markedly improving path precision and search velocity, signifying a breakthrough in the domain of robotic arm path planning.展开更多
This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to del...This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.展开更多
Effective path planning is crucial for mobile robots to quickly reach rescue destination and complete rescue tasks in a post-disaster scenario.In this study,we investigated the post-disaster rescue path planning probl...Effective path planning is crucial for mobile robots to quickly reach rescue destination and complete rescue tasks in a post-disaster scenario.In this study,we investigated the post-disaster rescue path planning problem and modeled this problem as a variant of the travel salesman problem(TSP)with life-strength constraints.To address this problem,we proposed an improved iterated greedy(IIG)algorithm.First,a push-forward insertion heuristic(PFIH)strategy was employed to generate a high-quality initial solution.Second,a greedy-based insertion strategy was designed and used in the destruction-construction stage to increase the algorithm’s exploration ability.Furthermore,three problem-specific swap operators were developed to improve the algorithm’s exploitation ability.Additionally,an improved simulated annealing(SA)strategy was used as an acceptance criterion to effectively prevent the algorithm from falling into local optima.To verify the effectiveness of the proposed algorithm,the Solomon dataset was extended to generate 27 instances for simulation.Finally,the proposed IIG was compared with five state-of-the-art algorithms.The parameter analysiswas conducted using the design of experiments(DOE)Taguchi method,and the effectiveness analysis of each component has been verified one by one.Simulation results indicate that IIGoutperforms the compared algorithms in terms of the number of rescue survivors and convergence speed,proving the effectiveness of the proposed algorithm.展开更多
This study focuses on the improvement of path planning efficiency for underwater gravity-aided navigation.Firstly,a Depth Sorting Fast Search(DSFS)algorithm was proposed to improve the planning speed of the Quick Rapi...This study focuses on the improvement of path planning efficiency for underwater gravity-aided navigation.Firstly,a Depth Sorting Fast Search(DSFS)algorithm was proposed to improve the planning speed of the Quick Rapidly-exploring Random Trees*(Q-RRT*)algorithm.A cost inequality relationship between an ancestor and its descendants was derived,and the ancestors were filtered accordingly.Secondly,the underwater gravity-aided navigation path planning system was designed based on the DSFS algorithm,taking into account the fitness,safety,and asymptotic optimality of the routes,according to the gravity suitability distribution of the navigation space.Finally,experimental comparisons of the computing performance of the ChooseParent procedure,the Rewire procedure,and the combination of the two procedures for Q-RRT*and DSFS were conducted under the same planning environment and parameter conditions,respectively.The results showed that the computational efficiency of the DSFS algorithm was improved by about 1.2 times compared with the Q-RRT*algorithm while ensuring correct computational results.展开更多
A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; s...A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; secondly, select one of the critical paths of the partially clustered directed acyclic graph; thirdly, try to zero one of graph communication edges; fourthly, repeat above three processes until all edges are zeroed; finally, check the generated clusters to see if some of them can be further merged without increasing the parallel time. Comparisons of the previous algorithms with edge-zeroing based on dynamic critical paths show that the new algorithm has not only a low complexity but also a desired performance comparable or even better on average to much higher complexity heuristic algorithms.展开更多
基金supported by the National Natural Science Foundation of China(No.62373027).
文摘In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.
文摘To improve the efficiency and accuracy of path planning for fan inspection tasks in thermal power plants,this paper proposes an intelligent inspection robot path planning scheme based on an improved A^(*)algorithm.The inspection robot utilizes multiple sensors to monitor key parameters of the fans,such as vibration,noise,and bearing temperature,and upload the data to the monitoring center.The robot’s inspection path employs the improved A^(*)algorithm,incorporating obstacle penalty terms,path reconstruction,and smoothing optimization techniques,thereby achieving optimal path planning for the inspection robot in complex environments.Simulation results demonstrate that the improved A^(*)algorithm significantly outperforms the traditional A^(*)algorithm in terms of total path distance,smoothness,and detour rate,effectively improving the execution efficiency of inspection tasks.
基金Supported by the EDD of China(No.80912020104)the Science and Technology Commission of Shanghai Municipality(No.22ZR1427700 and No.23692106900).
