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An Improved Image Steganography Security and Capacity Using Ant Colony Algorithm Optimization
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作者 Zinah Khalid Jasim Jasim Sefer Kurnaz 《Computers, Materials & Continua》 SCIE EI 2024年第9期4643-4662,共20页
This advanced paper presents a new approach to improving image steganography using the Ant Colony Optimization(ACO)algorithm.Image steganography,a technique of embedding hidden information in digital photographs,shoul... This advanced paper presents a new approach to improving image steganography using the Ant Colony Optimization(ACO)algorithm.Image steganography,a technique of embedding hidden information in digital photographs,should ideally achieve the dual purposes of maximum data hiding and maintenance of the integrity of the cover media so that it is least suspect.The contemporary methods of steganography are at best a compromise between these two.In this paper,we present our approach,entitled Ant Colony Optimization(ACO)-Least Significant Bit(LSB),which attempts to optimize the capacity in steganographic embedding.The approach makes use of a grayscale cover image to hide the confidential data with an additional bit pair per byte,both for integrity verification and the file checksumof the secret data.This approach encodes confidential information into four pairs of bits and embeds it within uncompressed grayscale images.The ACO algorithm uses adaptive exploration to select some pixels,maximizing the capacity of data embedding whileminimizing the degradation of visual quality.Pheromone evaporation is introduced through iterations to avoid stagnation in solution refinement.The levels of pheromone are modified to reinforce successful pixel choices.Experimental results obtained through the ACO-LSB method reveal that it clearly improves image steganography capabilities by providing an increase of up to 30%in the embedding capacity compared with traditional approaches;the average Peak Signal to Noise Ratio(PSNR)is 40.5 dB with a Structural Index Similarity(SSIM)of 0.98.The approach also demonstrates very high resistance to detection,cutting down the rate by 20%.Implemented in MATLAB R2023a,the model was tested against one thousand publicly available grayscale images,thus providing robust evidence of its effectiveness. 展开更多
关键词 STEGANOGRAPHY STEGANALYSIS capacity optimization ant colony algorithm
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Improved Ant Colony Algorithm for Vehicle Scheduling Problem in Airport Ground Service Support 被引量:3
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作者 Yaping Zhang Ye Chen +2 位作者 Yu Zhang Jian Mao Qian Luo 《Journal of Harbin Institute of Technology(New Series)》 CAS 2023年第1期1-12,共12页
Support vehicles are part of the main body of airport ground operations,and their scheduling efficiency directly impacts flight delays.A mathematical model is constructed and the responsiveness of support vehicles for... Support vehicles are part of the main body of airport ground operations,and their scheduling efficiency directly impacts flight delays.A mathematical model is constructed and the responsiveness of support vehicles for current operational demands is proposed to study optimization algorithms for vehicle scheduling.The model is based on the constraint relationship of the initial operation time,time window,and gate position distribution,which gives an improvement to the ant colony algorithm(ACO).The impacts of the improved ACO as used for support vehicle optimization are compared and analyzed.The results show that the scheduling scheme of refueling trucks based on the improved ACO can reduce flight delays caused by refueling operations by 56.87%,indicating the improved ACO can improve support vehicle scheduling.Besides,the improved ACO can jump out of local optima,which can balance the working time of refueling trucks.This research optimizes the scheduling scheme of support vehicles under the existing conditions of airports,which has practical significance to fully utilize ground service resources,improve the efficiency of airport ground operations,and effectively reduce flight delays caused by ground service support. 展开更多
关键词 airport surface traffic ground service support vehicle scheduling topology model improved ant colony algorithm response value
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Spatial quality evaluation for drinking water based on GIS and ant colony clustering algorithm 被引量:4
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作者 侯景伟 米文宝 李陇堂 《Journal of Central South University》 SCIE EI CAS 2014年第3期1051-1057,共7页
