Browsing by Author "Li, Wei-Chu"
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Item Monotonicity-Based Decomposition Methods for Design Optimization.(1988) Azarm, Shapour; Li, Wei-Chu; ISRThis paper describes applications of global and local monotonicity analysis within a decomposition framework. We present a general formulation and solution procedure, based on a bottom-level global monotoncity analysis, for a design optimization problem which is decomposed into three levels of subproblems. We then perform an optimality test to prove that the optimality conditions for the decomposed subproblems will form the optimality conditions of the overall problem. Furthermore, applications of a two-level decomposition method is presented in which an overall global monotonicity analysis or first-level local monotonicity analysis is performed. Well-known examples illustrate applications of the methods.Item Multi-Level Design Optimization Using Global Monotonicity.(1988) Azarm, Shapour; Li, Wei-Chu; ISRThis paper describes application of global monotonicity analysis within a multi-level design optimization framework. We present a general formulation and solution procedure, based on a bottom- level global monotonicity analysis, for a design optimization problem which is decomposed into three levels of subproblems. A well known gear reducer example illustrates application of the method.Item Optimal Design Using a Two-Level Monotonicity-Based Decomposition Method.(1987) Azarm, Shapour; Li, Wei-Chu; ISRIn this paper, a two-level decomposition method for optimal design is described. Using this method, an optimal design problem is decomposed into several subproblems in the first-level and a coordinating problem in the second-level. In the first level, the subproblems are analyzed using the global monotonicity concepts, then in the second level the analyses of the subproblems are coordinated to obtain the optimal solution. Two engineering design examples, namely a gear reducer (formulated and solved in the literature) and a flywheel (formulated and solved here), illustrate applications of the developed method.Item Optimal Design Using Decomposition Methods.(1986) Azarm, Shapour; Li, Wei-Chu; ISRIn this paper, a unified review of eight decomposition methods is presented. A two-level decomposition method is proposed, which is an extension of feasible model coordination methods. The method couples the global monotonicity analysis of the first- level subproblem(s) with an optimization method (single-level method) of the second-level. Three classes of problems are considered where in the first-level they have (1) one subproblem with one local variable, (2) several subproblems with one local variable, and (3) several subproblems with several local variables. Some test results have been presented which show the substantially improved performance of the proposed approach over a single-level optimization method.Item Optimality and Constrained Derivatives in Two-Level Design Optimization.(1989) Azarm, Shapour; Li, Wei-Chu; ISRThe objective of this paper is twofold. First, an optimality test is presented to show that the optimality conditions for a two- level design optimization problem before and after its decomposition are the same. Second, based on identification of active constraints and exploitation of problem structure, a simple approach for calculating the gradient of a "second-level" problem is presented. This gradient is an important piece of information which is needed for solution of two-level design optimization problems. Three examples are given to demonstrate applications of the approach.