[P] Feedback on research problem
I have been working on a home energy management problem, in which I want to schedule a series of domestic appliances over a period of time in a way that minimizes overall electricity costs. As not all domestic appliances are controllable, fixed household demands need to be taken into account.
As a preliminary exploration of this problem, I was able to schedule appliance operations by solving an instance of a job scheduling problem, although assuming that those fixed demands are known throughout the scheduling horizon.
Naturally, this is an unrealistic approach, as we cannot perfectly forecast the future. As such, I am thinking of considering a stochastic optimization approach, generating several load profiles (scenarios) over the fixed horizon. Then I would solve an optimization problem instance that minimizes average costs over all generated scenarios.
Does this approach seems viable? Is there anything seriously wrong with this?
Furthermore, i was considering applying Gaussian Processes to forecast loads over the scheduling horizon. The thing that attracted me to this technique is the fact that we can get a distribution for predictions, rather than simply the values. Thus, I could use this to generate the different load scenarios for stochastic optimization. However, I am unsure if this is an adequate fit for time series forecasting, particularly when forecasting multiple time instants. I did (admittedly not very extensive) some research on time series forecasting using Gaussian Processes and some authors report quite poor results with this technique, stating that GPs are not very well suited for multi-step forecasting.
Can anyone give some feedback on these ideas? Are there alternative approaches (perhaps best suited for my problem)?
Thanks in advance