In this paper, starting from a class of "K·m+n" (where k>0 and k≠1) type minimum problem, combining with relevant facts or axioms to explore its two broad applications-"straight line" mini...In this paper, starting from a class of "K·m+n" (where k>0 and k≠1) type minimum problem, combining with relevant facts or axioms to explore its two broad applications-"straight line" minimum value and "curved + linear" minimum value, two mathematical models of "Hu Bugui" and "As circle" are respectively generated from different starting points. According to the unique characteristics of both models and combining with "perpendicular axiom and line segment axiom", the proof of the models is given, and the discussion and application of the properties of the two models are given. That is, the coefficient is ingeniously changed into "1" by different methods, so as to achieve the purpose of "simplifying complexity" by using "perpendicular axiom" and "line segment axiom" respectively, and general application model problem-solving steps and skills are given after application, so as to solve such problems as "straight line type" and "curve type".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
Secure group communications are restrained by the number of the group size,number of changes and their distribution,all existing works do not meet the commands of applications with large group size and high dynamic me...Secure group communications are restrained by the number of the group size,number of changes and their distribution,all existing works do not meet the commands of applications with large group size and high dynamic members.In this paper,minimum exact cover problem for group key distribution(GMECP)is presented,and a heuristic solution is testified.Then an algorithm of batch rekeying with renewing cost tending to zero is illustrated,which can process any large number of change requests with best security guaranteed.Efficiency analysis and simulation test show that the achievement can improve the efficiency of any tree-based group key management.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
The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented ...The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented forest structure, then augments flows on the negative cost graphs until the optimal revolution is gained. Bottleneck structure is presented after analyzing the augmented forest structure. The negative cost augmented graphs are constructed with the bottleneck structure. The arcs that block the negative cost augmented graph are the elements of the bottleneck. The bottleneck analysis for the generalized circulation problem, the minimum circulation problem and the circulation problem are discussed respectively as the basal problems, then that for MCPGN is achieved. An example is presented at the end.展开更多
This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0...This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.展开更多
The optimal solution of the multi-constrained QoS multicast routing problem is a tree-like hierarchical structure in the topology graph. This multicast route contains a feasible path from the source node to each of th...The optimal solution of the multi-constrained QoS multicast routing problem is a tree-like hierarchical structure in the topology graph. This multicast route contains a feasible path from the source node to each of the destinations with respect to a set of QoS constraints while minimizing a cost function. Often, it is a tree. In other cases, the hierarchies can return several times to nodes and links of the topology graph. Similarly to Steiner problem, finding such a structure is an NP-hard problem. The usual tree and topology enumeration algorithms applied for the Steiner problem cannot be used to solve the addressed problem. In this paper, we propose an exact algorithm based on the Branch and Bound principle and improved by the Lookahead technique. We show relevant properties of the optimum hierarchy permitting efficient pruning of the search space. To our knowledge, our paper is the first to propose an exact algorithm for this non-trivial multi-constrained optimal multicast route computation. Simulations illustrate the efficiency of the proposed pruning operations. The analysis of the execution time shows that in simple topologies and with tight QoS constraints the exact algorithm requires relatively little execution time. With loose constraints the computation time cannot be tolerated even for off-line route computation. In these cases, the solution is close to a Steiner tree and heuristics can be applied. These results can serve as basis for the design of efficient, polynomial-time routing algorithms.展开更多
The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all ...The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.展开更多
Ants of artificial colony are able to generate good solutions to the famous traveling salesman problem (TSP). We propose an artificial ants algorithm for solving the minimum ratio TSP, which is more general than the s...Ants of artificial colony are able to generate good solutions to the famous traveling salesman problem (TSP). We propose an artificial ants algorithm for solving the minimum ratio TSP, which is more general than the standard TSP in combinatorial optimization area. In the minimum ratio TSP, another criterion concerning each edge is added, that is, the traveling salesman can have a benefit if he travels from one city to another. The objective is to minimize the ratio between total costs or distances and total benefits. The idea of this type of optimization is in some sense quite similar to that of traditional cost-benefit analysis in management science. Computational results substantiate the solution quality and efficiency of the algorithm.展开更多
The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is int...The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is introduced. Compared with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.展开更多
The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary ...The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary body to be in shape of an oblate spheroid. The equilibrium points are sought by the application of the propellant for which it would just balance the gravitational forces. The launching flight of such a satellite is seen to be applicable for having arbitrary space stations for these different missions. Specialty of the result of the investigation lies in the fact that an arbitrary space station can be formed to attain any specified mission.展开更多
文摘In this paper, starting from a class of "K·m+n" (where k>0 and k≠1) type minimum problem, combining with relevant facts or axioms to explore its two broad applications-"straight line" minimum value and "curved + linear" minimum value, two mathematical models of "Hu Bugui" and "As circle" are respectively generated from different starting points. According to the unique characteristics of both models and combining with "perpendicular axiom and line segment axiom", the proof of the models is given, and the discussion and application of the properties of the two models are given. That is, the coefficient is ingeniously changed into "1" by different methods, so as to achieve the purpose of "simplifying complexity" by using "perpendicular axiom" and "line segment axiom" respectively, and general application model problem-solving steps and skills are given after application, so as to solve such problems as "straight line type" and "curve type".
