Optimiser to get the best selection of a set of penalty values

Specific Domains Optimization (Mathematical)
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1

I have an optimisation model in Julia using Jump model and Cbc optimiser. The model is highly dependent on the initial inputs. What will be best method to select the initial input such that, the error penalty in the original optimiser problem is minimum? Is it possible to build another optimiser around the origia optimiser problem to get yne best initial values?

The objective of the original problem is different
( eg minimise the cost)
For my problem I have 3 initail values and it will affect 4 parameters ( I need to select the 3 values such that the 4 output parameters are minimised)

If so how can I proceed? Could someone suggest an better idea to select the initial values [I need a general method to select the initail values]

2

The model is highly dependent on the initial inputs

Do you have a reproducible example? The initial inputs can improve the speed of the solve, but you should find equivalent optimal solutions.

In general, there is no good way to construct initial values; it is problem dependent. (Indeed, a significant portion of solver technology is finding a good initial feasible solution.)

3

I am sorry, its a decomposition based optimisation problem and cant produce a simple example. ( too big) .Since its a decomposition one and coordination needs the intial values. I was wondering to create a optimiser problem that surround the original optimising problem. So that Outer optimiser will take the result from the solution original problem and depending on the erorr values it modify initial value and give to the original problem. This needs to br reapeat untill the error in the original problem is minimum

4

To clarify: when you talk about “initial values”, do you mean the parameter data needed to define the optimization problem? Or do you mean the initial starting values of the decision variables that you might provide as a guess for the solution?

5

Yes, What I means as the initial value is the parameter data needed to define the optimization problem. Its highly dependent on the main objective function. I need to select the knitial values optimimum such that, The error penalty ( from the solition of optimisation ) need to be minimum as possible

In short I need to adjust my initial values such that error penalty is minimum

6

I’m not sure I understand what you’re trying to do.

Do you have some model

V(p) = \min\limits_{x\in\mathcal{X}} f(x, p)

and then you want to solve

\min\limits_{p\in\mathcal{P}} V(p)

That’s just the same as solving

\min\limits_{p\in\mathcal{P},x\in\mathcal{X}} f(x, p)

I think you’ll need to share more information such as a formulation or some code so we can understand what you’re trying to achieve.