Generalized Reduced Trust-region Search and Its Applications to Statistical Multi-Objective Optimization
Date Issued
2008
Date
2008
Author(s)
Chen, Yen-Ting
Abstract
“Generalized Reduced Gradient” method is a popular NLP method, but it often incurs a zigzagging search path especially for the statistical multi-objective optimization (SMOO) problem where the objective function is a quartic function. In this study, we improve the “Trust Region (TR)” search method and develop the “Generalized Reduced Trust Region” (GRT) search method which combines the GRG method and the improved TR method. The GRT search transforms the constrained NLP problem to an unconstrained NLP problem consisting of only the nonbasic variables and searches the best improving direction in the reduced space. The proposed method is shown to overcome the zigzagging problem of the GRG method. To verify the performance of our methods, we study a well know test problem and three cases. The test problem is called Rosenbrock’s function which has a quartic objective function with two decision variables. The first case is a semiconductor design for manufacturing (DFM) problem. The second case is the problem to configure a robust semiconductor supply chain. The final case is the “Track System PEB CDU Optimization”. Compared against the result of the commercial software “Lingo”, the same or better solutions are obtained by our methods with comparable computation time.
Subjects
Nonlinear Programming
Statistical Multi-Objective Optimization
Generalized Reduced Gradient Method
Generalized Reduced Trust Region Method
Trust Region Method
Type
thesis
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