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.
基金Supported by the National Natural Science Foundation of China(60572049)
文摘Secure group communications are restrained by the number of the group size,number of changes and their distribution,all existing works do not meet the commands of applications with large group size and high dynamic members.In this paper,minimum exact cover problem for group key distribution(GMECP)is presented,and a heuristic solution is testified.Then an algorithm of batch rekeying with renewing cost tending to zero is illustrated,which can process any large number of change requests with best security guaranteed.Efficiency analysis and simulation test show that the achievement can improve the efficiency of any tree-based group key management.
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.
基金Supported by the National Natural Science Foundation of China (No. 60174046).
文摘The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented forest structure, then augments flows on the negative cost graphs until the optimal revolution is gained. Bottleneck structure is presented after analyzing the augmented forest structure. The negative cost augmented graphs are constructed with the bottleneck structure. The arcs that block the negative cost augmented graph are the elements of the bottleneck. The bottleneck analysis for the generalized circulation problem, the minimum circulation problem and the circulation problem are discussed respectively as the basal problems, then that for MCPGN is achieved. An example is presented at the end.
文摘This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.
文摘The optimal solution of the multi-constrained QoS multicast routing problem is a tree-like hierarchical structure in the topology graph. This multicast route contains a feasible path from the source node to each of the destinations with respect to a set of QoS constraints while minimizing a cost function. Often, it is a tree. In other cases, the hierarchies can return several times to nodes and links of the topology graph. Similarly to Steiner problem, finding such a structure is an NP-hard problem. The usual tree and topology enumeration algorithms applied for the Steiner problem cannot be used to solve the addressed problem. In this paper, we propose an exact algorithm based on the Branch and Bound principle and improved by the Lookahead technique. We show relevant properties of the optimum hierarchy permitting efficient pruning of the search space. To our knowledge, our paper is the first to propose an exact algorithm for this non-trivial multi-constrained optimal multicast route computation. Simulations illustrate the efficiency of the proposed pruning operations. The analysis of the execution time shows that in simple topologies and with tight QoS constraints the exact algorithm requires relatively little execution time. With loose constraints the computation time cannot be tolerated even for off-line route computation. In these cases, the solution is close to a Steiner tree and heuristics can be applied. These results can serve as basis for the design of efficient, polynomial-time routing algorithms.
文摘The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.
基金This project was supported by the Shanghai Education Development Foundation (No.2000SG30).
文摘Ants of artificial colony are able to generate good solutions to the famous traveling salesman problem (TSP). We propose an artificial ants algorithm for solving the minimum ratio TSP, which is more general than the standard TSP in combinatorial optimization area. In the minimum ratio TSP, another criterion concerning each edge is added, that is, the traveling salesman can have a benefit if he travels from one city to another. The objective is to minimize the ratio between total costs or distances and total benefits. The idea of this type of optimization is in some sense quite similar to that of traditional cost-benefit analysis in management science. Computational results substantiate the solution quality and efficiency of the algorithm.
文摘The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is introduced. Compared with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
文摘The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary body to be in shape of an oblate spheroid. The equilibrium points are sought by the application of the propellant for which it would just balance the gravitational forces. The launching flight of such a satellite is seen to be applicable for having arbitrary space stations for these different missions. Specialty of the result of the investigation lies in the fact that an arbitrary space station can be formed to attain any specified mission.
文摘最小负载着色问题(minimum load coloring problem,MLCP)源于构建光通信网络的波分复用(wavelength division multiplexing,WDM)技术,是一个被证明的NP完全问题.由于NP完全问题有着随问题规模呈指数增长的解空间,因此启发式算法常被用来解决这类问题.在对国内外相关工作的深入分析基础上得知,现有的多类求解MLCP问题的启发式算法中局部搜索算法表现是最好的.研究针对当前求解MLCP问题的局部搜索算法在数据预处理和邻域空间搜索上的不足,提出了两点相应的优化策略:一是在数据的预处理阶段,提出一度顶点规则来约简数据的规模,进而减小MLCP问题的搜索空间;二是在算法的邻域空间搜索阶段,提出两阶段多重选择策略(twostage best from multiple selections,TSBMS)来帮助局部搜索算法在面对不同规模的邻域空间时可以高效地选择一个高质量的邻居解,它有效地提高了局部搜索算法在处理不同规模数据时的求解表现.将这个优化后的局部搜索算法命名为IRLTS.采用74个经典的测试用例来验证IRLTS算法的有效性.实验结果表明,无论最优解还是平均解,IRLTS算法在大多数测试用例上都明显优于当前表现最好的3个局部搜索算法.此外,还通过实验验证了所提策略的有效性以及分析了关键参数对算法的影响.
