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AAE550_HW3_2011

AAE550_HW3_2011 - AAE 550 MULTIDISCIPLINARY DESIGN...

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AAE 550 MULTIDISCIPLINARY DESIGN OPTIMIZATION FALL 2011 HOMEWORK ASSIGNMENT #3 DUE NOVEMBER 30, 2011 I. NELDER-MEAD SIMPLEX The Matlab routine fminsearch uses the Nelder-Mead Simplex algorithm. On the Blackboard page for Homework 3, the file callNM.m invokes the algorithm, and the file NMfunc.m contains the “egg-crate” function used in class. When turning in the assignment, include a copy of your versions of the callNM.m and NMfunc.m files. Complete tables like those suggested in the questions below to summarize your results. There are many commonly used functions to test global optimization algorithms. The Ackley Function is a common multi-modal test function for global optimization methods. Use the Nelder-Mead Simplex to find the minimum of the 5-D version ( n = 5) of the Ackley Function: minimize f x ( ) = 20exp 0.2 1 n x i 2 i = 1 n exp 1 n cos 2 π x i ( ) i = 1 n + 20 + exp 1 ( ) 10 x i 10 A 2-D version of this function appears in the figure below to provide an idea of the local minima. The n -D version of the Ackley Function has a global minimum of x i ,…, x n = 0, f ( x * ) = 0. 1) Formulate an appropriate objective function for the Nelder-Mead Simplex to account for the bounds on the design variables. Recall that function and / or slope continuity is not a requirement when developing your penalty function. 2) Solve the problem starting from x 0 = [5 5 5 5 5] T . Be sure to use the first x * as x 0 for a re-start of the algorithm. Summarize these runs in a table like the one shown below.

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AAE 550 FALL 2011 HOMEWORK #3, PAGE 2 x 0 Function evaluations x * f ( x *) Run 1 5 5 5 5 5 **** *.**** **.**** Re-start **** **.**** 3) Solve the problem again starting from x 0 = [0.5 0.5 0.5 0.5 0.5] T . As before, use the first x * as x 0 for a re-start of the algorithm. Summarize these runs in a table like the one shown below. x 0 Function evaluations x * f ( x *) Run 1 0.5 0.5 0.5 0.5 0.5 **** **.**** Re-start **** **.**** 4) Solve the problem again starting from x 0 = [-0.1 -0.1 -0.1 -0.1 -0.1] T . Be sure to use the first x * as x 0 for a re- start of the algorithm. Summarize these runs in a table like the one shown below. x 0 Function evaluations x * f ( x *) Run 1 0.1 0.1 0.1 0.1 0.1 **** **.****
AAE 550 FALL 2011 HOMEWORK #3, PAGE 3 Re-start *.**** **** **.**** 5)

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AAE550_HW3_2011 - AAE 550 MULTIDISCIPLINARY DESIGN...

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