Method of selecting the optimal average combination of highest numbers?

I know of pairing functions, but my problem may involve three to five variables. When I have a few robots configured with certain parameters for movement, and I want to evaluate the robots based on how fast (F), how jerky (J) and how much energy (E) they consume, is there a statistical/mathematical technique of choosing the robot that has a high value of F, J and E?

F range = [0 to 100], J range = [0 to 1], E range = [0 to 100]
Assume F and E are normalized to range [0 to 1]

Robot1: F = 0.2, J = 0.9, E = 0.5
Robot2: F = 0.5, J = 0.6, E = 0.5
Robot3: F = 0.9, J = 0.9, E = 0.2
Robot4: F = 0.6, J = 0.2, E = 0.7

I need a method of choosing Robot2, because although Robot3 has excellent values for F and J, it’s E is low. But Robot2 has reasonable values for F,E and J. I may eventually use more variables than just F,E and J.

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Highest weight of a representation of a Lie Algebra

Given a Lie Algebra $ \mathfrak{g}$ , its Cartan Matrix $ A$ and a finite representation $ R$ , is there a way of determining its highest weight $ \Lambda$ in a simple way?

In my course, we consider $ \mathfrak{g}=A_2= \mathfrak{L}_{\mathbb{C}}(SU(3))$ . It is stated that the highest weight of the fundamental representation has Dynkin labels $ \Lambda = (1,0)$ and the highest weight of the adjoint representation has Dynkin labels $ \Lambda = (1,1)$ . Why is it so? From there, I can work out the other roots by removing weights given by the Cartan Matrix but it is of no use if I can’t compute the highest weight in the first place.

Taking an example, let $ \mathfrak{g}=B_2= \mathfrak{L}_{\mathbb{C}}(SO(5))$ . How do I work out the highest weight for the fundamental and adjoint representation?

Thanks in advance!

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What flight has the highest ratio of time difference to flight time?

Inspired by crossing four time zones in six hours today: what flight has the largest time difference per flight time?

For example, if there’s a 2-hour flight that has 4 hours time difference between the two ends, this has a ratio of 2:1 (2.0), while a 4-hr flight across two time zones would be 1:2 (0.5).

Also note that I’m interested in absolute (modulo 12) time difference: crossing the date line creates big differences on paper, but doesn’t really matter from a physiological perspective. In other words, -18 hours feels the same as +6.

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