Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and s...Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and search the way to eliminate the phenomenon. First this paper formulates a loose constrained linear programming model for the transportation problem, and gives the definition of the paradox which exists in it, some preliminary notions and one example is also given. Then it gives a table based algorithm for the loose constrained model, the steps of the algorithm and example will follow. The examples show that: (1) It is not a contradictory that transportation problem exists more for less paradox. (2) The loose constrained model is better used in practice for its less total cost. (3) The algorithm is easy to calculate, to study and highly speed to convergence. Finally, comparied with other ways it shows that the loose constrained model can thoroughly eliminate the paradox.展开更多
In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The ...In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algo...A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.展开更多
Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making prod...Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making production, the plan is not only decided by the steel-making scheduling, but also by the transportation equipment.This paper proposes a genetic algorithm to solve continuous and ingot casting scheduling problems. Based on the characteristics of the problems involved, a genetic algorithm is proposed for solving the bilevel programming problem in steel-making production. Furthermore, based on the simplex method, a new crossover operator is designed to improve the efficiency of the genetic algorithm. Finally, the convergence is analyzed. Using actual data the validity of the proposed algorithm is proved and the application results in the steel plant are analyzed.展开更多
Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allo...Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allocation mechanism has not been thoroughly studied under given content placement situation. In this paper, we formulate the joint optimization problem of user association and resource allocation as a mixed integer nonlinear programming(MINLP) problem aiming at deriving a balance between the total utility of data rates and the total data rates retrieved from caches. To solve this problem, we propose a distributed relaxing-rounding method. Simulation results demonstrate that the distributed relaxing-rounding method outperforms traditional max-SINR method and range-expansion method in terms of both total utility of data rates and total data rates retrieved from caches in practical scenarios. In addition, effects of storage and backhaul capacities on the performance are also studied.展开更多
文摘Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and search the way to eliminate the phenomenon. First this paper formulates a loose constrained linear programming model for the transportation problem, and gives the definition of the paradox which exists in it, some preliminary notions and one example is also given. Then it gives a table based algorithm for the loose constrained model, the steps of the algorithm and example will follow. The examples show that: (1) It is not a contradictory that transportation problem exists more for less paradox. (2) The loose constrained model is better used in practice for its less total cost. (3) The algorithm is easy to calculate, to study and highly speed to convergence. Finally, comparied with other ways it shows that the loose constrained model can thoroughly eliminate the paradox.
文摘In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
基金Project(61105057)supported by the National Natural Science Foundation of ChinaProject(13KJB520024)supported by the Natural Science Foundation of Jiangsu Higher Education Institutes of ChinaProject supported by Jiangsu Province Qing Lan Project,China
文摘A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.
基金Supported by the Educational Commission of Liaoning Province Science and Technology Research Projects(L2013237)
文摘Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making production, the plan is not only decided by the steel-making scheduling, but also by the transportation equipment.This paper proposes a genetic algorithm to solve continuous and ingot casting scheduling problems. Based on the characteristics of the problems involved, a genetic algorithm is proposed for solving the bilevel programming problem in steel-making production. Furthermore, based on the simplex method, a new crossover operator is designed to improve the efficiency of the genetic algorithm. Finally, the convergence is analyzed. Using actual data the validity of the proposed algorithm is proved and the application results in the steel plant are analyzed.
基金supported by National Natural Science Foundation of China under Grants No. 61371087 and 61531013The Research Fund of Ministry of Education-China Mobile (MCM20150102)
文摘Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allocation mechanism has not been thoroughly studied under given content placement situation. In this paper, we formulate the joint optimization problem of user association and resource allocation as a mixed integer nonlinear programming(MINLP) problem aiming at deriving a balance between the total utility of data rates and the total data rates retrieved from caches. To solve this problem, we propose a distributed relaxing-rounding method. Simulation results demonstrate that the distributed relaxing-rounding method outperforms traditional max-SINR method and range-expansion method in terms of both total utility of data rates and total data rates retrieved from caches in practical scenarios. In addition, effects of storage and backhaul capacities on the performance are also studied.