Note on Multi-objective optimization (ideal MO)

principle for an ideal multi-objective optimization procedure:

Step 1: Find multiple trade-off optimal solutions with a wide range of values for objectives.

Step 2: Choose one of the obtained solutions using higher-level information

1. Multi-objective optimization problems

- minimize f1

- minimize f2

- .

- .

- .

- minimize fk

subject to constraints

2. IDEAL Multi-objective optimizer

3. Multiple trade-off solutions found

4. Higher-level information

5. Choose one solution

Thus, there is a fundamental difference in using the problem information in both approaches. In the preference-based approach, a relative preference vector needs to be supplied without any knowledge of the possible consequences. However, in the proposed ideal approach, the problem information is used to choose one solution from the obtained set of trade-off solutions.