Virtual network embedding problem which is NP-hard is a key issue for implementing software-defined network which is brought about by network virtualization. Compared with other studies which focus on designing heuris...Virtual network embedding problem which is NP-hard is a key issue for implementing software-defined network which is brought about by network virtualization. Compared with other studies which focus on designing heuristic algorithms to reduce the hardness of the NP-hard problem we propose a robust VNE algorithm based on component connectivity in large-scale network. We distinguish the different components and embed VN requests onto them respectively. And k-core is applied to identify different VN topologies so that the VN request can be embedded onto its corresponding component. On the other hand, load balancing is also considered in this paper. It could avoid blocked or bottlenecked area of substrate network. Simulation experiments show that compared with other algorithms in large-scale network, acceptance ratio, average revenue and robustness can be obviously improved by our algorithm and average cost can be reduced. It also shows the relationship between the component connectivity including giant component and small components and the performance metrics.展开更多
Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most c...Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not. The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace. Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e.g., Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.展开更多
In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and pow...In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and power optimization are applied to improve system sum-rate. But max-rain optimization problem in power allocation is a NP-hard problem. In high Signal-to-Noise Ratio regime, this NP-hard problem is transformed into constrained polynomial optimization problem, which can be computed in polynomial time. Although it is a suboptimal solution, numerical simulations show that this strategy enhances the system sum-rate up to 45% as compared to a traditional four-phase strategy, and up to 13% as compared to the three-phase strategy without power optimization.展开更多
We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations...We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates(BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.展开更多
Rough set theory is an effective method to feature selection, which has recently fascinated many researchers. The essence of rough set approach to feature selection is to find a subset of the original features. It is,...Rough set theory is an effective method to feature selection, which has recently fascinated many researchers. The essence of rough set approach to feature selection is to find a subset of the original features. It is, however, an NP-hard problem finding a minimal subset of the features, and it is necessary to investigate effective and efficient heuristic algorithms. This paper presents a novel rough set approach to feature selection based on scatter search metaheuristic. The proposed method, called scatter search rough set attribute reduction （SSAR）, is illustrated by 13 well known datasets from UCI machine learning repository. The proposed heuristic strategy is compared with typical attribute reduction methods including genetic algorithm, ant colony, simulated annealing, and Tabu search. Computational results demonstrate that our algorithm can provide efficient solution to find a minimal subset of the features and show promising and competitive performance on the considered datasets.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant No.61471055
文摘Virtual network embedding problem which is NP-hard is a key issue for implementing software-defined network which is brought about by network virtualization. Compared with other studies which focus on designing heuristic algorithms to reduce the hardness of the NP-hard problem we propose a robust VNE algorithm based on component connectivity in large-scale network. We distinguish the different components and embed VN requests onto them respectively. And k-core is applied to identify different VN topologies so that the VN request can be embedded onto its corresponding component. On the other hand, load balancing is also considered in this paper. It could avoid blocked or bottlenecked area of substrate network. Simulation experiments show that compared with other algorithms in large-scale network, acceptance ratio, average revenue and robustness can be obviously improved by our algorithm and average cost can be reduced. It also shows the relationship between the component connectivity including giant component and small components and the performance metrics.
文摘Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not. The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace. Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e.g., Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.
基金Supported by the High Technology Research and Development Program of China (No. 2006AA01Z282 2007CB310608)
文摘In bi-directional three-node cooperation, one regenerative strategy with network coding and power optimization is proposed for system sum-rate under a total energy constraint. In this paper, the network coding and power optimization are applied to improve system sum-rate. But max-rain optimization problem in power allocation is a NP-hard problem. In high Signal-to-Noise Ratio regime, this NP-hard problem is transformed into constrained polynomial optimization problem, which can be computed in polynomial time. Although it is a suboptimal solution, numerical simulations show that this strategy enhances the system sum-rate up to 45% as compared to a traditional four-phase strategy, and up to 13% as compared to the three-phase strategy without power optimization.
基金supported by National Natural Science Foundation of China (Grant Nos. 11401364, 11322109, 11331012, 11471325 and 11461161005)the National High Technology Research and Development Program of China (863 Program) (Grant No. 2013AA122902)+1 种基金the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of SciencesNational Basic Research Program of China (973 Program) (Grant No. 2015CB856002)
文摘We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates(BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.
基金supported by the National Natural Science Foundation of China under Grant Nos.71271202 and 70801058
文摘Rough set theory is an effective method to feature selection, which has recently fascinated many researchers. The essence of rough set approach to feature selection is to find a subset of the original features. It is, however, an NP-hard problem finding a minimal subset of the features, and it is necessary to investigate effective and efficient heuristic algorithms. This paper presents a novel rough set approach to feature selection based on scatter search metaheuristic. The proposed method, called scatter search rough set attribute reduction （SSAR）, is illustrated by 13 well known datasets from UCI machine learning repository. The proposed heuristic strategy is compared with typical attribute reduction methods including genetic algorithm, ant colony, simulated annealing, and Tabu search. Computational results demonstrate that our algorithm can provide efficient solution to find a minimal subset of the features and show promising and competitive performance on the considered datasets.
