Integration and propagation of a multi-criteria decision making model in constraint programming

In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .     

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

提前还贷及其隐含期权的分析

可提前还款的定期贷款是隐含着期权的利率衍生物，本文建立CIR利率模型下可提前还款的定期贷款的数学模型，通过离散偏微分方程，建立了模型的计算方法，讨论了随机利率对提前还贷的影响．     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Jensen’s Inequality for Backward Stochastic Differential Equations

Abstract Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9]. *Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.     

Kuhn-Tucker条件与线性规划的对偶性

证明了线性规划的K uhn-Tucker条件蕴含着它的对偶问题,解释了L agrange乘子的意义.进而显示了K-T条件中的互补松驰性与对偶线性规划的互补松紧定理之间的联系.     

A new approach based on the surrogating method in the project time compression problems

This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.     

Quadratic distances for capacity and bi-capacity approximation and identification

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. The proposed approach, consisting in solving a strictly convex quadratic program, has been implemented within the GNU R kappalab package for capacity and nonadditive integral manipulation. Its application is illustrated on two examples.      

Algorithmic and explicit determination of the Lovász number for certain circulant graphs

We consider the problem of computing the Lovász theta function for circulant graphs C_n,J of degree four with n vertices and chord length J, 2?J?n. We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation. We also provide explicit formulas for the important special cases J=2 and J=3.