To develop a better approach for spatial evaluation of drinking water quality, an intelligent evaluation method integrating a geographical information system(GIS) and an ant colony clustering algorithm(ACCA) was used.... To develop a better approach for spatial evaluation of drinking water quality, an intelligent evaluation method integrating a geographical information system(GIS) and an ant colony clustering algorithm(ACCA) was used. Drinking water samples from 29 wells in Zhenping County, China, were collected and analyzed. 35 parameters on water quality were selected, such as chloride concentration, sulphate concentration, total hardness, nitrate concentration, fluoride concentration, turbidity, pH, chromium concentration, COD, bacterium amount, total coliforms and color. The best spatial interpolation methods for the 35 parameters were found and selected from all types of interpolation methods in GIS environment according to the minimum cross-validation errors. The ACCA was improved through three strategies, namely mixed distance function, average similitude degree and probability conversion functions. Then, the ACCA was carried out to obtain different water quality grades in the GIS environment. In the end, the result from the ACCA was compared with those from the competitive Hopfield neural network(CHNN) to validate the feasibility and effectiveness of the ACCA according to three evaluation indexes, which are stochastic sampling method, pixel amount and convergence speed. It is shown that the spatial water quality grades obtained from the ACCA were more effective, accurate and intelligent than those obtained from the CHNN. 展开更多
关键词 geographical information system (GIS) ant colony clustering algorithm (ACCA) quality evaluation drinking water spatial analysis
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Ant colony ATTA clustering algorithm of rock mass structural plane in groups 被引量:9
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作者 李夕兵 王泽伟 +1 位作者 彭康 刘志祥 《Journal of Central South University》 SCIE EI CAS 2014年第2期709-714,共6页
Based on structural surface normal vector spherical distance and the pole stereographic projection Euclidean distance,two distance functions were established.The cluster analysis of structure surface was conducted by ... Based on structural surface normal vector spherical distance and the pole stereographic projection Euclidean distance,two distance functions were established.The cluster analysis of structure surface was conducted by the use of ATTA clustering methods based on ant colony piles,and Silhouette index was introduced to evaluate the clustering effect.The clustering analysis of the measured data of Sanshandao Gold Mine shows that ant colony ATTA-based clustering method does better than K-mean clustering analysis.Meanwhile,clustering results of ATTA method based on pole Euclidean distance and ATTA method based on normal vector spherical distance have a great consistence.The clustering results are most close to the pole isopycnic graph.It can efficiently realize grouping of structural plane and determination of the dominant structural surface direction.It is made up for the defects of subjectivity and inaccuracy in icon measurement approach and has great engineering value. 展开更多
关键词 rock mass discontinuity cluster analysis ant colony ATTA algorithm distance function Silhouette index
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Algorithm for Low Altitude Penetration Aircraft Path Planning with Improved Ant Colony Algorithm 被引量:19
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作者 叶文 马登武 范洪达 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第4期304-309,共6页
The ant colony algorithm is a new class of population basic algorithm. The path planning is realized by the use of ant colony algorithm when the plane executes the low altitude penetration, which provides a new method... The ant colony algorithm is a new class of population basic algorithm. The path planning is realized by the use of ant colony algorithm when the plane executes the low altitude penetration, which provides a new method for the path planning. In the paper the traditional ant colony algorithm is improved, and measures of keeping optimization, adaptively selecting and adaptively adjusting are applied, by which better path at higher convergence speed can be found. Finally the algorithm is implemented with computer simulation and preferable results are obtained. 展开更多
关键词 ant colony algorithm path planning keeping optimization adaptively adiusting low altitude penetration
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Weapon target assignment problem satisfying expected damage probabilities based on ant colony algorithm 被引量:26
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作者 Wang Yanxia Qian Longjun Guo Zhi Ma Lifeng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期939-944,共6页
A weapon target assignment (WTA) model satisfying expected damage probabilities with an ant colony algorithm is proposed. In order to save armament resource and attack the targets effectively, the strategy of the we... A weapon target assignment (WTA) model satisfying expected damage probabilities with an ant colony algorithm is proposed. In order to save armament resource and attack the targets effectively, the strategy of the weapon assignment is that the target with greater threat degree has higher priority to be intercepted. The effect of this WTA model is not maximizing the damage probability but satisfying the whole assignment result. Ant colony algorithm has been successfully used in many fields, especially in combination optimization. The ant colony algorithm for this WTA problem is described by analyzing path selection, pheromone update, and tabu table update. The effectiveness of the model and the algorithm is demonstrated with an example. 展开更多
关键词 weapon target assignment ant colony algorithm optimization.
