Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the chall...Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.展开更多
The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the slid...The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.展开更多
In the paper, a new selection probability inspired by artificial bee colony algorithm is introduced into standard particle swarm optimization by improving the global extremum updating condition to enhance the capabili...In the paper, a new selection probability inspired by artificial bee colony algorithm is introduced into standard particle swarm optimization by improving the global extremum updating condition to enhance the capability of its overall situation search. The experiment result shows that the new scheme is more valuable and effective than other schemes in the convergence of codebook design and the performance of codebook, and it can avoid the premature phenomenon of the particles.展开更多
Swarm intelligence algorithms are a subset of the artificial intelligence(AI)field,which is increasing popularity in resolving different optimization problems and has been widely utilized in various applications.In th...Swarm intelligence algorithms are a subset of the artificial intelligence(AI)field,which is increasing popularity in resolving different optimization problems and has been widely utilized in various applications.In the past decades,numerous swarm intelligence algorithms have been developed,including ant colony optimization(ACO),particle swarm optimization(PSO),artificial fish swarm(AFS),bacterial foraging optimization(BFO),and artificial bee colony(ABC).This review tries to review the most representative swarm intelligence algorithms in chronological order by highlighting the functions and strengths from 127 research literatures.It provides an overview of the various swarm intelligence algorithms and their advanced developments,and briefly provides the description of their successful applications in optimization problems of engineering fields.Finally,opinions and perspectives on the trends and prospects in this relatively new research domain are represented to support future developments.展开更多
A novel bionic swarm intelligence algorithm, called ant colony algorithm based on a blackboard mechanism, is proposed to solve the autonomy and dynamic deployment of mobiles sensor networks effectively. A blackboard m...A novel bionic swarm intelligence algorithm, called ant colony algorithm based on a blackboard mechanism, is proposed to solve the autonomy and dynamic deployment of mobiles sensor networks effectively. A blackboard mechanism is introduced into the system for making pheromone and completing the algorithm. Every node, which can be looked as an ant, makes one information zone in its memory for communicating with other nodes and leaves pheromone, which is created by ant itself in naalre. Then ant colony theory is used to find the optimization scheme for path planning and deployment of mobile Wireless Sensor Network (WSN). We test the algorithm in a dynamic and unconfigurable environment. The results indicate that the algorithm can reduce the power consumption by 13% averagely, enhance the efficiency of path planning and deployment of mobile WSN by 15% averagely.展开更多
The traveling salesman problem( TSP) is a well-known combinatorial optimization problem as well as an NP-complete problem. A dynamic multi-swarm particle swarm optimization and ant colony optimization( DMPSO-ACO) was ...The traveling salesman problem( TSP) is a well-known combinatorial optimization problem as well as an NP-complete problem. A dynamic multi-swarm particle swarm optimization and ant colony optimization( DMPSO-ACO) was presented for TSP.The DMPSO-ACO combined the exploration capabilities of the dynamic multi-swarm particle swarm optimizer( DMPSO) and the stochastic exploitation of the ant colony optimization( ACO) for solving the traveling salesman problem. In the proposed hybrid algorithm,firstly,the dynamic swarms,rapidity of the PSO was used to obtain a series of sub-optimal solutions through certain iterative times for adjusting the initial allocation of pheromone in ACO. Secondly,the positive feedback and high accuracy of the ACO were employed to solving whole problem. Finally,to verify the effectiveness and efficiency of the proposed hybrid algorithm,various scale benchmark problems were tested to demonstrate the potential of the proposed DMPSO-ACO algorithm. The results show that DMPSO-ACO is better in the search precision,convergence property and has strong ability to escape from the local sub-optima when compared with several other peer algorithms.展开更多
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
