Lecture 5 (End of Chapter Questions)

Question 1

When would you use error minimization?

Answer 1

Apply error minimization if the number of indifference statements > number of objectives and there are no redundant statements.

Question 2

How do you conduct error minimization?

Answer 2

1. Introduce an error term for every equation such that f_i = e_i (-> under-determined system)
2. Convert the problem into a linear problem by replacing e_i by e_i(+) - e_i(-)
3. Search for the objective weights that minimizes the sum of absolute error terms (min sum [e_i(+) + e_i(-)])

Question 3

Why is a transformation of the objective function necessary?

Answer 3

The transformation is necessary because we would not have a linear problem otherwise. The decision function and constraints have to be linear in the decision variables.