49928 Design Optimisation for
Manufacturing
Time Allowed: 120 minutes.
Reading time: 10 minutes.
Reading time is for reading only. You are not permitted to write, calculate or mark your
paper in any way during reading time.
Open Book
The Final Exam will have 3-4 questions and the total marks will be 35.
Below are some sample questions.
Question 1:
Use Lagrange Multiplier method to solve the nonlinear programming problem:
Minimise 3x+2y
Subject to
Question 2:
In the Simplex Method for solving linear programming problem, when a corner point is
found, how to decide whether it is the optimal solution or not? How to improve the
solution if the corner point is not the optimal solution? Please explain the process and
give reasons why it works.
Question 3:
2
Formulate the problem as a linear programming problem.
Solve this linear programming problem graphically.
Question 4:
It is required to find the rectangular of the largest area (in the positive quadrant) that
can be transcribed within a given ellipse
and satisfy a prescribed linear
constraint
4 3 6 x1 x2
Formulate the problem as a nonlinear programming problem.
Solve this nonlinear programming problem graphically.
Question 5:
Explain the main idea of BFGS algorithm for unconstrained nonlinear programming
problems. Use the following example to compute the search direction in the first step of
BFGS algorithm assuming the starting point is
4, 3. x1 x2
Question 6:
Explain the main idea of SQP algorithm for constrained nonlinear programming problems.
Question 7:
Explain the principle, advantages and limitations of Genetic algorithm for nonlinear
optimisation.
Question 8:
3
Explain the key idea of golden section method for solving one dimensional nonlinear
programming problem.
Question 9:
Explain the key idea of branch and bound algorithm.
Question 10:
Use FOC and SOC to solve the following unconstrained optimization problem
Minimize
Question 11:
Explain the principle, advantages and limitations of the generic iteration based algorithm
for nonlinear optimisation.
Question 12:
Explain the principle, advantages and limitations of the Dynamic programming algorithm.
Question 13:
Explain the principle, advantages and limitations of the Golden Section method.
Question 14:
Explain the main idea of ALM algorithm for solving nonlinear programming problems.
Question 15:
Explain the main idea of Newton method for solving unconstrained nonlinear programming
problems. If the objective function is quadratic, what will happen?