文摘The traditional A^(*)algorithm exhibits a low efficiency in the path planning of unmanned surface vehicles(USVs).In addition,the path planned presents numerous redundant inflection waypoints,and the security is low,which is not conducive to the control of USV and also affects navigation safety.In this paper,these problems were addressed through the following improvements.First,the path search angle and security were comprehensively considered,and a security expansion strategy of nodes based on the 5×5 neighborhood was proposed.The A^(*)algorithm search neighborhood was expanded from 3×3 to 5×5,and safe nodes were screened out for extension via the node security expansion strategy.This algorithm can also optimize path search angles while improving path security.Second,the distance from the current node to the target node was introduced into the heuristic function.The efficiency of the A^(*)algorithm was improved,and the path was smoothed using the Floyd algorithm.For the dynamic adjustment of the weight to improve the efficiency of DWA,the distance from the USV to the target point was introduced into the evaluation function of the dynamic-window approach(DWA)algorithm.Finally,combined with the local target point selection strategy,the optimized DWA algorithm was performed for local path planning.The experimental results show the smooth and safe path planned by the fusion algorithm,which can successfully avoid dynamic obstacles and is effective and feasible in path planning for USVs.
文摘To address the shortcomings of traditional Genetic Algorithm (GA) in multi-agent path planning, such as prolonged planning time, slow convergence, and solution instability, this paper proposes an Asynchronous Genetic Algorithm (AGA) to solve multi-agent path planning problems effectively. To enhance the real-time performance and computational efficiency of Multi-Agent Systems (MAS) in path planning, the AGA incorporates an Equal-Size Clustering Algorithm (ESCA) based on the K-means clustering method. The ESCA divides the primary task evenly into a series of subtasks, thereby reducing the gene length in the subsequent GA process. The algorithm then employs GA to solve each subtask sequentially. To evaluate the effectiveness of the proposed method, a simulation program was designed to perform path planning for 100 trajectories, and the results were compared with those of State-Of-The-Art (SOTA) methods. The simulation results demonstrate that, although the solutions provided by AGA are suboptimal, it exhibits significant advantages in terms of execution speed and solution stability compared to other algorithms.
基金supported by the Shaanxi Province Natural Science Basic Research Program Project(2024JC-YBMS-572)partially funded by Yan’an University Graduate Education Innovation Program Project(YCX2023032,YCX2023033,YCX2024094,YCX2024097)the“14th Five Year Plan Medium and Long Term Major Scientific Research Project”(2021ZCQ015)of Yan’an University.
文摘Aiming to address the limitations of the standard Chimp Optimization Algorithm(ChOA),such as inadequate search ability and susceptibility to local optima in Unmanned Aerial Vehicle(UAV)path planning,this paper proposes a three-dimensional path planning method for UAVs based on the Improved Chimp Optimization Algorithm(IChOA).First,this paper models the terrain and obstacle environments spatially and formulates the total UAV flight cost function according to the constraints,transforming the path planning problem into an optimization problem with multiple constraints.Second,this paper enhances the diversity of the chimpanzee population by applying the Sine chaos mapping strategy and introduces a nonlinear convergence factor to improve the algorithm’s search accuracy and convergence speed.Finally,this paper proposes a dynamic adjustment strategy for the number of chimpanzee advance echelons,which effectively balances global exploration and local exploitation,significantly optimizing the algorithm’s search performance.To validate the effectiveness of the IChOA algorithm,this paper conducts experimental comparisons with eight different intelligent algorithms.The experimental results demonstrate that the IChOA outperforms the selected comparison algorithms in terms of practicality and robustness in UAV 3D path planning.It effectively solves the issues of efficiency in finding the shortest path and ensures high stability during execution.
基金Supported by the Tianjin University of Technology Graduate R esearch Innovation Project(YJ2281).