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Optimization of Air Route Network Nodes to Avoid ″Three Areas″ Based on An Adaptive Ant Colony Algorithm 被引量:9
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作者 Wang Shijin Li Qingyun +1 位作者 Cao Xi Li Haiyun 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2016年第4期469-478,共10页
Air route network(ARN)planning is an efficient way to alleviate civil aviation flight delays caused by increasing development and pressure for safe operation.Here,the ARN shortest path was taken as the objective funct... Air route network(ARN)planning is an efficient way to alleviate civil aviation flight delays caused by increasing development and pressure for safe operation.Here,the ARN shortest path was taken as the objective function,and an air route network node(ARNN)optimization model was developed to circumvent the restrictions imposed by″three areas″,also known as prohibited areas,restricted areas,and dangerous areas(PRDs),by creating agrid environment.And finally the objective function was solved by means of an adaptive ant colony algorithm(AACA).The A593,A470,B221,and G204 air routes in the busy ZSHA flight information region,where the airspace includes areas with different levels of PRDs,were taken as an example.Based on current flight patterns,a layout optimization of the ARNN was computed using this model and algorithm and successfully avoided PRDs.The optimized result reduced the total length of routes by 2.14% and the total cost by 9.875%. 展开更多
关键词 air route network planning three area avoidance optimization of air route network node adaptive ant colony algorithm grid environment
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Ant Colony Algorithm for Solving QoS Routing Problem 被引量:3
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作者 SUNLi-iuan WANGLiang-jun WANGRu-chuan 《Wuhan University Journal of Natural Sciences》 EI CAS 2004年第4期449-453,共5页
Based on the state transition rule, the local updating rule and the global updating rule of ant colony algorithm, we propose an improved ant colony algorithm of the least\|cost quality of service (QoS) unicast rou... Based on the state transition rule, the local updating rule and the global updating rule of ant colony algorithm, we propose an improved ant colony algorithm of the least\|cost quality of service (QoS) unicast routing. The algorithm is used for solving the routing problem with delay, delay jitter, bandwidth, and packet loss\|constrained. In the simulation, about 52.33% ants find the successful QoS routing , and converge to the best. It is proved that the algorithm is efficient and effective. 展开更多
关键词 ant colony algorithm QOS unicast routing
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Multi-group ant colony algorithm based on simulated annealing method 被引量:2
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作者 朱经纬 芮挺 +1 位作者 廖明 张金林 《Journal of Shanghai University(English Edition)》 CAS 2010年第6期464-468,共5页
To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulat... To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulated annealing method is introduced to the algorithm. Through setting the temperature changing with the iterations, after each turn of tours, the solution set obtained by the ants is taken as the candidate set. The update set is obtained by adding the solutions in the candidate set to the previous update set with the probability determined by the temperature. The solutions in the candidate set are used to update the trail information. In each turn of updating, the current best solution is also used to enhance the trail information on the current best route. The trail information is reset when the algorithm is in stagnation state. The computer experiments demonstrate that the proposed algorithm has higher stability and convergence speed. 展开更多
关键词 ant colony algorithm simulated annealing method MULTI-GROUP candidate set update set
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Robot Global Path Planning Based on an Improved Ant Colony Algorithm 被引量:20
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作者 Jingang Cao 《Journal of Computer and Communications》 2016年第2期11-19,共9页
Aiming at the disadvantages of the basic ant colony algorithm, this paper proposes an improved ant colony algorithm for robot global path planning. First, adjust the pheromone evaporation rate dynamically to enhance t... Aiming at the disadvantages of the basic ant colony algorithm, this paper proposes an improved ant colony algorithm for robot global path planning. First, adjust the pheromone evaporation rate dynamically to enhance the global search ability and convergence speed, and then modify the heuristic function to improve the state transition probabilities in order to find the optimal solution as quickly as possible;and finally change the pheromone update strategy to avoid premature by strengthening pheromone on the optimal path and limiting pheromone level. Simulation results verify the effectiveness of the improved algorithm. 展开更多
关键词 Path Planning ant colony algorithm Grid Method
