Robust Optimization: Design in MEMS - University of California ...

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21in two different ways. One is to keep track and limit the total number of unsuccessfulsearches. A second method would be to limit the number of sequential searches thatfail.3.5 Algorithm SummaryTo summarize, we were able to exploit the polynomial structure of the objectivefunction and constraints which allowed us to find the feasible regions and minimizethe objective function easily for the scalar problem. For problems in IR n , we used anaffine transformation to do global line searches. The heart of the algorithm lies in thechoosing the search direction, which is done each iteration. Because of the randomnessinvolved in choosing search directions, the algorithm is not deterministic.
22Chapter 4Optimization ExamplesWe will present several example problems in this section to illustrate our rationalpolynomial algorithm presented in chapter 3. These are pure optimization examplesin constrained global minimization and do not directly relate to the robust designproblem posed in chapter 2.4.1 Inventory Control ProblemThe first example is an inventory control problem taken from [10]. The problemhas three non-negative design variables and a single constraint. We will define thedesign vector to be x = [x 1 x 2 x 3 ] T .Objective Functionminxf(x) = 5x2 1x 2 x 3 + 50, 000x 2 x 3 + 20x 1 x 2 2x 3 + 72, 000x 1 x 3 + 10x 1 x 2 x 2 3 + 144, 000x 1 x 2x 1 x 2 x 3Variable Boundsx 1 ≥ 0x 2 ≥ 0x 3 ≥ 0
Page 1 and 2: Robust Optimization:Design in MEMSb
Page 4 and 5: 36 Conclusion 46Bibliography 48A Al
Page 6 and 7: 5List of Tables3.1 Probabilities wi
Page 8 and 9: 7Chapter 1IntroductionMicro-electro
Page 11 and 12: 10performance, f(x, 0), is equal to
Page 13 and 14: 12function f(x), there are several
Page 15 and 16: 14Chapter 3Optimization AlgorithmIn
Page 17 and 18: 16paribus. This can be very effecti
Page 19 and 20: 18to the active linear constraints
Page 21: 20can all the constraints be satisf
Page 25 and 26: 2475007300220200t 1t2t 37100180Cost
Page 27 and 28: 26design variables, other than the
Page 29 and 30: 28Chapter 5Robust Design Examples5.
Page 31 and 32: 30where ¯f is the w 2 design , Σ
Page 33 and 34: 32design along the line c 2 (x) = 0
Page 35 and 36: 34550500450(5)global solutionPath 1
Page 37 and 38: 36Figure 5.6: Diagram of Six Variab
Page 39 and 40: 38problem is well-defined. Before a
Page 41 and 42: 405.2.3 Robust DesignWe will use th
Page 43 and 44: 42evident by noting that the c 2 (x
Page 45 and 46: 44Robust Uncorrelated DesignAverage
Page 47 and 48: 46Chapter 6ConclusionIn this report
Page 49 and 50: 48Bibliography[1] What is MEMS Tech
Page 51: 50Appendix AAlkylation Constantsi c

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