4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER

BINDING IN ALEPH OPEN THE ACQUISITIONSSERIALS MODULE
MODULE 1 INTRODUCTION À LA FORMATION
MODULE 12 AIRES PROTEGEES TRANSFRONTALIERES

MODULE 3 DEFINITIONS CHAMP D’APPLICATION PRINCIPES
MODULE 6 REGLEMENT ÉVALUATION DE L’IMPACT
MODULE SPECIFICATION IMPORTANT NOTES – PLEASE READ

What theories have been put forward to explain the fertility transition

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MODULE CODE FEEG6009W1






UNIVERSITY OF SOUTHAMPTON FEEG6009W1



SEMESTER 2 EXAMINATION 2016/17


Design Search and Optimisation


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 100 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.

Part A (Short Questions)

Answer all four questions.





  1. The function 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER is to be minimized using inverse parabolic interpolation starting from evaluations at 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER . Carry out two iterations of the scheme, clearly showing how you have derived each new iterate.

[15 marks]


  1. The performance of a manufacturing process is characterised by the performance index 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER where 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER is a control variable set by the users in the range 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER . If4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER is to be as low as possible what is the optimal setting of 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER ? If 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER is subject to uniform random noise such that the probability density function of the noise takes the form of a unit square centred at the nominal value, derive an expression for the mean value of the performance index and hence determine what value of 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER will give the lowest mean value. What percentage deterioration in nominal performance must be accepted when using this optimal setting?

[15 marks]


  1. A multi-objective optimization problem is defined by two goal functions of a single variable4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER . Both functions must be minimized and are given by 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER and 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER . Find the two end points of the Pareto front for this problem in terms of the design variable4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER and equivalent function values 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER and 4 MODULE CODE FEEG6009W1 UNIVERSITY OF SOUTHAMPTON FEEG6009W1 SEMESTER . Also find the point on the Pareto front where the goal functions are given equal weight.

[15 marks]




PLEASE TURN OVER






  1. A genetic algorithm is being used to maximize a single valued function with five members in its population and a total replacement, rank based, roulette wheel strategy for selecting the mating pool. The selection probabilities are arranged on the roulette wheel in ascending order with worst member first. Given that the population members to be chosen from have variable values of 1, 3, 6, 7 and 11 and their objective functions are 0.1, 0.55, 0.4, 0.2 and 0.15, respectively, decide the makeup of the mating pool using the following five random numbers in the range 0-1: 0.0975, 0.2785, 0.5469, 0.9575 and 0.9649.

[15 marks]







PLEASE TURN OVER

Part B (Long Questions)


Answer only one of these three questions.

Only the first answer on your script will be marked.



  1. Describe how design requirements may be codified as optimization problems and the role parameterization plays in design optimization & search. In your answer please pay particular attention to the differences between goals and constraints, between bounds and limits and deterministic versus probabilistic approaches. Address also issues of flexibility, robustness, ease of use and development cost.


[40 marks]



  1. Describe the various types of optimizers available to tackle non-linear search problems and the range of typical problem types encountered in design. In your answer please pay particular attention to speed accuracy, robustness and usability.

[40 marks]



  1. Describe how uncertainty impacts on the use of design search and optimization methods. In your answer please pay particular attention to uncertain goals and constraints, uncertainty in design analysis methods and uncertainty in the optimization tools being used.

[40 marks]




END OF PAPER



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