Table of Content

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.