Browsing by Author "Li, HL"

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A diagnostic reasoning and optimal treatment model for bacteria infections with fuzzy information
(2005-01-01)
Kao, HY
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Li, HL
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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 study proposes an optimization model for optimal treatment of bacterial infections. Using an influence diagram as the knowledge and decision model, we can conduct two kinds of reasoning simultaneously: diagnostic reasoning and treatment planning. The input information of the reasoning system are conditional probability distributions of the network model, the costs of the candidate antibiotic treatments, the expected effects of the treatments, and extra constraints regarding belief propagation. Since the prevalence of the pathogens and infections are determined by many site-by-site factors, which are not compliant with conventional approaches for approximate reasoning, we introduce fuzzy information. The output results of the reasoning model are the Likelihood of a bacterial infection, the most likely pathogen(s), the suggestion of optimal treatment, the gain of life expectancy for the patient related to the optimal treatment, the probability of coverage associated with the antibiotic treatment, and the cost-effect analysis of the treatment prescribed. (C) 2004 Elsevier Ireland Ltd. All rights reserved.
A distributed global optimization method for packing problems
(2003-04-01)
Li, HL
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Tsai, JF
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Hu, NZ
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Packing optimization problems aim to seek the best way of placing a given set of rectangular cartons within a minimum volume rectangular container. Currently, packing optimization methods either have difficulty in finding a globally optimal solution or are computationally inefficient, because models involve too many 0-1 variables and because use of just a single computer. This study proposes a distributed computation method for solving a packing problem by a set of personal computers via the Internet. First, the traditional packing optimization model is converted into an equivalent model containing many fewer 0-1 variables. Then the model is decomposed into several sub-problems by dividing the objective value into many intervals. Each of these sub-problems is a linearized logarithmic program expressed as a linear mixed 0-1 problem. The whole problem is solvable and reaches a globally optimal solution. The numerical examples demonstrate that the proposed method can obtain the global optimum of a packing problem effectively.
A fast algorithm for assortment optimization problems
(2001-10-01)
Li, HL
;
Tsai, JF
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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 optimization problems intend to seek the best way of placing a given set of rectangles within a minimum-area rectangle. Such problems are often formulated as a quadratic mixed 0-1 program. Many current methods for assortment problems are either unable to find an optimal solution or being computationally inefficient for reaching an optimal solution. This paper proposes a new method which finds the optimum of assortment problem by solving few linear mixed 0-1 programs. Numerical examples show that the proposed method is more computationally efficient than current methods.
A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients
(2000-01-01)
Li, HL
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Yu, CS
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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 general piecewise necessity regression analysis based on linear programming
(1999-08-01)
Yu, JR
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Tzeng, GH
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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
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Yu, CS
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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 global optimization method for packing problems
(2006-09-01)
Tsai, JF
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Li, HL
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The objective of packing problems is to determine an optimal way of placing a given set of three-dimensional (3D) rectangular cartons within a minimum volume 3D rectangular container. Current packing optimization methods either use too many extra 0-1 variables or find it difficult to obtain a globally optimal solution. This study proposes an efficient method for finding the global optimum of packing problems. First the traditional packing optimization problem is converted into an equivalent program containing many fewer 0-1 variables than contained in current methods. Then the global optimum of the converted program is found by utilizing piecewise linearization techniques. The numerical examples demonstrate that the proposed method is capable of finding the global optimum of a packing problem.
A linear programming approach for identifying a consensus sequence on DNA sequences
(2005-05-01)
Li, HL
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Fu, CJ
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Motivation: Maximum-likelihood methods for solving the consensus sequence identification (CSI) problem on DNA sequences may only find a local optimum rather than the global optimum. Additionally, such methods do not allow logical constraints to be imposed on their models. This study develops a linear programming technique to solve CSI problems by finding an optimum consensus sequence. This method is computationally more efficient and is guaranteed to reach the global optimum. The developed method can also be extended to treat more complicated CSI problems with ambiguous conserved patterns. Results: A CSI problem is first formulated as a non-linear mixed 0-1 optimization program, which is then converted into a linear mixed 0-1 program. The proposed method provides the following advantages over maximum-likelihood methods: (1) It is guaranteed to find the global optimum. (2) It can embed various logical constraints into the corresponding model. (3) It is applicable to problems with many long sequences. (4) It can find the second and the third best solutions. An extension of the proposed linear mixed 0-1 program is also designed to solve CSI problems with an unknown spacer length between conserved regions. Two examples of searching for CRP-binding sites and for FNR-binding sites in the Escherichia coli genome are used to illustrate and test the proposed method.
