In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,...In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,we convert the problem(MLFP)to a problem(EP2)that is equivalent to it.Secondly,by applying the convex relaxation technique to problem(EP2),a convex quadratic relaxation problem(CQRP)is obtained.Then,the overall framework of the algorithm is given and its convergence is proved,the worst-case iteration number is also estimated.Finally,experimental data are listed to illustrate the effectiveness of the algorithm.展开更多
Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in net...Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.展开更多
Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied af...Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied after random deployment.In this paper,we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage.In particular,two problems are studied:relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost.These two problems were formulated as 0–1 integer linear programming(ILP).The formulation is computationally intractable because of integrality and complicated constraints.Therefore,we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming.Theoretical analysis and simulation were performed to verify the effectiveness of our approach.展开更多
In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be...In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.展开更多
A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of a...A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of assistant sets, an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane. A simple numerical example shows that the algorithm is efficient for some problems, and therefore, of practical interest.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.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
一方面,为提高主动配电网供电恢复过程中的孤岛运行模式的供电可靠性,另一方面,为充分协调调压设备和网络重构以提高电能质量,本文综合考虑调压设备、微电网、网络重构等作用,建立基于混合整数线性规划(mixed integer linear programmin...一方面,为提高主动配电网供电恢复过程中的孤岛运行模式的供电可靠性,另一方面,为充分协调调压设备和网络重构以提高电能质量,本文综合考虑调压设备、微电网、网络重构等作用,建立基于混合整数线性规划(mixed integer linear programming,MILP)模型的主动配电网供电恢复模型。该模型以开关操作的动作成本、电压调节设备的调节成本、失负荷成本组成的总成本为目标,以线性化潮流约束、DG模型、ZIP负荷模型、电压调节设备模型等为约束条件,建立了主动配电网供电恢复优化的MILP模型。在53节点配电系统的仿真结果验证了电压调节设备控制和微电网对配电网供电恢复的改善作用。展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071133 and 11871196).
文摘In this paper,we study the minimax linear fractional programming problem on a non-empty bounded set,called problem(MLFP),and we design a branch and bound algorithm to find a globally optimal solution of(MLFP).Firstly,we convert the problem(MLFP)to a problem(EP2)that is equivalent to it.Secondly,by applying the convex relaxation technique to problem(EP2),a convex quadratic relaxation problem(CQRP)is obtained.Then,the overall framework of the algorithm is given and its convergence is proved,the worst-case iteration number is also estimated.Finally,experimental data are listed to illustrate the effectiveness of the algorithm.
基金supported by the National Basic Research Program of China(973 Program)under Grant 2013CB329005
文摘Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.
基金supported by the NSFC(U1536206,61232016,U1405254,61373133,61502242,71401176)BK20150925the PAPD fund
文摘Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied after random deployment.In this paper,we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage.In particular,two problems are studied:relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost.These two problems were formulated as 0–1 integer linear programming(ILP).The formulation is computationally intractable because of integrality and complicated constraints.Therefore,we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming.Theoretical analysis and simulation were performed to verify the effectiveness of our approach.
基金Supported by the Natural Science Foundation of Henan Province（0511012000 0511013600） Supported by the Science Foundation for Pure Research of Natural Science of the Education Department of Henan Province（200512950001）
文摘In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.
文摘A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of assistant sets, an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane. A simple numerical example shows that the algorithm is efficient for some problems, and therefore, of practical interest.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
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.
文摘一方面,为提高主动配电网供电恢复过程中的孤岛运行模式的供电可靠性,另一方面,为充分协调调压设备和网络重构以提高电能质量,本文综合考虑调压设备、微电网、网络重构等作用,建立基于混合整数线性规划(mixed integer linear programming,MILP)模型的主动配电网供电恢复模型。该模型以开关操作的动作成本、电压调节设备的调节成本、失负荷成本组成的总成本为目标,以线性化潮流约束、DG模型、ZIP负荷模型、电压调节设备模型等为约束条件,建立了主动配电网供电恢复优化的MILP模型。在53节点配电系统的仿真结果验证了电压调节设备控制和微电网对配电网供电恢复的改善作用。
