Browsing by Author "Hu, Nian-Ze"

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A Superior Representation Method for Piecewise Linear Functions
(2009-03-01)
Li, Han-Lin
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Lu, Hao-Chun
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Huang, Chia-Hui
;
Hu, Nian-Ze
;
資訊管理與財務金融系註：原資管所+財金所
Many nonlinear programs can be piecewisely linearized by adding extra binary variables. For the last four decades, several techniques of formulating a piecewise linear function have been developed. By expressing a piecewise linear function with m+1 break points, the current method requires us to use m additional binary variables and 4m constraints, which causes heavy computation when m is large. This study proposes a superior way of expressing the same piecewise linear function, where only [log(2)m] binary variables and 8+8 [log(2)m] additive constraints are used. Various numerical experiments demonstrate that the proposed method is more computationally efficient than current methods.
Solving Packing Problems by a Distributed Global Optimization Algorithm
(2012)
Hu, Nian-Ze
;
Li, Han-Lin
;
Tsai, Jung-Fa
;
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."