A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of...A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.展开更多
During the operation and installation of offshore pipelines, high axial forces and pressures are experienced, and their effects cannot be neglected. In this article, the effect of internal flow velocity and functional...During the operation and installation of offshore pipelines, high axial forces and pressures are experienced, and their effects cannot be neglected. In this article, the effect of internal flow velocity and functional loads on vortex-induced vibration （VIV） response is investigated. On the basis of the Hamilton principle, a differential equation was derived to describe the motion of a pinned-pinned tensioned spanning pipeline conveying fluid. The VIV response was calculated according to DNV-RP-F105 under different functional loads. The results showed that functional loads influence free spanning pipeline VIV response by changing the natural frequency. Internal flow velocity was found less important for VIV response than other functional load factors, such as effective axial force, because the speed in reality is not high enough to be significant. The research may provide a reference for sensitivity studies of the effect of functional loads on allowable free span lengths.展开更多
In Corley′s algorithm for all efficient spanning trees, final solutions include many spanning trees, which are not all efficient. In this paper, a new algorithm is presented, which corrects and modifies Corley′s alg...In Corley′s algorithm for all efficient spanning trees, final solutions include many spanning trees, which are not all efficient. In this paper, a new algorithm is presented, which corrects and modifies Corley′s algorithm. A necessary condition is developed for the subtree of an efficient spanning tree. According to the condition the new algorithm is established and its efficiency is proved.展开更多
At present, most researches on the vortex-induced vibration of submarine free spanning pipelines ignore the effect of internal flowing fluid; furthermore, there are no research reports considering the coupling effect ...At present, most researches on the vortex-induced vibration of submarine free spanning pipelines ignore the effect of internal flowing fluid; furthermore, there are no research reports considering the coupling effect of internal and external fluid with the free span. In this paper, combining Iwan's wake oscillator model with the differential equation derived for the dynamic response of submarine free spanning pipelines with inclusion of internal flow, the pipe-fluid coupling equations are developed to investigate the effect of internal flow on the vortex-induced vibration of the free spans. The finite element approximation is implemented to derive the matrix equations of equilibrium. The Newmark method combined with simple iteration is used to solve the system of equations. The results indicate that the internal fluid flow may cause the shift of resonance band to the lower frequency and a slight decrease in the peak value; the effect will be more pronounced with the increase of the span length and can be weakened in the presence of the axial tension.展开更多
Seismic load has a significant effect on the response of a free spanning submarine pipeline when the pipeline is constructed in a seismically active region. The model experiment is performed on an underwater shaking t...Seismic load has a significant effect on the response of a free spanning submarine pipeline when the pipeline is constructed in a seismically active region. The model experiment is performed on an underwater shaking table to simulate the response of submarine pipelines under dynamic input. In consideration of the effects of the terrestrial and submarine pipeline, water depth, support condition, distance from seabed, empty and full pipeline, and span on dynamic response, 120 groups of experiments are conducted. Affecting factors are analyzed and conclusions are drawn for reference. For the control of dynamic response, the span of a submarine pipeline is by far more important than the other factors. Meanwhile, the rosponse difference between a submarine pipeline under sine excitation and that under random excitation exists in experiments.展开更多
Considering the effect of the internal flowing fluid and the external marine environmental condition, the differential equation for the vortex induced vibration (VIV) of the free spanning pipeline is derived and is d...Considering the effect of the internal flowing fluid and the external marine environmental condition, the differential equation for the vortex induced vibration (VIV) of the free spanning pipeline is derived and is discretized by the Hermit interpolation function. The free vibration equation with the damping term is solved by the complex damping method for the natural frequency, and then the effect of fluid damping on the natural frequency of the free spanning pipeline is analyzed. The results show that fluid damping has a significant influence on the damped natural frequency of the free spanning pipeline in the lock in state, while it has little influence when the pipeline is out of the lock in state. In the meantime, the change of the free span length has the same effect on the damped natural frequency and the undamped natural frequency.展开更多
A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model ...A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morisen equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, diseretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.展开更多
As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packa...As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packages such as LINDO, and furthermore this model is extendedinto the stochastic version, that is, the minimal spanning tree problem for the digraph with theweights is not constant but random variables. Several algorithms are also developed to solve themodels. Finally, a numerical demonstration is given.展开更多
The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that ther...The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.展开更多
Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line（IL）vortex-induced vibrations（VIV） analysis of the free spans is an important subject for design of pip...Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line（IL）vortex-induced vibrations（VIV） analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.展开更多
As far as the weighted digraph is considered, an optimal directed spanning tree algorithm called table based algorithm (TBA) is proposed in the paper based on the table instead of the weighted digraph. The optimality ...As far as the weighted digraph is considered, an optimal directed spanning tree algorithm called table based algorithm (TBA) is proposed in the paper based on the table instead of the weighted digraph. The optimality is proved, and a numerical example is demonstrated.展开更多
As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a nume...As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.展开更多
There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning ...There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.展开更多
Free spanning pipelines are suspended between two points on an uneven seaffoor. The variations of structural conditions, such as the changes in soil property, flow velocity, axial force and span length etc., directly ...Free spanning pipelines are suspended between two points on an uneven seaffoor. The variations of structural conditions, such as the changes in soil property, flow velocity, axial force and span length etc., directly affect working performance of the whole submarine pipeline system. But until now few researches have focused on condition identification for free span （CIFS）. A method to identify the operational conditions of free spanning submarine pipelines based on vibration measurements is proposed in this paper. Firstly, the ill-posedness of CIFS is analyzed in detail. Secondly, the framework for CIFS based on the nonlinear kernel discriminant analysis （KDA） is established. Thirdly, the internal structural characteristics of natural frequencies, normalized frequencies and frequency change ratios are studied. And then the condition feature vector for CIFS is extracted by use of the vibration measurements. Finally, the validity of the proposed approach is evaluated by a case study. The results demonstrate that the proposed approach can effectively identify each condition of free span when condition variation occurs even if under measurement noise. It is concluded that the proposed method is a promising tool for CIFS in real applications.展开更多
With the purpose of making calculation more efficient in practical hydraulic simulations, an improved algorithm was proposed and was applied in the practical water distribution field. This methodology was developed by...With the purpose of making calculation more efficient in practical hydraulic simulations, an improved algorithm was proposed and was applied in the practical water distribution field. This methodology was developed by expanding the traditional loop-equation theory through utilization of the advantages of the graph theory in efficiency. The utilization of the spanning tree technique from graph theory makes the proposed algorithm efficient in calculation and simple to use for computer coding. The algorithms for topological generation and practical implementations are presented in detail in this paper. Through the application to a practical urban system, the consumption of the CPU time and computation memory were decreased while the accuracy was greatly enhanced compared with the present existing methods.展开更多
Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a f...Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.展开更多
In Wireless Sensor Networks (WSNs), sensor nodes are developed densely. They have limit processing ca-pability and low power resources. Thus, energy is one of most important constraints in these networks. In some appl...In Wireless Sensor Networks (WSNs), sensor nodes are developed densely. They have limit processing ca-pability and low power resources. Thus, energy is one of most important constraints in these networks. In some applications of sensor networks, sensor nodes sense data from the environment periodically and trans-mit these data to sink node. In order to decrease energy consumption and so, increase network’s lifetime, volume of transmitted data should be decreased. A solution, which is suggested, is aggregation. In aggrega-tion mechanisms, the nodes aggregate received data and send aggregated result instead of raw data to sink, so, the volume of the transmitted data is decreased. Aggregation algorithms should construct aggregation tree and transmit data to sink based on this tree. In this paper, we propose an automaton based algorithm to con-struct aggregation tree by using energy and distance parameters. Automaton is a decision-making machine that is able-to-learn. Since network’s topology is dynamic, algorithm should construct aggregation tree peri-odically. In order to aware nodes of topology and so, select optimal path, routing packets must be flooded in entire network that led to high energy consumption. By using automaton machine which is in interaction with environment, we solve this problem based on automat learning. By using this strategy, aggregation tree is reconstructed locally, that result in decreasing energy consumption. Simulation results show that the pro-posed algorithm has better performance in terms of energy efficiency which increase the network lifetime and support better coverage.展开更多
Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatoria...Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.展开更多
基金The NSF(11601209,11471151,11401069 and 11671064)of Chinathe Research Foundation (201601239)for Doctor of Liaoning Province+2 种基金the Scientific Research Fund(L201683660)of Liaoning Provincial Education Departmentthe Youth Foundation(LS2015L002)of Liaoning Normal Universitya grant of the Fundamental Research Funds(DUT16LK40)for the Central Universities
文摘A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.
