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15 December 2011, Volume 15 Issue 4
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Original Articles
Some Results On the Laplacian Spectral Radii of Tricyclic Graphs
CHEN Yan, YUAN Xi-Ying, HAN Miao-Miao
2011, 15(4): 1-8.
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A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. Let $\Delta(G)$ and $\mu(G)$ denote the maximum degree and the Laplacian spectral radius of a graph $G$, respectively. Let $\mathcal {T}(n)$ be the set of tricyclic graphs on $n$ vertices.~In this paper,~it is proved that,~for two graphs $H_{1}$ and $H_{2}$ in $\mathcal {T}(n)$,~if $\Delta(H_{1})> \Delta(H_{2})$ and $\Delta(H_{1})\geq \frac{n+7}{2}$,~then $\mu (H_{1})> \mu (H_{2}).$ As an application of this result,~we determine the seventh to the nineteenth largest values of the Laplacian spectral radii among all the graphs in $\mathcal {T}(n)(n\geq9)$ together with the corresponding graphs.
Parametric Well-posedness for Weak Vector Equilibrium Problems
MA Bo-Chang, WU Jian-Jun, GONG Xun-Hua
2011, 15(4): 9-22.
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The paper studied two kinds of parametric well-posedness for weak vector equilibrium problems in real Banach spaces. It established some metric characterizations of uniquely well-posedness and well-posedness for the problems. It proved that under suitable conditions, the uniquely well-posedness is equivalent to the existence and uniqueness of solutions. Finally, it gave sufficient conditions to well-posedness in finite dimensional space.
Optimization Methods for a Class of Integer Polynomial Programming Problems
TIAN Jing, WU Zhi-You, J. Ugon
2011, 15(4): 23-35.
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In this paper, a class of integer polynomial programming problems is considered. This class of integer polynomial programming problems has a wide range of practical applications and is NP hard. For these problems, necessary global optimality conditions and sufficient global optimality conditions have been presented recently. We will design some optimization methods to this class of integer polynomial programming problems by using these global optimality conditions. Firstly, a local optimization method is designed according to the necessary global optimality conditions for these integer polynomial programming problems. Moreover, a new global optimization method for this class of integer polynomial programming problems is presented by combining the sufficient global optimality conditions, the local optimization method and an auxiliary function. Some numerical examples are presented to illustrate the efficiency and reliability of these optimization methods.
The Wiener Index of Trees with Prescribed Diameter
XING Bao-Hua, Cai-Gai-Xiang
2011, 15(4): 36-44.
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The Wiener index W(G) of a graph G is defined as the sum of dG(u,v) over all pairs of vertices, where dG(u,v)is the distance between vertices u and v in G . In this paper, we characterize the trees with third-minimum Wiener index and intrduce the method of obtaining the order of Wiener indices among all the trees with n vertices and diameter d, respectively.
The BP Neural Network Hydrological Forecasting Algorithm Based on Tunneling Function Method
WANG Sheng-Gang, ZHANG Ying, XU Ying-Tao
2011, 15(4): 45-54.
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BP neural network is widely used in hydrological forecasting. Aiming at the handicaps in present methods such as slow convergence and easily getting into local optimization, this paper presents a novel hydrological forecasting method based on the tunneling function which is one of the effective deterministic methods. The tunneling function method can find a lower minimizer by leaving the minimizer previously found. By repeating these processes, a global minimizer can be obtained at last. Experiments show the proposed method not only can obtain high accuracy in flood forecasting, but also has longer effective real-time. The hydrological forecasting method can be used in operational hydrological forecasting.
A Multiplier Sequential Partial Penalization Algorithm for Mathematical Programs with Complementarity Constraints
LIU Shui-Xia, CHEN Guo-Qing
2011, 15(4): 55-64.
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By using the Lagrangian function of the complementarity problem, a mathematical program with complementarity constraints (MPCC) is reformulated as a constrained optimization problem with the multiplier parameter. The simple modified strategy of the multiplier parameter is provided. Based on this, a multiplier sequential partial penalization algorithm for MPCC is proposed. Without requiring the second-order necessary condition, we show the limited point of the sequence (generated from the algorithm) is an M-stationary point if it is the feasible to MPCC and the MPCC linear independence constraint qualification (LICQ) holds. Moreover, it is B-stationary point if the upper lever strict complementarity(ULSC) holds.
Two-machine open shop scheduling with machine-dependent processing times
Zhen-Wei WEN
2011, 15(4): 65-74.