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Optimizing Fresh Logistics Distribution Route Based on Improved Ant Colony Algorithm 被引量:3
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作者 Daqing Wu Ziwei Zhu +1 位作者 Dong Hu Romany Fouad Mansour 《Computers, Materials & Continua》 SCIE EI 2022年第10期2079-2095,共17页
With the rapid development of the fresh cold chain logistics distribution and the prevalence of low carbon concept,this paper proposed an optimization model of low carbon fresh cold chain logistics distribution route ... With the rapid development of the fresh cold chain logistics distribution and the prevalence of low carbon concept,this paper proposed an optimization model of low carbon fresh cold chain logistics distribution route considering customer satisfaction,and combined with time,space,weight,distribution rules and other constraints to optimize the distribution model.At the same time,transportation cost,penalty cost,overloading cost,carbon tax cost and customer satisfaction were considered as the components of the objective function,and the thought of cost efficiency was taken into account,so as to establish a distribution model based on the ratio of minimum total cost to maximum satisfaction as the objective function.Then,the improved A∗algorithm and ant colony algorithm were used to construct the model solution.Through the simulation analysis results of different calculation examples,the effectiveness,efficiency and correctness of the design of the single target low-carbon fresh agricultural products cold chain model by using the improved ant colony algorithm were verified. 展开更多
关键词 Carbon tax cost vehicle routing problem cold chain ant colony algorithm
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Optimization design of drilling string by screw coal miner based on ant colony algorithm 被引量:3
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作者 张强 毛君 丁飞 《Journal of Coal Science & Engineering(China)》 2008年第4期686-688,共3页
It took that the weight minimum and drive efficiency maximal were as double optimizing target,the optimization model had built the drilling string,and the optimization solution was used of the ant colony algorithm to ... It took that the weight minimum and drive efficiency maximal were as double optimizing target,the optimization model had built the drilling string,and the optimization solution was used of the ant colony algorithm to find in progress.Adopted a two-layer search of the continuous space ant colony algorithm with overlapping or variation global ant search operation strategy and conjugated gradient partial ant search operation strat- egy.The experiment indicates that the spiral drill weight reduces 16.77% and transports the efficiency enhance 7.05% through the optimization design,the ant colony algorithm application on the spiral drill optimized design has provided the basis for the system re- search screw coal mine machine. 展开更多
关键词 screw coal miner optimization design ant colony algorithm two-layer search
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Research on UAV cloud control system based on ant colony algorithm 被引量:2
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作者 ZHANG Lanyong ZHANG Ruixuan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2022年第4期805-811,共7页
In the cloud era, the control objects are becoming larger and the information processing is more complex, and it is difficult for traditional control systems to process massive data in a timely manner. In view of the ... In the cloud era, the control objects are becoming larger and the information processing is more complex, and it is difficult for traditional control systems to process massive data in a timely manner. In view of the difficulty of data processing in the cloud era, it is extremely important to perform massive data operations through cloud servers. Unmanned aeriel vehicle(UAV) control is the representative of the intelligent field. Based on the ant colony algorithm and incorporating the potential field method, an improved potential field ant colony algorithm is designed. To deal with the path planning problem of UAVs, the potential field ant colony algorithm shortens the optimal path distance by 6.7%, increases the algorithm running time by39.3%, and increases the maximum distance by 24.1% compared with the previous improvement. The cloud server is used to process the path problem of the UAV and feedback the calculation results in real time. Simulation experiments verify the effectiveness of the new algorithm in the cloud environment. 展开更多
关键词 ant colony algorithm potential field method cloud server path planning
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Research on Data Routing Model Based on Ant Colony Algorithms 被引量:1
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作者 龚跃 吴航 +2 位作者 鲍杰 王君军 张艳秋 《Defence Technology(防务技术)》 SCIE EI CAS 2010年第4期269-272,共4页