基金Supported by the National Natural Science Foundation of China (No. 50879013)China National 111 Project (No.B07019)
文摘During the operation and installation of offshore pipelines, high axial forces and pressures are experienced, and their effects cannot be neglected. In this article, the effect of internal flow velocity and functional loads on vortex-induced vibration （VIV） response is investigated. On the basis of the Hamilton principle, a differential equation was derived to describe the motion of a pinned-pinned tensioned spanning pipeline conveying fluid. The VIV response was calculated according to DNV-RP-F105 under different functional loads. The results showed that functional loads influence free spanning pipeline VIV response by changing the natural frequency. Internal flow velocity was found less important for VIV response than other functional load factors, such as effective axial force, because the speed in reality is not high enough to be significant. The research may provide a reference for sensitivity studies of the effect of functional loads on allowable free span lengths.
文摘In Corley′s algorithm for all efficient spanning trees, final solutions include many spanning trees, which are not all efficient. In this paper, a new algorithm is presented, which corrects and modifies Corley′s algorithm. A necessary condition is developed for the subtree of an efficient spanning tree. According to the condition the new algorithm is established and its efficiency is proved.
基金This Project was fincianlly supported by the National Natural Science Foundation of China (Grant No. 50379050)
文摘At present, most researches on the vortex-induced vibration of submarine free spanning pipelines ignore the effect of internal flowing fluid; furthermore, there are no research reports considering the coupling effect of internal and external fluid with the free span. In this paper, combining Iwan's wake oscillator model with the differential equation derived for the dynamic response of submarine free spanning pipelines with inclusion of internal flow, the pipe-fluid coupling equations are developed to investigate the effect of internal flow on the vortex-induced vibration of the free spans. The finite element approximation is implemented to derive the matrix equations of equilibrium. The Newmark method combined with simple iteration is used to solve the system of equations. The results indicate that the internal fluid flow may cause the shift of resonance band to the lower frequency and a slight decrease in the peak value; the effect will be more pronounced with the increase of the span length and can be weakened in the presence of the axial tension.
基金This research is financially supported by the Science and Technology Foundation of Liaoning Province (Grant No.972240)
文摘Seismic load has a significant effect on the response of a free spanning submarine pipeline when the pipeline is constructed in a seismically active region. The model experiment is performed on an underwater shaking table to simulate the response of submarine pipelines under dynamic input. In consideration of the effects of the terrestrial and submarine pipeline, water depth, support condition, distance from seabed, empty and full pipeline, and span on dynamic response, 120 groups of experiments are conducted. Affecting factors are analyzed and conclusions are drawn for reference. For the control of dynamic response, the span of a submarine pipeline is by far more important than the other factors. Meanwhile, the rosponse difference between a submarine pipeline under sine excitation and that under random excitation exists in experiments.
文摘Considering the effect of the internal flowing fluid and the external marine environmental condition, the differential equation for the vortex induced vibration (VIV) of the free spanning pipeline is derived and is discretized by the Hermit interpolation function. The free vibration equation with the damping term is solved by the complex damping method for the natural frequency, and then the effect of fluid damping on the natural frequency of the free spanning pipeline is analyzed. The results show that fluid damping has a significant influence on the damped natural frequency of the free spanning pipeline in the lock in state, while it has little influence when the pipeline is out of the lock in state. In the meantime, the change of the free span length has the same effect on the damped natural frequency and the undamped natural frequency.
基金supported jointly by the National Natural Science Foundation of China and Korea Scienceand Engineering Foundation(Grant No.50811140341)
文摘A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morisen equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, diseretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.
文摘As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packages such as LINDO, and furthermore this model is extendedinto the stochastic version, that is, the minimal spanning tree problem for the digraph with theweights is not constant but random variables. Several algorithms are also developed to solve themodels. Finally, a numerical demonstration is given.