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Abstract A two-machine open shop scheduling problem with machine-dependent processing times O2 | pij = pi, p2< p1< 2p2, Non-Idle | ΣCj is examined. Xiang & Tang prove that this problem can be transformed to an assignment problem which is polynomially solvable. Yu & Ying give an explicit solution of this problem, and proves its optimality. In addition they present that the explicit solution is not exclusive and other optimal solutions are possible exist. We give a simple proof of the optimality of the explicit solution Yu & Ying proposed and discuss the uniqueness of the optimal solution.
The $\tau$-value of Cooperative Games Restricted by Graph
WANG Wen-Wen, SUN Hao, HAN Wei-Bin
2011, 15(4): 75-84.
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We first study the $\tau$-value for graph-restricted games and provide its explicit construction. The one-point solution could be considered as a natural extension of the $\tau$-value introduced by Tijs for classical cooperative games. When the cooperation graph is complete, the $\tau$-value for graph-restricted games coincides with the $\tau$-value for classical cooperative games. Then we provide an axiomatization of the $\tau$-value for graph-restricted games via component efficiency, relative invariance under S-equivalence and restricted proportionality. The last section introduces the $\tau$-value for two special classes of graph-restricted games.
Fuzzy programming approach for Multilevel linear programming
SONG Wei, ZHAO Mao-Xian, WANG Xiang-Rong
2011, 15(4): 85-92.
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In this paper, membership functions of fuzzy set theory described each objective of multilevel linear programming, after the first decision-maker gives a minimum satisfaction level, by solving the corresponding levels of fuzzy programming to determine the minimum satisfaction degree of each level, and ultimately gets a satisfactory solution of the problem. The proposed method only needs to solve a series of linear programming problems, with better complexity and feasibility, the last example further verifies the validity of the method.
Disaster Spots Inventory Policy with Emergency Item Unidirectional Transshipment
WANG Chuan-Xu-, JIANG Liang-Kui
2011, 15(4): 93-101.
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To analyzes disaster spots inventory policy with unidirectional transshipment among disaster spots in emergency relief logistics, the situation considered in this paper is a single-echelon system consisting of a number of disaster spots with unidirectional emergency item transshipment. Firstly, based on fixed replenishment point for individual disaster spots, a model is developed to determine the fraction of demand directly satisfied from stock at disaster spots and the fraction of demand satisfied by transshipment from stock at other disaster spots. Secondly, an integer non-linear program model is developed to determine the optimal relief item replenishment point for individual disaster spots, in which the time-based relief efficiency constraint is considered. Meanwhile, an implicit enumeration-based method is developed to solve the proposed model. At last, a numerical example is given to demonstrate the efficiency and practicability of the model.
A Polynomial Time Algorithm for the Economic Lot-size Problem with Multiple Suppliers and Multiple Retailers
XU Jian-Teng, ZHANG Yu-Zhong, BAI Qing-Guo
2011, 15(4): 102-114.
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The economic lot size problem with quantity discount policy in a supply chain consisted of multi-supplier and multi-retailer is considered. Via constructing optimization models, some special optimal properties are proposed for the cases where order cost is all-unit quantity discount and incremental quantity discount, respectively. With the help of these optimal properties, the searching range of the optimal solutions is reduced under dynamic programming method. The polynomial time algorithms are developed for a special case of the model with all-unit quantity discount cost structure and the model with incremental quantity discount cost structure. Finally, the numerical examples illustrates the efficiency and implementation processes of the algorithms.
A new augmented lagrangian function based on inequalty constraints problem
LIU Mu-Hua, SHANG You-Lin, LI Pu
2011, 15(4): 115-123.
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A new kind of augmented lagrangian function is proposed in this paper. We proved that there are the 1-1 corresponding relationships between the stable point of the lagrangian function and KKT point of the original problem. The same results are obtained for the both global minimum point. The local minimum point of the augmented lagrangian function is the local minimum point of the original problem.
CRS algorithm based on the simulated annealing
TANG Dan
2011, 15(4): 124-128.
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In this paper, a new algorithm is proposed for the nonlinear programming problems, The algorithm applied the simulated annealing to the CRS algorithm, According to the simulated annealing reflects on concentrates and proliferates in each iteration, Enables the CRS algorithm to search the global optimization more easier rather than the local optimization. Finally, the proposed algorithm is applied to two typical function optimization problems, and the numerical results illustrate the accuracy and efficiency of the algorithm.
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Periodicals Agency of Shanghai University
Journal of Chongqing Normal University (Natural Science)
Operations Research Society of China
International Federation of Operational Research Societies
Information
Quarterly, Founded in 1997
Superintendent by:China Association for Science and Technology
Sponsored by:Operations Research Society of China
Organized by:Shanghai University
Editor-in-Chief:HU Xudong
ISSN 1007-6093
CN 31-1732/O1