文摘An improved version of the sparse A^(*)algorithm is proposed to address the common issue of excessive expansion of nodes and failure to consider current ship status and parameters in traditional path planning algorithms.This algorithm considers factors such as initial position and orientation of the ship,safety range,and ship draft to determine the optimal obstacle-avoiding route from the current to the destination point for ship planning.A coordinate transformation algorithm is also applied to convert commonly used latitude and longitude coordinates of ship travel paths to easily utilized and analyzed Cartesian coordinates.The algorithm incorporates a hierarchical chart processing algorithm to handle multilayered chart data.Furthermore,the algorithm considers the impact of ship length on grid size and density when implementing chart gridification,adjusting the grid size and density accordingly based on ship length.Simulation results show that compared to traditional path planning algorithms,the sparse A^(*)algorithm reduces the average number of path points by 25%,decreases the average maximum storage node number by 17%,and raises the average path turning angle by approximately 10°,effectively improving the safety of ship planning paths.
基金The National Natural Science Foundation of China(No.62272239,62303214)Jiangsu Agricultural Science and Tech-nology Independent Innovation Fund(No.SJ222051).
文摘To tackle the path planning problem,this study introduced a novel algorithm called two-stage parameter adjustment-based differential evolution(TPADE).This algorithm draws inspiration from group behavior to implement a two-stage scaling factor variation strategy.In the initial phase,it adapts according to environmental complexity.In the following phase,it combines individual and global experiences to fine-tune the orientation factor,effectively improving its global search capability.Furthermore,this study developed a new population update method,ensuring that well-adapted individuals are retained,which enhances population diversity.In benchmark function tests across different dimensions,the proposed algorithm consistently demonstrates superior convergence accuracy and speed.This study also tested the TPADE algorithm in path planning simulations.The experimental results reveal that the TPADE algorithm outperforms existing algorithms by achieving path lengths of 28.527138 and 31.963990 in simple and complex map environments,respectively.These findings indicate that the proposed algorithm is more adaptive and efficient in path planning.
基金the support of the National Natural Science Foundation of China(No.52272382)the Aeronautical Science Foundation of China(No.20200017051001)the Fundamental Research Funds for the Central Universities,China。
文摘For autonomous Unmanned Aerial Vehicles(UAVs)flying in real-world scenarios,time for path planning is always limited,which is a challenge known as the anytime problem.Anytime planners address this by finding a collision-free path quickly and then improving it until time runs out,making UAVs more adaptable to different mission scenarios.However,current anytime algorithms based on A^(*)have insufficient control over the suboptimality bounds of paths and tend to lose their anytime properties in environments with large concave obstacles.This paper proposes a novel anytime path planning algorithm,Anytime Radiation A^(*)(ARa A^(*)),which can generate a series of suboptimal paths with improved bounds through decreasing search step sizes and can generate the optimal path when time is sufficient.The ARa A^(*)features two main innovations:an adaptive variable-step-size mechanism and elliptic constraints based on waypoints.The former helps achieve fast path searching in various environments.The latter allows ARa A^(*)to control the suboptimality bounds of paths and further enhance search efficiency.Simulation experiments show that the ARa A^(*)outperforms Anytime Repairing A^(*)(ARA^(*))and Anytime D^(*)(AD^(*))in controlling suboptimality bounds and planning time,especially in environments with large concave obstacles.Final flight experiments demonstrate that the paths planned by ARa A^(*)can ensure the safe flight of quadrotors.
基金supported by the Guangzhou City School Joint Found Project(SL2022A03J01009)the National Nature Science Foundation of China(Grant No.51975135)the Natural Science Foundation of Guangdong Province(2018A030310063).
文摘Solving the path planning problem of Autonomous Underwater Vehicles(AUVs)is crucial for reducing energy waste and improving operational efficiency.However,two main challenges hinder further development:Firstly,existing algorithms often treat this as a single-objective optimization problem,whereas in reality,it should be multi-objective,considering factors such as distance,safety,and smoothness simultaneously.Secondly,the limited availability of optimization results arises due to they are single-path,which fail to meet real-world conditions.To address these challenges,first of all,an improved AUV path planning model is proposed,in which the collisions of path and obstacles are classified more specifically.Subsequently,a novel Altruistic Nurturing Algorithm(ANA)inspired by natural altruism is introduced.In the algorithm,nurturing cost considering Pareto rank and crowd distance is introduced as guidance of evolution to avoid futile calculation,abandonment threshold is self-adaptive with descendant situation to help individuals escape from local optima and double selection strategy combining crowd and k-nearest neighbors selection helps to get a better-distributed Pareto front.Experimental results comparing ANA with existing algorithms in AUV path planning demonstrate its superiority.Finally,a user-friendly interface,the Multi-Objective AUV Path Planner,is designed to provide users with a group of paths for informed decisionmaking.
