How to combine two algorithms in one by using optimization results as input for second optimization

I have Parameter estimation algorithm . This parameters are either constant or variables.

The case when these parameters are constant (under certain conditions) , it is possible to do the parameter estimation and took the results as inputs for Second optimization.

But actually these parameters generally are variables (under certain conditions)

So when I optimise First optimization , the condition my changed and passe new information

I think I now i want to modify the workflow so that:

• I optimise for "first optimization"
• Grab selected outputs from the optimisation of "first optimization"
• These outputs become initial condition or inputs for "Second optimization"
• Optimise "Second optimization".

but that feels like a cumbersome solution that might be quite slow. Is anyone able to point me towards an example or guidance on how I might tackle this in a more efficient way?

Especially if we know that this is an online optimization and require a strong algorithm such as GA, ANN or metaheuristics..