The wireless sensor network(WSN)is widely employed in the application scenarios of the Internet of Things(IoT)in recent years.Extending the lifetime of the entire system had become a significant challenge due to the e...The wireless sensor network(WSN)is widely employed in the application scenarios of the Internet of Things(IoT)in recent years.Extending the lifetime of the entire system had become a significant challenge due to the energy-constrained fundamental limits of sensor nodes on the perceptual layer of IoT.The clustering routing structures are currently the most popular solution,which can effectively reduce the energy consumption of the entire network and improve its reliability.This paper introduces an enhanced hybrid intelligential algorithm based on particle swarm optimization(PSO)and ant colony optimization(ACO)method.The enhanced PSO is deployed to select the optimal cluster heads for establishing the clustering architecture.An improved ACO is introduced to realize the data transmission from terminal sensor nodes to the base station.Our proposed algorithm can effectively reduce the entire energy consumption and extend the lifetime of IoT sensor networks.Compared with the traditional algorithms,the simulation results show that the presented novel algorithm in this paper has obvious optimization and improvement in network lifetime and energy utilization efficiency.展开更多
Dead fine fuel moisture content(DFFMC)is a key factor affecting the spread of forest fires,which plays an important role in evaluation of forest fire risk.In order to achieve high-precision real-time measurement of DF...Dead fine fuel moisture content(DFFMC)is a key factor affecting the spread of forest fires,which plays an important role in evaluation of forest fire risk.In order to achieve high-precision real-time measurement of DFFMC,this study established a long short-term memory(LSTM)network based on particle swarm optimization(PSO)algorithm as a measurement model.A multi-point surface monitoring scheme combining near-infrared measurement method and meteorological measurement method is proposed.The near-infrared spectral information of dead fine fuels and the meteorological factors in the region are processed by data fusion technology to construct a spectral-meteorological data set.The surface fine dead fuel of Mongolian oak(Quercus mongolica Fisch.ex Ledeb.),white birch(Betula platyphylla Suk.),larch(Larix gmelinii(Rupr.)Kuzen.),and Manchurian walnut(Juglans mandshurica Maxim.)in the maoershan experimental forest farm of the Northeast Forestry University were investigated.We used the PSO-LSTM model for moisture content to compare the near-infrared spectroscopy,meteorological,and spectral meteorological fusion methods.The results show that the mean absolute error of the DFFMC of the four stands by spectral meteorological fusion method were 1.1%for Mongolian oak,1.3%for white birch,1.4%for larch,and 1.8%for Manchurian walnut,and these values were lower than those of the near-infrared method and the meteorological method.The spectral meteorological fusion method provides a new way for high-precision measurement of moisture content of fine dead fuel.展开更多
为解决现有粒子群改进策略无法帮助已陷入局部最优和过早收敛的粒子恢复寻优性能的问题,提出一种陷阱标记联合懒蚂蚁的自适应粒子群优化(adaptive particle swarm optimization based on trap label and lazy ant, TLLA-APSO)算法。陷...为解决现有粒子群改进策略无法帮助已陷入局部最优和过早收敛的粒子恢复寻优性能的问题,提出一种陷阱标记联合懒蚂蚁的自适应粒子群优化(adaptive particle swarm optimization based on trap label and lazy ant, TLLA-APSO)算法。陷阱标记策略为粒子群提供动态速度增量,使其摆脱最优解的束缚。利用懒蚂蚁寻优策略多样化粒子速度,提升种群多样性。通过惯性认知策略在速度更新中引入历史位置,增加粒子的路径多样性和提升粒子的探索性能,使粒子更有效地避免陷入新的局部最优。理论证明了引入历史位置的粒子群算法的收敛性。仿真实验结果表明,所提算法不仅能有效解决粒子群已陷入局部最优和过早收敛的问题,且与其他算法相比,具有较快的收敛速度和较高的寻优精度。展开更多
为解决快速扩展随机树算法(rapid-exploration random tree,RRT*)在三维环境中盲目搜索路径以及缺乏节点扩展记忆性等问题,提出一种融合蚁群算法的双向搜索算法ACO-RRT*。为适应精细化三维建模环境和解决地面起伏不平坦等问题,对RRT*算...为解决快速扩展随机树算法(rapid-exploration random tree,RRT*)在三维环境中盲目搜索路径以及缺乏节点扩展记忆性等问题,提出一种融合蚁群算法的双向搜索算法ACO-RRT*。为适应精细化三维建模环境和解决地面起伏不平坦等问题,对RRT*算法进行改进优化。采用双向搜索策略,在起点和终点同时运行改进后的RRT算法和蚁群算法,相向而行,对路径长度和运行时间进行优化。针对生成路径不够平滑等问题,引入B样条曲线平滑策略优化路径。仿真结果表明,所提算法能够有效用于机器人三维路径规划。展开更多
Based on biologically inspired algorithms,a thermodynamic model to describe the vapor-liquid equilibrium of binary complex mixtures containing supercritical fluids and ionic liquids,is presented.The Peng-Robinson equa...Based on biologically inspired algorithms,a thermodynamic model to describe the vapor-liquid equilibrium of binary complex mixtures containing supercritical fluids and ionic liquids,is presented.The Peng-Robinson equation of state with the Wong-Sandler mixing rules are used to evaluate the fugacity coefficient on the systems.Then,a hybrid particle swarm-ant colony optimization was used to minimize the difference between calculated and experimental bubble pressure,and calculate the binary interaction parameters for the excess Gibbs free energy of all systems used.Simulations are carried out in nine systems with imidazolium-based ionic liquids.The results show that the bubble pressures were correlated with low deviations between experimental and calculated values.These deviations show that the proposed hybrid algorithm is the preferable method to describe the phase equilibrium of these complex mixtures,and can be used for other similar systems.展开更多
基金jointly supported by the Jiangsu Postgraduate Research and Practice Innovation Project under Grant KYCX22_1030,SJCX22_0283 and SJCX23_0293the NUPTSF under Grant NY220201.
