Browsing by Author "LI, HL"

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A GLOBAL APPROACH FOR GENERAL 0-1 FRACTIONAL-PROGRAMMING
(1994-03-24)
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
Current methods of general 0-1 fractional programming (G-FP) can only find the local optimum. This paper proposes a new method of solving G-FP problems by a mixed 0-1 linear program to obtain a global optimum. Given a mixed 0-1 polynomial term xy where x is a 0-1 variable and 0 < y less-than-or-equal-to 1, we develop a theorem to transfer the xy term into a set of mixed 0-1 linear inequalities. Based on this theorem, a G-FP problem can be solved by a branch-and-bound method to obtain the global solution.
A GLOBAL APPROACH FOR NONLINEAR MIXED DISCRETE PROGRAMMING IN DESIGN OPTIMIZATION
(1994)
LI, HL
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CHOU, CT
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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
Most current nonlinear mixed discrete programs can only find locally optimal solutions. This paper proposes an optimization method to find the global solution of a nonlinear mixed discrete program. Based on the fact that: ''For a discrete variable x(i), iff x(i) is-an-element-of {k1, k2, . . ., k(m)} then (x(i) - k1) (x(i) - k2) ... (x(i)k(m)) = 0'', the original mixed discrete program is transformed into a penalty optimization program with continuous variables. This penalty optimization program is then solved to find a local optimum. Utilizing the Multi-Level Single Linkage technique, enough starting points are systematically generated to search for most local optima within the feasible region. A global optimum is then found at a prespecified sufficiently high confidence level such as 99.5%. Some examples of design optimization in literature are tested, which demonstrate that the proposed method is superior to current methods for finding the global optimum.
A NEW GLOBAL APPROACH FOR 0-1 POLYNOMIAL PROGRAMS
(1994-03-01)
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
;
Department of Information Management and Finance
Given a 0-1 polynomial expression SIGMA(k=1)N-1 SIGMA(m=k+1)N x(k)x(m), where x(k) and x(m) are 0-1 variables, the famous Glover and Woolsey method required to use N(N - 1)/2 additional continuous variables and 2N(N - 1) linear constraints to transform this expression into a linear form. This paper proposes a method which first reformulates the above expression as a new expression SIGMA(k=1)N x(k)y(k), y(k) = SIGMA(m=k+1)N x(m); then to transform the expression into a linear form where x(k) and y(k) are separated. The proposed transformation method only required to use 2(N - 1) additional continuous variables and 8(N - 1) linear constraints. Based on the new transformation, a 0-1 polynomial program can be more effectively solved to obtain a global optimum.
ABDUCTIVE REASONING BY CONSTRUCTING PROBABILISTIC DEDUCTION GRAPHS FOR SOLVING THE DIAGNOSIS PROBLEM
(1991-05-01)
LI, HL
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YANG, CC
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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
An algorithm is proposed for finding optimal solutions of the diagnosis problem by using deduction graphs (DG) to accomplish abductions of multiple causes and multiple symptoms. The relationship among causes, symptoms, and possible intermediaries is represented by a causal network. The algorithm accomplishes the abduction by constructing a deduction graph DG(C,S) from the cause set C to the symptom set S representing the subnetwork such that the product of the prior probability, P(C), of C and the conditional probability, P(SC), of DG(C,S) is maximized. An optimal solution is achieved by solving a 0/1 linear integer programming problem. Based on some assumptions, the algorithm can deal with a causal network involving various mutually independent deduction graphs.
AN APPROXIMATE METHOD FOR LOCAL OPTIMA FOR NONLINEAR MIXED INTEGER PROGRAMMING-PROBLEMS
(1992-07-01)
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
;
Department of Information Management and Finance
For a nonlinear 0-1 integer programming problem with constraint set X = (x1,...,x(n)), we first add new constraints [GRAPHICS] to the constraint set, thus to convert the integer problem into a nonlinear programming problem. Then we utilize a modified penalty function method to solve this nonlinear program to obtain a local optima Running the proposed method by a widely commercialized nonlinear program software shows that this method is more convenient than current approaches as branch-and-bound method and implicit enumeration method. One issue remained for studies is to expand this method into a global method by systematically generating suitable starting points then to perform optimization processes from each of these points.
GLOBAL OPTIMIZATION FOR MIXED 0-1 PROGRAMS WITH CONVEX OR SEPARABLE CONTINUOUS-FUNCTIONS
(1994-09-01)
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
;
Department of Information Management and Finance
This paper proposes a global approach for solving mixed 0-1 programming problems containing convex or separable continuous functions. Given a mixed 0-1 polynomial term z = x1x2...x(n)g(Y) where x1, x2,..., x(n) are 0-1 integer variables and g(Y) is a convex or a separable continuous function, we can transform z into a set of inequalities where x1, x2,..., x(n) and g(Y) are separated from each other. Based on this transformation, the original mixed 0-1 program can then be solved by a branch-and-bound method to obtain a global optimum.
OPTIMAL COMPETENCE SET EXPANSION USING DEDUCTION GRAPHS
(1994-01-01)
LI, HL
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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
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Department of Information Management and Finance
A competence set is a collection of skills used to solve a problem. Based on deduction graph concepts, this paper proposes a method of finding an optimal process so as to expand a decision maker's competence set to enable him to solve his problem confidently. Using the concept of minimum spanning tree, Yu and Zhang addressed the problem of the optimal expansion of competence sets. In contrast, the method proposed here enjoys the following advantages: it can deal with more general problems involving intermediate skills and compound skills; it can find the optimal solution by utilizing a 0-1 integer program; and it can be directly extended to treat multilevel competence set problems, and thus is more practically useful.