# Quantifying Feasibility

I have a scheduling model formulation ( experimental setup) that takes in product states as input (sample points) and checks the model status (response) and returns feasible or infeasible.

My plan is to be able to represent the feasible space of the facility with an algebraic predictor and for this, I need to sample effectively. This is basically how I thought of the problem:

1. Started with an Initial LHS sample for the whole input space generated 200 samples
2. For each sample check if the model is feasible(-1) or infeasible (1).
3. With that, we have an initial dataset
4. Initiate an adaptive sampling procedure to generate more relevant points.
5. Do this until we have a total of 1000 dataset (inputs and responses)

Here is my main problem: the responses are discrete, because of this I find it hard to perform the usual adaptive sampling procedure because they are all suited for cases where the response is continuous.

Are their ways to do adaptive sampling for cases where the response is binary? Also, are their ways to better approach the problem, such that the infeasibilities are described by continuous functions?

• Regarding describing infeasibilities by continuous functions, I don't really understand what you are trying to do,but perhaps you can borrow from Machine Learning Classification and use tanhor sigmoid to get a continuous interpolation of a discrete "classification" (as either feasible or infeasible)..Those both go from -1 to `. Or invert them, depending on which direction you're going. – Mark L. Stone Aug 30 at 11:11
• Thanks for the response. To be clear, you mean I should get a continuous latent value using the inputs and use the squashing function to classify the latent values? – Dare Badejo Aug 30 at 19:47
• I'm just throwing it out there for your consideration,. I'm not telling you what you should do. Just a way of getting a "smooth" continuous score out of what is really discrete. Machine Learning people do that all the time. – Mark L. Stone Aug 30 at 20:00
• Oh yes, I know this, I was trying to gain clarity. Thanks once again. – Dare Badejo Aug 30 at 20:41
• Dare, are you using GUSS and Gurobi? – Rob Sep 2 at 5:10