文摘Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment.Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios.In this work,the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm(HPSO-EABC)has been proposed,which hybrids our presented Evolutionary Artificial Bee Colony(EABC),and Hierarchical Particle Swarm Optimization(HPSO)algorithm.The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm.Comprehensive testing including evaluations of algorithm convergence speed,resource execution time,load balancing,and operational costs has been done.The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm.Compared with the Particle Swarm Optimization algorithm,the HPSO algorithmnot only improves the global search capability but also effectively mitigates getting stuck in local optima.As a result,the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed.Moreover,it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments,effectively reducing execution time and cost,which also is verified by the ablation experimental.
文摘The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.
基金Sponsored by the Qing Lan Project of Jiangsu Province
文摘In the paper, a new selection probability inspired by artificial bee colony algorithm is introduced into standard particle swarm optimization by improving the global extremum updating condition to enhance the capability of its overall situation search. The experiment result shows that the new scheme is more valuable and effective than other schemes in the convergence of codebook design and the performance of codebook, and it can avoid the premature phenomenon of the particles.
基金supported in part by the National Natural Science Foundation of China(62073330)in part by the Natural Science Foundation of Hunan Province(2019JJ20021,2020JJ4339)in part by the Scientific Research Fund of Hunan Province Education Department(20B272)。
文摘Swarm intelligence algorithms are a subset of the artificial intelligence(AI)field,which is increasing popularity in resolving different optimization problems and has been widely utilized in various applications.In the past decades,numerous swarm intelligence algorithms have been developed,including ant colony optimization(ACO),particle swarm optimization(PSO),artificial fish swarm(AFS),bacterial foraging optimization(BFO),and artificial bee colony(ABC).This review tries to review the most representative swarm intelligence algorithms in chronological order by highlighting the functions and strengths from 127 research literatures.It provides an overview of the various swarm intelligence algorithms and their advanced developments,and briefly provides the description of their successful applications in optimization problems of engineering fields.Finally,opinions and perspectives on the trends and prospects in this relatively new research domain are represented to support future developments.
基金National "863" Project of China (Grant no. 2007AA04Z224)
文摘A novel bionic swarm intelligence algorithm, called ant colony algorithm based on a blackboard mechanism, is proposed to solve the autonomy and dynamic deployment of mobiles sensor networks effectively. A blackboard mechanism is introduced into the system for making pheromone and completing the algorithm. Every node, which can be looked as an ant, makes one information zone in its memory for communicating with other nodes and leaves pheromone, which is created by ant itself in naalre. Then ant colony theory is used to find the optimization scheme for path planning and deployment of mobile Wireless Sensor Network (WSN). We test the algorithm in a dynamic and unconfigurable environment. The results indicate that the algorithm can reduce the power consumption by 13% averagely, enhance the efficiency of path planning and deployment of mobile WSN by 15% averagely.
基金National Natural Science Foundation of China(No.70971020)the Subject of Ministry of Education of Hunan Province,China(No.13C818)+3 种基金the Project of Industrial Science and Technology Support of Hengyang City,Hunan Province,China(No.2013KG63)the Open Project Program of Artificial Intelligence Key Laboratory of Sichuan Province,Sichuan University of Science and Engineering,China(No.2012RYJ03)the Fund Project of Humanities and Social Sciences,Ministry of Education of China(No.13YJCZH147)the Special Fund for Shanghai Colleges' Outstanding Young Teachers' Scientific Research Projects,China(No.ZZGJD12033)
文摘The traveling salesman problem( TSP) is a well-known combinatorial optimization problem as well as an NP-complete problem. A dynamic multi-swarm particle swarm optimization and ant colony optimization( DMPSO-ACO) was presented for TSP.The DMPSO-ACO combined the exploration capabilities of the dynamic multi-swarm particle swarm optimizer( DMPSO) and the stochastic exploitation of the ant colony optimization( ACO) for solving the traveling salesman problem. In the proposed hybrid algorithm,firstly,the dynamic swarms,rapidity of the PSO was used to obtain a series of sub-optimal solutions through certain iterative times for adjusting the initial allocation of pheromone in ACO. Secondly,the positive feedback and high accuracy of the ACO were employed to solving whole problem. Finally,to verify the effectiveness and efficiency of the proposed hybrid algorithm,various scale benchmark problems were tested to demonstrate the potential of the proposed DMPSO-ACO algorithm. The results show that DMPSO-ACO is better in the search precision,convergence property and has strong ability to escape from the local sub-optima when compared with several other peer algorithms.
文摘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.