Improved traditional ant colony algorithms,a data routing model used to the data remote exchange on WAN was presented.In the model,random heuristic factors were introduced to realize multi-path search.The updating mod... Improved traditional ant colony algorithms,a data routing model used to the data remote exchange on WAN was presented.In the model,random heuristic factors were introduced to realize multi-path search.The updating model of pheromone could adjust the pheromone concentration on the optimal path according to path load dynamically to make the system keep load balance.The simulation results show that the improved model has a higher performance on convergence and load balance. 展开更多
关键词 computer software data transmission ant colony algorithm routing model
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Time-Based Dynamic Trust Model Using Ant Colony Algorithm 被引量:1
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作者 TANG Zhuo LU Zhengding LI Kai 《Wuhan University Journal of Natural Sciences》 CAS 2006年第6期1462-1466,共5页
The trust in distributed environment is uncertain, which is variation for various factors. This paper introduces TDTM, a model for time-based dynamic trust. Every entity in the distribute environment is endowed with a... The trust in distributed environment is uncertain, which is variation for various factors. This paper introduces TDTM, a model for time-based dynamic trust. Every entity in the distribute environment is endowed with a trust-vector, which figures the trust intensity between this entity and the others. The trust intensity is dynamic due to the time and the inter-operation between two entities, a method is proposed to quantify this change based on the mind of ant colony algorithm and then an algorithm for the transfer of trust relation is also proposed. Furthermore, this paper analyses the influence to the trust intensity among all entities that is aroused by the change of trust intensity between the two entities, and presents an algorithm to resolve the problem. Finally, we show the process of the trusts' change that is aroused by the time's lapse and the inter-operation through an instance. 展开更多
关键词 dynamic trust ant colony algorithm Inter-operation time-based
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Ant colony algorithm based on genetic method for continuous optimization problem 被引量:1
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作者 朱经纬 蒙培生 王乘 《Journal of Shanghai University(English Edition)》 CAS 2007年第6期597-602,共6页
A new algorithm is presented by using the ant colony algorithm based on genetic method (ACG) to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of componen... A new algorithm is presented by using the ant colony algorithm based on genetic method (ACG) to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of component, trail information and fitness. The ant chooses a seed from the seed set with the possibility determined by trail information and fitness of the seed. The genetic method is used to form new solutions from the solutions got by the ants. Best solutions are selected to update the seeds in the sets and trail information of the seeds. In updating the trail information, a diffusion function is used to achieve the diffuseness of trail information. The new algorithm is tested with 8 different benchmark functions. 展开更多
关键词 ant colony algorithm genetic method diffusion function continuous optimization problem.
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Hybridization of Fuzzy and Hard Semi-Supervised Clustering Algorithms Tuned with Ant Lion Optimizer Applied to Higgs Boson Search 被引量:1
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作者 Soukaina Mjahed Khadija Bouzaachane +2 位作者 Ahmad Taher Azar Salah El Hadaj Said Raghay 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第11期459-494,共36页
This paper focuses on the unsupervised detection of the Higgs boson particle using the most informative features and variables which characterize the“Higgs machine learning challenge 2014”data set.This unsupervised ... This paper focuses on the unsupervised detection of the Higgs boson particle using the most informative features and variables which characterize the“Higgs machine learning challenge 2014”data set.This unsupervised detection goes in this paper analysis through 4 steps:(1)selection of the most informative features from the considered data;(2)definition of the number of clusters based on the elbow criterion.The experimental results showed that the optimal number of clusters that group the considered data in an unsupervised manner corresponds to 2 clusters;(3)proposition of a new approach for hybridization of both hard and fuzzy clustering tuned with Ant Lion Optimization(ALO);(4)comparison with some existing metaheuristic optimizations such as Genetic Algorithm(GA)and Particle Swarm Optimization(PSO).By employing a multi-angle analysis based on the cluster validation indices,the confusion matrix,the efficiencies and purities rates,the average cost variation,the computational time and the Sammon mapping visualization,the results highlight the effectiveness of the improved Gustafson-Kessel algorithm optimized withALO(ALOGK)to validate the proposed approach.Even if the paper gives a complete clustering analysis,its novel contribution concerns only the Steps(1)and(3)considered above.The first contribution lies in the method used for Step(1)to select the most informative features and variables.We used the t-Statistic technique to rank them.Afterwards,a feature mapping is applied using Self-Organizing Map(SOM)to identify the level of correlation between them.Then,Particle Swarm Optimization(PSO),a metaheuristic optimization technique,is used to reduce the data set dimension.The second contribution of thiswork concern the third step,where each one of the clustering algorithms as K-means(KM),Global K-means(GlobalKM),Partitioning AroundMedoids(PAM),Fuzzy C-means(FCM),Gustafson-Kessel(GK)and Gath-Geva(GG)is optimized and tuned with ALO. 展开更多
