Browsing by Author "Tsai, Jung-Fa"

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A distributed computation algorithm for solving portfolio problems with integer variables
(2008-04-16)
Li, Han-Lin
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Tsai, Jung-Fa
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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 portfolio problem with integer variables can facilitate the use of complex models, including models containing discrete asset values, transaction costs, and logical constraints. This study proposes a distributed algorithm for solving a portfolio program to obtain a global optimum. For a portfolio problem with n integer variables, the objective function first is converted into an ellipse function containing n separated quadratic terms. Next, the problem is decomposed into m equal-size separable programming problems solvable by a distributed computation system composed of rn personal computers linked via the Internet. The numerical examples illustrate that the proposed method can obtain the global optimum effectively for large scale portfolio problems involving integral variables. (c) 2007 Elsevier B.V. All rights reserved.
An optimization algorithm for cutting stock problems in the TFT-LCD industry
(2009-10-01)
Tsai, Jung-Fa
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Hsieh, Ping-Lun
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Huang, Yao-Huei
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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
Due to lack of efficient approaches of mixed production, the present production approach of the TFT-LCD industry is batch production that each glass substrate is cut into LCD plates of one size only. This study proposes an optimization algorithm for cutting stock problems of the TFT-LCD industry. The proposed algorithm minimizes the number of glass substrates required to satisfy the orders, therefore reducing the production costs. Additionally, the solution of the proposed algorithm is a global optimum which is different from a local optimum or a feasible solution that is found by the heuristic algorithm. Numerical examples are also presented to illustrate the usefulness of the proposed algorithm. (C) 2009 Elsevier Ltd. All rights reserved.
Convex underestimation for posynomial functions of positive variables
(2008-06-01)
Li, Han-Lin
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Tsai, Jung-Fa
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Floudas, Christodoulos A.
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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 approximation of the convex envelope of nonconvex functions is an essential part in deterministic global optimization techniques (Floudas in Deterministic Global Optimization: Theory, Methods and Application, 2000). Current convex underestimation algorithms for multilinear terms, based on arithmetic intervals or recursive arithmetic intervals (Hamed in Calculation of bounds on variables and underestimating convex functions for nonconvex functions, 1991; Maranas and Floudas in J Global Optim 7: 143-182, (1995); Ryoo and Sahinidis in J Global Optim 19: 403-424, (2001)), introduce a large number of linear cuts. Meyer and Floudas (Trilinear monomials with positive or negative domains: Facets of convex and concave envelopes, pp. 327-352, (2003); J Global Optim 29: 125-155, (2004)), introduced the complete set of explicit facets for the convex and concave envelopes of trilinear monomials with general bounds. This study proposes a novel method to underestimate posynomial functions of strictly positive variables.
Solving Packing Problems by a Distributed Global Optimization Algorithm
(2012)
Hu, Nian-Ze
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Li, Han-Lin
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Tsai, Jung-Fa
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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 boxes within a minimum volume rectangular box. Current packing optimization methods either find it difficult to obtain an optimal solution or require too many extra 0-1 variables in the solution process. This study develops a novel method to convert the nonlinear objective function in a packing program into an increasing function with single variable and two fixed parameters. The original packing program then becomes a linear program promising to obtain a global optimum. Such a linear program is decomposed into several subproblems by specifying various parameter values, which is solvable simultaneously by a distributed computation algorithm. A reference solution obtained by applying a genetic algorithm is used as an upper bound of the optimal solution, used to reduce the entire search region."