文摘The wireless sensor network(WSN)is widely employed in the application scenarios of the Internet of Things(IoT)in recent years.Extending the lifetime of the entire system had become a significant challenge due to the energy-constrained fundamental limits of sensor nodes on the perceptual layer of IoT.The clustering routing structures are currently the most popular solution,which can effectively reduce the energy consumption of the entire network and improve its reliability.This paper introduces an enhanced hybrid intelligential algorithm based on particle swarm optimization(PSO)and ant colony optimization(ACO)method.The enhanced PSO is deployed to select the optimal cluster heads for establishing the clustering architecture.An improved ACO is introduced to realize the data transmission from terminal sensor nodes to the base station.Our proposed algorithm can effectively reduce the entire energy consumption and extend the lifetime of IoT sensor networks.Compared with the traditional algorithms,the simulation results show that the presented novel algorithm in this paper has obvious optimization and improvement in network lifetime and energy utilization efficiency.
基金supported by the National Key R&D Program of China (Project No.2020YFC2200800,Task No.2020YFC2200803)the Key Projects of the Natural Science Foundation of Heilongjiang Province (Grant No.ZD2021E001)。
文摘Dead fine fuel moisture content(DFFMC)is a key factor affecting the spread of forest fires,which plays an important role in evaluation of forest fire risk.In order to achieve high-precision real-time measurement of DFFMC,this study established a long short-term memory(LSTM)network based on particle swarm optimization(PSO)algorithm as a measurement model.A multi-point surface monitoring scheme combining near-infrared measurement method and meteorological measurement method is proposed.The near-infrared spectral information of dead fine fuels and the meteorological factors in the region are processed by data fusion technology to construct a spectral-meteorological data set.The surface fine dead fuel of Mongolian oak(Quercus mongolica Fisch.ex Ledeb.),white birch(Betula platyphylla Suk.),larch(Larix gmelinii(Rupr.)Kuzen.),and Manchurian walnut(Juglans mandshurica Maxim.)in the maoershan experimental forest farm of the Northeast Forestry University were investigated.We used the PSO-LSTM model for moisture content to compare the near-infrared spectroscopy,meteorological,and spectral meteorological fusion methods.The results show that the mean absolute error of the DFFMC of the four stands by spectral meteorological fusion method were 1.1%for Mongolian oak,1.3%for white birch,1.4%for larch,and 1.8%for Manchurian walnut,and these values were lower than those of the near-infrared method and the meteorological method.The spectral meteorological fusion method provides a new way for high-precision measurement of moisture content of fine dead fuel.
文摘为解决现有粒子群改进策略无法帮助已陷入局部最优和过早收敛的粒子恢复寻优性能的问题,提出一种陷阱标记联合懒蚂蚁的自适应粒子群优化(adaptive particle swarm optimization based on trap label and lazy ant, TLLA-APSO)算法。陷阱标记策略为粒子群提供动态速度增量,使其摆脱最优解的束缚。利用懒蚂蚁寻优策略多样化粒子速度,提升种群多样性。通过惯性认知策略在速度更新中引入历史位置,增加粒子的路径多样性和提升粒子的探索性能,使粒子更有效地避免陷入新的局部最优。理论证明了引入历史位置的粒子群算法的收敛性。仿真实验结果表明,所提算法不仅能有效解决粒子群已陷入局部最优和过早收敛的问题,且与其他算法相比,具有较快的收敛速度和较高的寻优精度。
文摘为解决快速扩展随机树算法(rapid-exploration random tree,RRT*)在三维环境中盲目搜索路径以及缺乏节点扩展记忆性等问题,提出一种融合蚁群算法的双向搜索算法ACO-RRT*。为适应精细化三维建模环境和解决地面起伏不平坦等问题,对RRT*算法进行改进优化。采用双向搜索策略,在起点和终点同时运行改进后的RRT算法和蚁群算法,相向而行,对路径长度和运行时间进行优化。针对生成路径不够平滑等问题,引入B样条曲线平滑策略优化路径。仿真结果表明,所提算法能够有效用于机器人三维路径规划。
文摘Based on biologically inspired algorithms,a thermodynamic model to describe the vapor-liquid equilibrium of binary complex mixtures containing supercritical fluids and ionic liquids,is presented.The Peng-Robinson equation of state with the Wong-Sandler mixing rules are used to evaluate the fugacity coefficient on the systems.Then,a hybrid particle swarm-ant colony optimization was used to minimize the difference between calculated and experimental bubble pressure,and calculate the binary interaction parameters for the excess Gibbs free energy of all systems used.Simulations are carried out in nine systems with imidazolium-based ionic liquids.The results show that the bubble pressures were correlated with low deviations between experimental and calculated values.These deviations show that the proposed hybrid algorithm is the preferable method to describe the phase equilibrium of these complex mixtures,and can be used for other similar systems.