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MODULE CODEW1

UNIVERSITY OF SOUTHAMPTONSESG6018W1

SEMESTER 1 EXAMINATION 2012/13

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.

Part A (Short Questions)

Answer all four questions.

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

[10 marks]

  1. The function is to be minimized inside a circle of radius 2 centred at the origin. Use the method of Lagrange multipliers to find the location of all minima clearly showing how you have dealt with the constraint.

[10 marks]

  1. Thefunction is to be minimized using the Golden Section search starting from evaluations at . Carry out two iterations of the scheme, clearly showing how you have derived each new iterate. The Golden Section ratio may be assumed to be 0.618 : 0.382.

[10 marks]

  1. The function 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
Part B (Long Questions)

Answer only one of the three questions.

Only the first answer on your script will be marked.

  1. Describe the way that design requirements may be codified as optimization problems. Pay particular attention to the differences between goals and constraints, between bounds and limits and deterministic versus probabilistic approaches.

[40 marks]

  1. Describe the steps involved in using a surrogate model to support a design optimization process. Pay particular attention to experiment and surrogate design, validation and updating.

[40 marks]

  1. Describe how uncertainty impacts on the use of design search and optimization methods. Pay particular attention to uncertain goals, uncertainty in design analysis methods and uncertainty in the optimization tools being used.

[40 marks]

END OF PAPER