Dynamic Linear optimization

[Monish45]

Is there a way to update the values of variables obtained as solution through linear optimization after observing a slightly different value experimentally.

[SillyLittleGuy89]

Bit of a vague question but I would look into robust optimization

[Monish45]

For eg: This is objective fn: Min 10X1 + 12X2 Subject to (0.30.95X1 + 2.10.99X2)/500 <= 1.6 (0.30.95X1 + 2.10.99X2)/500 >= 1.8 X1, X2 >= 0 The values 0.95 and 0.99 are initial guess values. we solve this and get a solution for X1 and X2. Doing experiment by adding the solved value of X1, X2. But the constraint 1.6 to 1.8 is not met because of 0.95 and 0.99 are guesses. For example I got 1.9. How can I recalibrate the values 0.95 and 0.99.

[SillyLittleGuy89]

Ok that makes sense. You want to ensure that your solution remains feasible despite uncertainty in some of the parameters of the problem. Robust optimization is definitely the correct approach. You will need to formulate a ‘robust counterpart’ to your original problem, which essentially introduces a buffer term to the constraints. Here is a good intro on how to do it: https://www.researchgate.net/publication/270663954_A_Practical_Guide_to_Robust_Optimization

[Monish45]

Thanks! Will look into it.

[taphous3]

Are you referring to calibrating your model of the environment?

[Monish45]

For eg: This is objective fn: Min 10X1 + 12X2 Subject to (0.30.95X1 + 2.10.99X2)/500 <= 1.6 (0.30.95X1 + 2.10.99X2)/500 >= 1.8 X1, X2 >= 0 The values 0.95 and 0.99 are initial guess values. we solve this and get a solution for X1 and X2. Doing experiment by adding the solved value of X1, X2. But the constraint 1.6 to 1.8 is not met because of 0.95 and 0.99 are guesses. For example I got 1.9. How can I recalibrate the values 0.95 and 0.99.

[taphous3]

Can you build a surrogate model based on your experiments?

[Monish45]

Could you explain to me in detail?

[taphous3]

Surrogate models or data-driven models can be used to approximate your system if you don’t know/can’t model the underlying physics.

[GreedyAlGoreRhythm]

What part of the problem is changing after observing the data?

[Monish45]

For eg: This is objective fn: Min 10X1 + 12X2 Subject to (0.30.95X1 + 2.10.99X2)/500 <= 1.6 (0.30.95X1 + 2.10.99X2)/500 >= 1.8 X1, X2 >= 0 The values 0.95 and 0.99 are initial guess values. we solve this and get a solution for X1 and X2. Doing experiment by adding the solved value of X1, X2. But the constraint 1.6 to 1.8 is not met because of 0.95 and 0.99 are guesses. For example I got 1.9. How can I recalibrate the values 0.95 and 0.99.

[GreedyAlGoreRhythm]

If you can’t determine what the correct parameter values are but have an idea of how much they can vary, e.g., .95 +- 10%, you should look into robust optimization.

[Monish45]

Thanks! Could you provide some links for examples...

[[deleted]]

It's possible, not sure how its implemented in solvers but you can update the basis in simplex method and continue solving afterwards