A necessary and sufficient condition for minimizing a convex Frechet differentiable function on a certain hyperplane
(2001-01-01)
Li, HL
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Liu, YH
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Matache, V
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Yu, PL
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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.
An algorithm for generalized fuzzy binary linear programming problems
(2001-09-16)
Yu, CS
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Li, HL
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Fuzzy binary linear programming (FBLP) problems are very essential in many fields such as assignment and assembly line balancing problems in operational research, multiple projects, locations, and candidates selection cases in management science, as well as representing and reasoning with prepositional knowledge in artificial intelligence. Although FBLP problems play a significant role in human decision environment, not very much research has focused on FBLP problems. This work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term. A method of linearizing absolute terms is also presented. The developed goal programming (GP) model weighted by decision-makers' (DMs) preference aims to optimize the expected objective function and minimize the sum of possible membership functions' deviations. After presented a novel way of linearizing product terms, the solution algorithm is proposed to generate a crisp trade-off promising solution that is also an optimal solution in a certain sense. Three examples, equipment purchasing choice, investment project selection, and assigning clients to project leaders, illustrate that the proposed algorithm can effectively solve generalized FBLP problems. (C) 2001 Elsevier Science B.V. All rights reserved.
An approximate approach of global optimization for polynomial programming problems
(1998-06-16)
Li, HL
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Chang, CT
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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.
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 efficient method for solving linear goal programming problems
(1996-08-01)
Li, HL
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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 note proposes a solution algorithm for linear goal programming problems. The proposed method simplifies the traditional solution methods. Also, the proposed method is computationally efficient.
An efficient method for solving linear goal programming problems
(1996-08-01)
Li, HL
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交大名義發表
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資訊管理與財務金融系註：原資管所+財金所
;
National Chiao Tung University
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Department of Information Management and Finance
This note proposes a solution algorithm for linear goal programming problems. The proposed method simplifies the traditional solution methods. Also, the proposed method is computationally efficient.
Answering queries on graphical decision models with fuzzy parameters: Algorithms and comparisons
(2004)
Kao, HY
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Huang, CH
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Li, HL
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
The reasoning strategy is a critical component for expert systems or decision support systems. After thorough self-evaluation and environmental scan, the knowledge workers need a reliable mechanism for diagnosis and an optimal suggestion for problem solving. This paper designs a reasoning model with a well-known graphical decision model, influence diagrams. In the proposed model, fuzzy probabilities as well as crisp probabilities are involved. The influence diagrams work compactly in problem diagnosis and decision making aid. Two algorithms to handle the fuzzy parameters, piecewise linearization and alpha-cut methods will be implemented and compared.
Approximately global optimization for assortment problems using piecewise linearization techniques
(2002-08-01)
Li, HL
;
Chang, CT
;
Tsai, JF
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Recently, Li and Chang proposed an approximate model for assortment problems. Although their model is quite promising to find approximately global solution, too many 0-1 variables are required in their solution process. This paper proposes another way for solving the same problem. The proposed method uses iteratively a technique of piecewise linearization of the quadratic objective function. Numerical examples demonstrate that the proposed method is computationally more efficient than the Li and Chang method. (C) 2002 Elsevier Science B.V. All rights reserved.
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.
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.
Constrained abductive reasoning with fuzzy parameters in Bayesian networks
(2005-01-01)
Li, HL
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Kao, HY
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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 work proposes a novel approach for solving abductive reasoning problems in Bayesian networks involving fuzzy parameters and extra constraints. The proposed method formulates abduction problems using nonlinear programming. To maximize the sum of the fuzzy membership functions subjected to various constraints, such as boundary, dependency and disjunctive conditions, unknown node belief propagation is completed. The model developed here can be built on any exact propagation methods, including clustering, joint tree decomposition, etc. (C) 2003 Elsevier Ltd. All rights reserved.
General fuzzy piecewise regression analysis with automatic change-point detection
(2001-04-16)
Yu, JR
;
Tzeng, GH
;
Li, HL
;
管理學院
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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.