文摘In the current era of intelligent technologies,comprehensive and precise regional coverage path planning is critical for tasks such as environmental monitoring,emergency rescue,and agricultural plant protection.Owing to their exceptional flexibility and rapid deployment capabilities,unmanned aerial vehicles(UAVs)have emerged as the ideal platforms for accomplishing these tasks.This study proposes a swarm A^(*)-guided Deep Q-Network(SADQN)algorithm to address the coverage path planning(CPP)problem for UAV swarms in complex environments.Firstly,to overcome the dependency of traditional modeling methods on regular terrain environments,this study proposes an improved cellular decomposition method for map discretization.Simultaneously,a distributed UAV swarm system architecture is adopted,which,through the integration of multi-scale maps,addresses the issues of redundant operations and flight conflicts inmulti-UAV cooperative coverage.Secondly,the heuristic mechanism of the A^(*)algorithmis combinedwith full-coverage path planning,and this approach is incorporated at the initial stage ofDeep Q-Network(DQN)algorithm training to provide effective guidance in action selection,thereby accelerating convergence.Additionally,a prioritized experience replay mechanism is introduced to further enhance the coverage performance of the algorithm.To evaluate the efficacy of the proposed algorithm,simulation experiments were conducted in several irregular environments and compared with several popular algorithms.Simulation results show that the SADQNalgorithmoutperforms othermethods,achieving performance comparable to that of the baseline prior algorithm,with an average coverage efficiency exceeding 2.6 and fewer turning maneuvers.In addition,the algorithm demonstrates excellent generalization ability,enabling it to adapt to different environments.
基金supported by Hunan Provincial Natural Science Foundation(2024JJ5173,2023JJ50047)Hunan Provincial Department of Education Scientific Research Project(23A0494)Hunan Provincial Innovation Foundation for Postgraduate(CX20231221).
文摘To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and inte-grates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evo-lution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection opti-mization of paths, gradually reducing algorithmic space, accele-rating convergence, and enhances path cooperativity. Simula-tion experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demon-strate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. More-over it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collabora-tive path planning. The experiments are conducted in three col-laborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality.
基金Industry-University-Research Cooperation Fund Project of the Eighth Research Institute of China Aerospace Science and Technology Corporation(No.USCAST2022-11)。
文摘The path planning problem of complex wild environment with multiple elements still poses challenges.This paper designs an algorithm that integrates global and local planning to apply to the wild environmental path planning.The modeling process of wild environment map is designed.Three optimization strategies are designed to improve the A-Star in overcoming the problems of touching the edge of obstacles,redundant nodes and twisting paths.A new weighted cost function is designed to achieve different planning modes.Furthermore,the improved dynamic window approach(DWA)is designed to avoid local optimality and improve time efficiency compared to traditional DWA.For the necessary path re-planning of wild environment,the improved A-Star is integrated with the improved DWA to solve re-planning problem of unknown and moving obstacles in wild environment with multiple elements.The improved fusion algorithm effectively solves problems and consumes less time,and the simulation results verify the effectiveness of improved algorithms above.
基金supported by Shaanxi Provincial Key Research and Development Program of China(Nos.2024GX-YBXM-305,2024GX-YBXM-178)Shaanxi Province Qinchuangyuan“Scientists+Engineers”Team Construction(No.2022KXJ032)。
文摘In order to solve the problem of path planning of tower cranes,an improved ant colony algorithm was proposed.Firstly,the tower crane was simplified into a three-degree-of-freedom mechanical arm,and the D-H motion model was established to solve the forward and inverse kinematic equations.Secondly,the traditional ant colony algorithm was improved.The heuristic function was improved by introducing the distance between the optional nodes and the target point into the function.Then the transition probability was improved by introducing the security factor of surrounding points into the transition probability.In addition,the local path chunking strategy was used to optimize the local multi-inflection path and reduce the local redundant inflection points.Finally,according to the position of the hook,the kinematic inversion of the tower crane was carried out,and the variables of each joint were obtained.More specifically,compared with the traditional ant colony algorithm,the simulation results showed that improved ant colony algorithm converged faster,shortened the optimal path length,and optimized the path quality in the simple and complex environment.
