UNIVERSITY OF SOUTHAMPTON
SESG6018W1
SEMESTER 1 EXAMINATION 2013/14
Design Search and Optimisation 1
Duration: 120 mins
Answer all four short questions in Part A and one of the three long
essay questions in Part B (only the first long essay question on your
script will be marked).
A total of 80 marks are available for this paper.
Marks available for answering parts of the questions are shown in
brackets thus [ ]
Only University approved calculators may be used.
An Engineering Data Book by Calvert and Farrar is provided
A foreign language translation dictionary (paper version) is permitted
provided it contains no notes, additions or annotations.
Copyright 2013/2014 ©University of Southampton
Number of Pages
4
MODULE CODEW1
2
Part A (Short Questions)
Answer all four questions.
1. The function f ( x1, x2 )  x1  x2  2x1 x2 2  x23 is to be minimized using
the Hooke and Jeeves method, starting from the point (0,1) with
an initial step size of +0.1. Carry out two iterations of the
scheme, clearly showing how you have decided the correct
pattern moves and whether these have been accepted and thus
how you have derived the new iterates.
[10 marks]
2. A least squares parabolic curve fit to four data points may be
obtained using SVD. If the data points are given at x  1,0,1,2
write down the matrix equation relating the function values of
y  1,0,1,2 at these x values and the coefficients of the fitting
parabola a, b and c. What then are the values of a, b and c for the
parabolic curve fit given these data? Derive an estimate of the
function value at x  0.5 .
1  1 1



0
0 1 
'
You may assume that if the SVD of 
 isU .w.V then it
1 1 
1


2 1 
4
may be shown that
 0.25
 0.25  0.25 0.25 




0
.
55
0
.
15
0
.
35
0
.
05

V .diag(1/ w j ).U '  
.
0.55
0.45  0.15
 0.15




[10 marks]
PLEASE TURN OVER
3
MODULE CODEW1
3. The eigenvector method is to be used to assign objective
function weights to a problem with three goals. Goal 1 is
considered to be twice as important as goal 2, which in turn is
three times as important as goal 3. By assuming the appropriate
largest eigenvalue for consistent input data, derive the resulting
normalized weight vector.
[10 marks]
4. The function f ( x1, x2 )  x1  x2  2x12  2x1 x2  x23 is to be minimized
using the method of steepest descent, starting from the point
(0,1). Carry out one iteration of the scheme, clearly showing how
you have decided the correct step length and search direction
and thus how you have derived the new iterate.
[10 marks]
PLEASE TURN OVER
4
MODULE CODEW1
Part B (Long Questions)
Answer only one of the three questions.
Only the first answer on your script will be marked.
5. Describe the role of curve and function fitting in optimization
methods, paying particular attention to the differences between
implicit and explicit curve fits, local versus global approaches,
interpolation versus regression and the roles of experiment and
surrogate design, validation and updating. Give examples of
different search methods to illustrate your discussion.
[40 marks]
6. Describe how uncertainty impacts on the use of design search
and optimization methods. Pay particular attention to uncertainty
in the final product and its operation, uncertain goals and
constraints, uncertainty in design analysis methods and any
uncertainty in the optimization tools being used. Illustrate your
discussion with typical examples.
[40 marks]
7. Describe how optimization methods can be used to help
formalize approaches to seeking design improvements. Pay
particular attention to the role of goals, constraints, limits and
parameters in an optimization formalism and how these can be
related to real world problems. Discuss the limitations of such
methods and how they impact on the role of experience and
intuition in design. Illustrate your discussion with typical
examples.
[40 marks]
END OF PAPER