Free Printable Scalarization-based methods

1.

How can we convert an objective function to be minimized into an objective function to be maximized?

a)

Multiple it by $\frac{1}{f\left(x\right)}$

b)

Add -1

c)

Multiply it by -1

d)

You cannot

2.

If a multiobjective optimization problem has no constraints, what is the feasible set $S$ ?

a)

It is undefined

b)

Depends on the image $F\left(x\right)$

c)

The whole domain of $x$ , i.e., $R^n$

d)

It can be specified by a domain expert (a decision maker)

3.

Which of the given statements concerning the three sets of objective vectors in the figure are true?

a)

All the sets are Pareto optimal

b)

Set A and B are Pareto optimal

c)

Set C is weakly Pareto optimal

d)

All the sets are weakly Pareto optimal

4.

When computing a trade-off as given in (6), in which given case should we be extra careful?

a)

There is no need to be careful

b)

$f_2$ is greater than $f_1$

c)

$f_1$ is greater than $f_2$

d)

The denominator is zero

5.

Which of the following statements is true concerning the solutions shown in the figure below?

a)

The circles are properly Pareto optimal, but the squares are not

b)

The squares are properly Pareto optimal, but the circles are not

c)

The circles and squares and properly Pareto optimal, but the stars are not

d)

The stars are properly Pareto optimal

6.

What is the ideal point, and what is the nadir point according to the payoff-table?

a)

ideal: $(-3.2,\ 2.2,-4.2)$ nadir: $(3.9,\ 4.3,-2.2)$

b)

nadir: $(-3.2,\ 2.2,-4.2)$ ideal: $(3.9,\ 4.3,-2.2)$

c)

Impossible to say

d)

ideal: $\left(3.1,\ 2.2,\ -2.2\right)$ nadir: $(-2.2,\ 3.9,\ 3.1)$

7.

Why do we need an utopian point $z^{\cdot\cdot}$ ?

a)

Because we go always one step beyond

b)

There is no special reason, just for fun

c)

To avoid dividing by zero

d)

As a counterpoint to the dystopian point

8.

If the reference point given in goal programming $\overline{z}$ is feasible (i.e., it is contained in $Z$ , the image of the feasible region), what problem can arise?

a)

The goals are unachievable

b)

We divide by zero

c)

The constraint is not feasible

d)

The solution found might not be Pareto optimal

Scalarization-based methods

Total questions: 8

Worksheet time: 8mins

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