c$)(8$ points, $2$ points each$)$ Answer the following questions by circling the correct answer.

iv$.$ Consider a bi$-$objective optimization problem. For one of the objective functions, there

are alternative optima. Each of these alternative optimum solutions have to be a Pareto

efficient solution for the bi$-$objective model. True or False?

True

False

v$.$ Which of the following is a supervised method to reduce a multi$-$objective optimization

model into a single$-$objective optimization model.

$[1]$ Minimizing the maximum deviation

$[2]$ Minimizing the distance to the ideal point

$[3]$ Optimizing a weighted average of the objective function using specific weights

vi$.$ Which of the following is true about weighted goal programming?

$[1]$ It sequentially optimizes goals while maintaining the achieved levels of prior

goals.

$[2]$ It minimizes the maximum of the deviations from individual goals.

$[3]$ It assigns penalties to deviations from the goals and minimizes the total

penalty.

vii. Which of the following best describes preemptive goal programming?

$[1]$ It sequentially optimizes goals while maintaining the achieved levels of prior

goals.

$[2]$ It minimizes the maximum of the deviations from individual goals.

$[3]$ It assigns penalties to deviations from the goals and minimizes the total

penalty.