Multiobjective optimization

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Multiobjective optimization is somewhat of a misnomer -- you actually have to have predefined weightings for each of the objectives you care about, or implement them as constraints.
0:00 - Intro
0:31 - Weighted sum method
2:37 - Pareto fronts
4:24 - Epsilon-constraint method
5:10 - Conclusion
Accompanying Python notebook:
openmdao.github.io/PracticalM...
Referenced paper for Pareto data, Brooks 2020: doi.org/10.2514/1.C035699 or www.researchgate.net/profile/...
See Chapter 9 in Engineering Design Optimization by Martins and Ning for a more in-depth view: mdobook.github.io/
Links to other relevant lectures TODO:

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6 июл 2024

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Комментарии : 12

@marcelohenrique3000 Месяц назад

0:01 you won me here k +1 subscriber

@ChathuraJayasundaraIMD 9 месяцев назад

This video saved me. thank you so much ❤

@MahbuburRahman-ro2xy Минуту назад

for weighted sum method how do u determine the scale factor. is it max of that value.?

@rpapa 4 месяца назад

Great Video! thank you so much...................

@flourishomotola5306 Год назад

How is this video free? Thanks a lot. Very clear and concise.

@antonmaier2263 Год назад

secondly if you find yourself optimizing multiple outcomes you might want to think about your optimization space. for example: maybe you dont want to optimize fuel burn and zero-fuel weight but want to optimize ROI on that plane for your given business model. answering that question will give you weights or a greater function that you might want to optimize.

@sarangeulo 6 месяцев назад

Hi sir, for the study i am conducting right now in high school, i have only one decision variable that correlates to two conflicting functions that i want to minimize. this means the objective space would only have a Pareto front and not any "surfaces" of different combinations of the two objectives, because defining the value of one function immediately locks my only variable and hence the second function as well. my question is... in such cases, is it reasonable to approach these situations with the same MOO techniques? or if not, could you please guide me to some other ways that I can achieve such MOO with only one decision variable? Thanks in advance.

@OpenMDAO 5 месяцев назад

Thanks for explaining your situation well! This is a sort of special case because you have only one design variable and two functions of interest. If you only have one design variable, you're pretty limited in how much optimization you can do in that space. If possible, reformulating your problem to have more design freedom would be helpful, otherwise there's not much to do to explore the space.

@antonmaier2263 Год назад

wait a second, my intuition would be not to add the variables but to multiply them. am i wrong?

@OpenMDAO Год назад

That's another way to combine objectives. What that means is that each objective would be weighted by the current value of the other, whereas adding them together assumes no such weighting. The most common type of multiobjective optimization adds the objectives together with different pre-defined weights, as shown in the latter part of this lesson.

@octaviodelmazoalvarado1241 Год назад

I second @flourishomotola5306, there are paid videos FAR from the quality of this content. Straight to the point, clear, well explained, and high quality content overall. Thanks @OpenMDAO

@OpenMDAO 5 месяцев назад

Thank you! Comments like this really propel us!