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An approximately global optimization method for assortment problems
(1998-03-16)
Li, HL
;
Chang, CT
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Assortment problems occur when we want to cut a number of small rectangular pieces from a large rectangle to get the minimum area within the rectangle. Recently, Chen et al. proposed a useful model for assortment problems. Although Chen et al.'s model is quite promising to find solutions, there are two inadequacies in their model: firstly, the objective function in their model is a polynomial term, which may not lead to a globally optimal solution; secondly, too many 0-1 variables are used to formulate the non-overlapping constraints. We propose a new method to reformulate an assortment model. Our model is not only able to find the approximately global optimal solution, but involves less 0-1 variables for formulating non-overlapping constraints. (C) 1998 Elsvier Science B.V.
An approximate approach of global optimization for polynomial programming problems
(1998-06-16)
Li, HL
;
Chang, CT
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Many methods for solving polynomial programming problems can only find locally optimal solutions. This paper proposes a method for finding the approximately globally optimal solutions of polynomial programs. Representing a bounded continuous variable x(i) as the addition of a discrete variable d(i) and a small variable epsilon(i), a polynomial term x(i)x(j) can be expanded as the sum of d(i)x(j), d(j) epsilon(i) and epsilon(i) epsilon(j). A procedure is then developed to fully linearize d(i)x(j) and d(j) epsilon(i), and to approximately linearize epsilon(i) epsilon(j) with an error below a pre-specified tolerance. This linearization procedure can also be extended to higher order polynomial programs. Several polynomial programming examples in the literature are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a pre-specified error. (C) 1998 Elsevier Science B.V.
Solve least absolute value regression problems using modified goal programming techniques
(1998-12-01)
Li, HL
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Comments on "Fuzzy programming with nonlinear membership functions..."
(1999-01-01)
Li, HL
;
Yu, CS
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Yang ct al., in their paper "Fuzzy programming with nonlinear membership functions...", published in Fuzzy Sets and Systems 41 (1991), declared that their model can solve a fuzzy program with an S-shaped membership function by adding only one 0-1 variable. This paper indicates that their declaration is correct only for a specific type of S-shape membership functions. We propose another model to treat the fuzzy programs which cannot be solved effectively by Yang et al. (C) 1999 Elsevier Science B.V. All rights reserved.
A general piecewise necessity regression analysis based on linear programming
(1999-08-01)
Yu, JR
;
Tzeng, GH
;
Li, HL
;
運輸與物流管理系註：原交通所+運管所
;
資訊管理與財務金融系註：原資管所+財金所
In possibilistic regression analysis proposed by Tanaka and Ishibuchi (1992), linear programming (LP) formulation of necessity analysis has no feasible solution under the enormous variation of the given data. This work proposes a general piecewise necessity regression analysis based on LP rather than a non-linear interval model that they recommended to obtain the necessity area of the given data. In addition to maintaining a linear property, the proposed method prevents the necessity analysis from having no feasible solution. The problematic univariate example and a multivariate example with respect to different number of change-points are demonstrated by the general piecewise necessity regression. The proposed method characteristic is that, according to data distribution, practitioners can specify the number and the positions of change-points. The proposed method maintains the linear interval model and the order of necessity regression function does not need to be determined. (C) 1999 Elsevier Science B.V. All rights reserved.
A global optimization method for nonconvex separable programming problems
(1999-09-01)
Li, HL
;
Yu, CS
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0-1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0-1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizing these absolute terms allows us to convert a NSP problem into a linearly mixed 0-1 program solvable for reaching a solution which is extremely close to the global optimum. (C) 1999 Elsevier Science B.V. All rights reserved.
A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients
(2000-01-01)
Li, HL
;
Yu, CS
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
A method is proposed for solving a fuzzy multi-objective linear programming problem (FMP) with quasiconcave membership functions and fuzzy coefficients. The proposed method first expresses a piecewise function as the summation of absolute terms. Then we search for the interval where the optimal solution is allocated by finding the corresponding points with same value of membership functions. After that, the problem is solved by goal programming techniques. Comparing with other FMP methods, the proposed method does not need to add extra zero-one variables, to divide the original problem into several sub-problems, or transforming all original quasiconcave functions into concave functions. In addition, the proposed method could solve a FMP problem with fuzzy coefficients;to obtain a solution closing to a global optimum. (C) 2000 Elsevier Science B.V. All rights reserved.
A necessary and sufficient condition for minimizing a convex Frechet differentiable function on a certain hyperplane
(2001-01-01)
Li, HL
;
Liu, YH
;
Matache, V
;
Yu, PL
;
資訊管理與財務金融系註：原資管所+財金所
A convex Frechet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic. (C) 2001 Academic Press.
General fuzzy piecewise regression analysis with automatic change-point detection
(2001-04-16)
Yu, JR
;
Tzeng, GH
;
Li, HL
;
管理學院
;
運輸與物流管理系註：原交通所+運管所
Yu et al. (Fuzzy Sets and Systems 105 (1999) 429) performed general piecewise necessity regression analysis based on linear programming (LP) to obtain the necessity area. Their method is the same as that according to data distribution, even if the data are irregular, practitioners must specify the number and the positions of change-points. However, as the sample size increases, the number of change-points increases and the piecewise linear interval model also becomes complex. Therefore, this work devises general fuzzy piecewise regression analysis with automatic change-point detection to simultaneously obtain the fuzzy regression model and the positions of change-points. Fuzzy piecewise possibility and necessity regression models are employed when the function behaves differently in different parts of the range of crisp input variables. As stated, the above problem can be formulated as a mixed-integer programming problem. The proposed fuzzy piecewise regression method has three advantages: (a) Previously specifying the number of change-points, then the positions of change-points and the fuzzy piecewise regression model are obtained simultaneously. (b) It is more robust than conventional fuzzy regression. The conventional regression is sensitive to outliers. In contrast, utilizing piecewise concept, the proposed method can deal with outliers by automatically segmenting the data. (c) By employing the mixed integer programming, the solution is the global optimal rather than local optimal solution. For illustrating more detail, two numerical examples are shown in this paper. By using the proposed method, the fuzzy piecewise regression model with detecting change-points can be derived simultaneously. (C) 2001 Elsevier Science B.V. All rights reserved.
Method for solving quasi-concave and non-concave fuzzy multi-objective programming problems
(2001-09-01)
Yu, CS
;
Li, HL
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we find the convex-type break points acid transform all quasi-concave membership functions into concave functions. After that, the converted program is solved by linear programming techniques to obtain a global optimum. Tn addition to not containing any of the zero-one variables, the proposed method does not require dividing the quasi-concave FMOP problem into large sub-problems as in conventional methods. The extension of the proposed method can treat general non-concave FMOP problems by merely adding less number of zero-one variables. (C) 2001 Elsevier Science B.V. All rights reserved.

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