基金supported by National Natural Science Foundation of China(No.42302336)Project of the Department of Science and Technology of Sichuan Province(No.2024YFHZ0098,No.2023NSFSC0751)Open Project of Chengdu University of Information Technology(KYQN202317,760115027,KYTZ202278,KYTZ202280).
文摘Unmanned aerial vehicle(UAV)paths in the field directly affect the efficiency and accuracy of payload data collection.Path planning of UAV advancing along river valleys in wild environments is one of the first and most difficult problems faced by unmanned surveys of debris flow valleys.This study proposes a new hybrid bat optimization algorithm,GRE-Bat(Good point set,Reverse learning,Elite Pool-Bat algorithm),for unmanned exploration path planning of debris flow sources in outdoor environments.In the GRE-Bat algorithm,the good point set strategy is adopted to evenly distribute the population,ensure sufficient coverage of the search space,and improve the stability of the convergence accuracy of the algorithm.Subsequently,a reverse learning strategy is introduced to increase the diversity of the population and improve the local stagnation problem of the algorithm.In addition,an Elite pool strategy is added to balance the replacement and learning behaviors of particles within the population based on elimination and local perturbation factors.To demonstrate the effectiveness of the GRE-Bat algorithm,we conducted multiple simulation experiments using benchmark test functions and digital terrain models.Compared to commonly used path planning algorithms such as the Bat Algorithm(BA)and the Improved Sparrow Search Algorithm(ISSA),the GRE-Bat algorithm can converge to the optimal value in different types of test functions and obtains a near-optimal solution after an average of 60 iterations.The GRE-Bat algorithm can obtain higher quality flight routes in the designated environment of unmanned investigation in the debris flow gully basin,demonstrating its potential for practical application.
基金supported by National Natural Science Foundation of China(71904006)Henan Province Key R&D Special Project(231111322200)+1 种基金the Science and Technology Research Plan of Henan Province(232102320043,232102320232,232102320046)the Natural Science Foundation of Henan(232300420317,232300420314).
文摘Reducing casualties and property losses through effective evacuation route planning has been a key focus for researchers in recent years.As part of this effort,an enhanced sparrow search algorithm(MSSA)was proposed.Firstly,the Golden Sine algorithm and a nonlinear weight factor optimization strategy were added in the discoverer position update stage of the SSA algorithm.Secondly,the Cauchy-Gaussian perturbation was applied to the optimal position of the SSA algorithm to improve its ability to jump out of local optima.Finally,the local search mechanism based on the mountain climbing method was incorporated into the local search stage of the SSA algorithm,improving its local search ability.To evaluate the effectiveness of the proposed algorithm,the Whale Algorithm,Gray Wolf Algorithm,Improved Gray Wolf Algorithm,Sparrow Search Algorithm,and MSSA Algorithm were employed to solve various test functions.The accuracy and convergence speed of each algorithm were then compared and analyzed.The results indicate that the MSSA algorithm has superior solving ability and stability compared to other algorithms.To further validate the enhanced algorithm’s capabilities for path planning,evacuation experiments were conducted using different maps featuring various obstacle types.Additionally,a multi-exit evacuation scenario was constructed according to the actual building environment of a teaching building.Both the sparrow search algorithm and MSSA algorithm were employed in the simulation experiment for multiexit evacuation path planning.The findings demonstrate that the MSSA algorithm outperforms the comparison algorithm,showcasing its greater advantages and higher application potential.