关键词 ant lion optimization binary clustering clustering algorithms Higgs boson feature extraction dimensionality reduction elbow criterion genetic algorithm particle swarm optimization
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Path Planning for Lunar Surface Robots Based on Improved Ant Colony Algorithm 被引量:1
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作者 SONG Ting SUN Yuqi +2 位作者 YUAN Jianping YANG Haiyue WU Xiande 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2022年第6期672-683,共12页
In the real-world situation,the lunar missions’scale and terrain are different according to various operational regions or worksheets,which requests a more flexible and efficient algorithm to generate task paths.A mu... In the real-world situation,the lunar missions’scale and terrain are different according to various operational regions or worksheets,which requests a more flexible and efficient algorithm to generate task paths.A multi-scale ant colony planning method for the lunar robot is designed to meet the requirements of large scale and complex terrain in lunar space.In the algorithm,the actual lunar surface image is meshed into a gird map,the path planning algorithm is modeled on it,and then the actual path is projected to the original lunar surface and mission.The classical ant colony planning algorithm is rewritten utilizing a multi-scale method to address the diverse task problem.Moreover,the path smoothness is also considered to reduce the magnitude of the steering angle.Finally,several typical conditions to verify the efficiency and feasibility of the proposed algorithm are presented. 展开更多
关键词 ant colony algorithm grid map multi scale path smoothing
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The Study of Extracting River Nets Based on Intelligence Ant Colony Algorithm on MODIS Remote Sensing Images 被引量:1
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作者 时向勇 李先华 郑成建 《Journal of Donghua University(English Edition)》 EI CAS 2010年第5期673-680,共8页
How to extract river nets effectively is of great significance for water resources investigation,flood forecasting and environmental monitoring,etc.In the paper,combining with ant colony algorithm,a new approach of ex... How to extract river nets effectively is of great significance for water resources investigation,flood forecasting and environmental monitoring,etc.In the paper,combining with ant colony algorithm,a new approach of extracting river nets on moderate-resolution imaging spectroradiometer(MODIS)remote sensing images was proposed through analyzing two general extraction methods of river nets.The experiment results show that river nets can be optimized by ant colony algorithm efficiently,and difference ratio between the experimental vectorgraph and the data of National Fundamental Geographic Information System is down to 8.7%.The proposed algorithm can work for extracting river nets on MODIS remote sensing images effectively. 展开更多
关键词 ant colony algorithm river nets MODIS remote sensing images
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AN ANT COLONY ALGORITHM FOR MINIMUM UNSATISFIABLE CORE EXTRACTION 被引量:1
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作者 Zhang Jianmin Shen Shengyu Li Sikun 《Journal of Electronics(China)》 2008年第5期652-660,共9页
Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that ex... Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that excludes all irrelevant information is generally of interest.A smallest-cardinality unsatisfiable subset called a minimum unsatisfiable core can provide a succinct explanation of infea-sibility and is valuable for applications.However,little attention has been concentrated on extraction of minimum unsatisfiable core.In this paper,the relationship between maximal satisfiability and mini-mum unsatisfiability is presented and proved,then an efficient ant colony algorithm is proposed to derive an exact or nearly exact minimum unsatisfiable core based on the relationship.Finally,ex-perimental results on practical benchmarks compared with the best known approach are reported,and the results show that the ant colony algorithm strongly outperforms the best previous algorithm. 展开更多
关键词 Electronic Design Automation (EDA) Formal verification of hardware Minimum unsatisfiable core ant colony algorithm Maximal satisfiable subformula
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