文摘The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51479135,51525803 and51679167)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51321065)the Major State Basic Research Development Program of China(973 Program,Grant No.2014CB046801)
文摘Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line（IL）vortex-induced vibrations（VIV） analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.
基金the National Natural Science Foundation of China (No. 79870030).
文摘As far as the weighted digraph is considered, an optimal directed spanning tree algorithm called table based algorithm (TBA) is proposed in the paper based on the table instead of the weighted digraph. The optimality is proved, and a numerical example is demonstrated.
文摘As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.
文摘There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.
基金supported by the Key Program of National Natural Science Foundation of China(GrantNo.50439010)the Main Program of the Ministry of Education of China(Grant No.305003)
文摘Free spanning pipelines are suspended between two points on an uneven seaffoor. The variations of structural conditions, such as the changes in soil property, flow velocity, axial force and span length etc., directly affect working performance of the whole submarine pipeline system. But until now few researches have focused on condition identification for free span （CIFS）. A method to identify the operational conditions of free spanning submarine pipelines based on vibration measurements is proposed in this paper. Firstly, the ill-posedness of CIFS is analyzed in detail. Secondly, the framework for CIFS based on the nonlinear kernel discriminant analysis （KDA） is established. Thirdly, the internal structural characteristics of natural frequencies, normalized frequencies and frequency change ratios are studied. And then the condition feature vector for CIFS is extracted by use of the vibration measurements. Finally, the validity of the proposed approach is evaluated by a case study. The results demonstrate that the proposed approach can effectively identify each condition of free span when condition variation occurs even if under measurement noise. It is concluded that the proposed method is a promising tool for CIFS in real applications.
文摘With the purpose of making calculation more efficient in practical hydraulic simulations, an improved algorithm was proposed and was applied in the practical water distribution field. This methodology was developed by expanding the traditional loop-equation theory through utilization of the advantages of the graph theory in efficiency. The utilization of the spanning tree technique from graph theory makes the proposed algorithm efficient in calculation and simple to use for computer coding. The algorithms for topological generation and practical implementations are presented in detail in this paper. Through the application to a practical urban system, the consumption of the CPU time and computation memory were decreased while the accuracy was greatly enhanced compared with the present existing methods.
文摘Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.
文摘In Wireless Sensor Networks (WSNs), sensor nodes are developed densely. They have limit processing ca-pability and low power resources. Thus, energy is one of most important constraints in these networks. In some applications of sensor networks, sensor nodes sense data from the environment periodically and trans-mit these data to sink node. In order to decrease energy consumption and so, increase network’s lifetime, volume of transmitted data should be decreased. A solution, which is suggested, is aggregation. In aggrega-tion mechanisms, the nodes aggregate received data and send aggregated result instead of raw data to sink, so, the volume of the transmitted data is decreased. Aggregation algorithms should construct aggregation tree and transmit data to sink based on this tree. In this paper, we propose an automaton based algorithm to con-struct aggregation tree by using energy and distance parameters. Automaton is a decision-making machine that is able-to-learn. Since network’s topology is dynamic, algorithm should construct aggregation tree peri-odically. In order to aware nodes of topology and so, select optimal path, routing packets must be flooded in entire network that led to high energy consumption. By using automaton machine which is in interaction with environment, we solve this problem based on automat learning. By using this strategy, aggregation tree is reconstructed locally, that result in decreasing energy consumption. Simulation results show that the pro-posed algorithm has better performance in terms of energy efficiency which increase the network lifetime and support better coverage.
基金This work is supported by the National Natural Science Foundation of China under Grant 61772179the Hunan Provincial Natural Science Foundation of China under Grant 2019JJ40005+3 种基金the Science and Technology Plan Project of Hunan Province under Grant 2016TP1020the Double First-Class University Project of Hunan Province under Grant Xiangjiaotong[2018]469the Open Fund Project of Hunan Provincial Key Laboratory of Intelligent Information Processing and Application for Hengyang Normal University under Grant IIPA19K02the Science Foundation of Hengyang Normal University under Grant 19QD13.
文摘Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.