文摘The burgeoning robotics industry has catalyzed significant strides in the development and deployment of industrial and service robotic arms, positioning path planning as a pivotal facet for augmenting their operational safety and efficiency. Existing path planning algorithms, while capable of delineating feasible trajectories, often fall short of achieving optimality, particularly concerning path length, search duration, and success likelihood. This study introduces an enhanced Rapidly-Exploring Random Tree (RRT) algorithm, meticulously designed to rectify the issues of node redundancy and the compromised path quality endemic to conventional RRT approaches. Through the integration of an adaptive pruning mechanism and a dynamic elliptical search strategy within the Informed RRT* framework, our algorithm efficiently refines the search tree by discarding branches that surpass the cost of the optimal path, thereby refining the search space and significantly boosting efficiency. Extensive comparative analysis across both two-dimensional and three-dimensional simulation settings underscores the algorithm’s proficiency in markedly improving path precision and search velocity, signifying a breakthrough in the domain of robotic arm path planning.
基金supported by Northern Border University,Arar,Kingdom of Saudi Arabia,through the Project Number“NBU-FFR-2024-2248-03”.
文摘This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.
基金supported by the Opening Fund of Shandong Provincial Key Laboratory of Network based Intelligent Computing,the National Natural Science Foundation of China(52205529,61803192)the Natural Science Foundation of Shandong Province(ZR2021QE195)+1 种基金the Youth Innovation Team Program of Shandong Higher Education Institution(2023KJ206)the Guangyue Youth Scholar Innovation Talent Program support received from Liaocheng University(LCUGYTD2022-03).
文摘Effective path planning is crucial for mobile robots to quickly reach rescue destination and complete rescue tasks in a post-disaster scenario.In this study,we investigated the post-disaster rescue path planning problem and modeled this problem as a variant of the travel salesman problem(TSP)with life-strength constraints.To address this problem,we proposed an improved iterated greedy(IIG)algorithm.First,a push-forward insertion heuristic(PFIH)strategy was employed to generate a high-quality initial solution.Second,a greedy-based insertion strategy was designed and used in the destruction-construction stage to increase the algorithm’s exploration ability.Furthermore,three problem-specific swap operators were developed to improve the algorithm’s exploitation ability.Additionally,an improved simulated annealing(SA)strategy was used as an acceptance criterion to effectively prevent the algorithm from falling into local optima.To verify the effectiveness of the proposed algorithm,the Solomon dataset was extended to generate 27 instances for simulation.Finally,the proposed IIG was compared with five state-of-the-art algorithms.The parameter analysiswas conducted using the design of experiments(DOE)Taguchi method,and the effectiveness analysis of each component has been verified one by one.Simulation results indicate that IIGoutperforms the compared algorithms in terms of the number of rescue survivors and convergence speed,proving the effectiveness of the proposed algorithm.
基金the National Natural Science Foundation of China(Grant No.42274119)the Liaoning Revitalization Talents Program(Grant No.XLYC2002082)+1 种基金National Key Research and Development Plan Key Special Projects of Science and Technology Military Civil Integration(Grant No.2022YFF1400500)the Key Project of Science and Technology Commission of the Central Military Commission.
文摘This study focuses on the improvement of path planning efficiency for underwater gravity-aided navigation.Firstly,a Depth Sorting Fast Search(DSFS)algorithm was proposed to improve the planning speed of the Quick Rapidly-exploring Random Trees*(Q-RRT*)algorithm.A cost inequality relationship between an ancestor and its descendants was derived,and the ancestors were filtered accordingly.Secondly,the underwater gravity-aided navigation path planning system was designed based on the DSFS algorithm,taking into account the fitness,safety,and asymptotic optimality of the routes,according to the gravity suitability distribution of the navigation space.Finally,experimental comparisons of the computing performance of the ChooseParent procedure,the Rewire procedure,and the combination of the two procedures for Q-RRT*and DSFS were conducted under the same planning environment and parameter conditions,respectively.The results showed that the computational efficiency of the DSFS algorithm was improved by about 1.2 times compared with the Q-RRT*algorithm while ensuring correct computational results.
文摘A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. The main ideas of the algorithm are as follows: firstly suppose that all of the tasks are in different clusters; secondly, select one of the critical paths of the partially clustered directed acyclic graph; thirdly, try to zero one of graph communication edges; fourthly, repeat above three processes until all edges are zeroed; finally, check the generated clusters to see if some of them can be further merged without increasing the parallel time. Comparisons of the previous algorithms with edge-zeroing based on dynamic critical paths show that the new algorithm has not only a low complexity but also a desired performance comparable or even better on average to much higher complexity heuristic algorithms.
