Table of Content

15 June 2010, Volume 14 Issue 2

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Original Articles

Dense Schedule for Open Shop Problems with at Most   Two Idle Intervals on the Last Complete Machine

CHEN Rong-Jun, HUANG Wan-Zhen, TANG Guo-Chun

2010, 14(2):  1-10. 

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For open shop problem, if the principle of avoiding unnecessary machine idleness is applied when arranging jobs, a dense schedule is obtained. It is conjectured that the makespan of any dense schedule is at most $2-1/m$ times the optimal makespan of the problem, where m is the number of machines. The conjecture remains unproved when the number of machine is greater than six. In this paper, by introducing characteristic functions of jobs and machines and non-interruption of machines about jobs, we propose  sufficient conditions under which the conjecture is true for general number of machines, provided that the last complete machine in the dense schedule has no more than two idle intervals.

A Smoothing Approximation to the Lower Order Exact Penalty Function

HE Zhen-Hua, BAI Fu-Sheng

2010, 14(2):  11-22. 

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In this paper, we propose a smoothing approximation to the lower order exact penalty functions for inequality-constrained optimization problems. An algorithm is presented to obtain an approximate global solution of the original optimization problem by searching a global solution of the smoothed penalty problem. Several numerical examples are given to illustrate the effectiveness of the present smoothing method.  

The Pos/Neg-weighted 2-Median Problem on Interval Graphs

CHENG Yu-Kun

2010, 14(2):  23-36. 

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This paper deals with the facility location problem on interval graphs with ositive and negative interval weights. We consider two different objective functions: the sum of the minimum weighted distances (MWD) of the intervals from the facilities and the sum of the weighted minimum distances (WMD). Two $O(n^2)$ time algorithms for both models of the 2-median problem have been developed.    

A Hybrid  PSO Algorithm Based on Penalty Function for Solving Zero-One Nonlinear Programming Problems

Gao-Yue-Lin, LEI Fan-Fan, LI Hui-Rong

2010, 14(2):  37-44. 

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Using penalty function,we transform  zero-one nonlinear programming problems into unconstrained optimization problem. Then we combine particle swarm optimization with penalty function method  to produce a PSO hybrid algorithm based on penalty function. It can be shown by the numerical results that the proposed algorithm is effective.    

 Optimality and Duality for a Class of  Nonsmooth  Optimization Problems

ZHAO Ke-Quan, TANG Li-Ping, YANG Xin-Min

2010, 14(2):  45-54. 

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In this paper, a class of nonsmooth multiobjective optimization problems in which involved equality constraints and inequality constraints is considered. The generalized Karush-Kuhn-Tucker necessary and sufficient optimality conditions are given. Furthermore, mixed type dual model is discussed, and theorems of weak duality, strong duality, converse duality, strict converse duality and restricted converse duality are presented.

On the Extremal Wiener Indices of Some Graphs

LIN Xiao-Xia

2010, 14(2):  55-60. 

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 The Wiener index of a graph is defined as the sum of distances between all pairs of vertices of the graph. It has been found extensive applications in chemistry. In this paper, we characterize the graphs which minimize the Wiener index among all graphs with given order and specific parameter, such as the chromatic number or clique number, and the graphs which maximize the Wiener index among all graphs with given order and clique number.

 Analysis of a Discrete-Time Preemptive Priority Queue

LI Gang, ZHANG Hua-Juan

2010, 14(2):  61-69. 

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In this paper, we consider a discrete-time preemptive priority queue with a single server and two types of customers. The stationary probabilities are presented in a matrix form with respect to the background state space. Applying the matrix analytic method, it is shown that certain reasonable conditions lead to a geometric decay of the tail probabilities as the level goes to infinity.

 A System Equations Method with Arbitrary Initial Point for Semi-infinite Programming

SUN Qing-Ying, GAO Bao, SANG Zhao-Yang, TIAN Feng-Ting

2010, 14(2):  70-78. 

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 Based on discretization technique and  diagonal-sparse quasi-Newton method, an improved system equations method with arbitrary initial point for semi-infinite programming is presented. The global and super-linear convergence properties of the new method are discussed. The numerical results illustrate that the new method is more effective than the original algorithm.

Bounding the Efficiency Loss with Mixed Equilibrium Associated  with User Equilibrium and Logit-Based

LUO Wen-Chang

2010, 14(2):  79-86. 

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In a transportation network with users classified into two categories, the first category chooses the route according to user equilibrium(UE)  principle and the second category chooses the route according to Logit-based stochastic user  equilibrium(LSUE)  principle. In this paper, a variational inequality is proposed to  formulate the mixed equilibrium travel behavior associated with user equilibrium and Logit-based stochastic user  equilibrium. Likewise, the upper bound of efficiency loss for the  mixed equilibrium is described as a general formula. It is shown that the upper bound is related to the  topological structure of networks, transportation demand and the demand  ratio.  

A Problem on Electricity Distribution and Payment   Related to Electricity Bidding Price System

QIU Xiao-Ling

2010, 14(2):  87-94. 

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This article is to set up the ambulant equation of electricity supply and demand on the basis of electric exchange centres; and then prove  the existence, uniqueness of the clearing price, discuss the continuity of clearing price and profits nctions about price function, finally to demonstrate the  existence theorem of  equilibria in different power plants' profits according to the theory of Schauder fixed points. The payment on clearing price may realize the economic Pareto optimizing.  

The Cone Optimization Analysis of Coherent Risk Measures

REN Feng-Ying, LI Xing-Si

2010, 14(2):  95-105. 

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The axiomatic system of coherent risk measures has set up by Artzner et.al. owever, the mathematics underlying it is closely related to the ideas of convex otimization, specifically the duality theory. This paper simply proved the general  expression of coherent risk measures by the cone duality theorem in finite dimension space.  We have analyzed the core role of acceptable set in coherent risk measure and the properties  of conventional risk measures. In spite of the size of acceptable set may be used for controlling the risk management strictly or loosely, but we do not know how to express it quantitatively.   The paper suggest  In addition we suggest relaxing no arbitrage condition in view of the flexibility of coherent  risk measures and the achieved results may be used to pricing option in incomplete market.  

Optimal   Investment Strategy for  Insurers under Linear Constraint

ZENG Yan, LI Zhong-Fei

2010, 14(2):  106-118. 

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In practice, investment behaviors of  an insurer will be subjected to some constraints from Insurance Law and the insurer's own risk management. Additionally,  an insurer should draw certain reserve to satisfy regulatory requirements. Therefore, in this paper we suppose the time when its surplus first comes up to the floor level of reserve as the ``ruin'' time; the target of the insurance company is to minimize the ``ruin'' probability; the surplus process of the insurer is derived by a diffusion model and its investment behaviors are subjected to a linear constraint. By solving the corresponding HJB equation,  the optimal investment strategy and value function are derived explicitly when the insurer is allowed to investment on a risk-free asset and a risky asset. In the end, economic analysis and numerical examples are provided.

A Class of Filled Function for Constrained  Global Optimization

ZHAO De-Fen, WANG Wei

2010, 14(2):  119-128. 

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In this paper, a class of filled function for constrained global optimization is proposed.Also,its filled properties and other analytical properties are proved under several mild assumptions. In addition, according to the theoretical analysis, a new algorithm and two numerical experiments are presented , the computational results show that our algorithm is effective.